diff --git a/.gitattributes b/.gitattributes index 1ef325f1b111266a6b26e0196871bd78baa8c2f3..b049fa7ca0926ad016813fedea7cfac40d1f1e68 100644 --- a/.gitattributes +++ b/.gitattributes @@ -57,3 +57,33 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text # Video files - compressed *.mp4 filter=lfs diff=lfs merge=lfs -text *.webm filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2007_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2007_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2008_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2008_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2009_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2009_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2010_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2012_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2012_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2013_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2013_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2015_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2015_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2016_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2016_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2017_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2017_2.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2018_1.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2019_1_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2019_2_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2020_1_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2020_2_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2021_1_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2021_2_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2022_1_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2022_2_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2023_1_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2023_2_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2024_1_English.pdf filter=lfs diff=lfs merge=lfs -text +JEE_papers/papers/JEE_2024_2_English.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/JEE_papers/JSON/JEE_2007_1.jsonl b/JEE_papers/JSON/JEE_2007_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..a3979a4593f896a1bc690f82e1f552960f20ba1c --- /dev/null +++ b/JEE_papers/JSON/JEE_2007_1.jsonl @@ -0,0 +1,66 @@ +{"id": 1, "question": "A resistance of 2 \u03a9 is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 \u03a9, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is", "response_choices": "(A) 3 \u03a9 (B) 4 \u03a9 (C) 5 \u03a9 (D) 6 \u03a9", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,", "response_choices": "(A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is", "response_choices": "(A) F/2m \u221a(a^2 - x^2) (B) F/2m \u221a(a^2 - x^2) (C) Fx/2ma (D) F/2m \u221a(a^2 - x^2) * x", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.", "response_choices": "(A) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder\n(B) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder\n(C) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders\n(D) No potential difference appears between the two cylinders when same charge density is given to both the cylinders", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,", "response_choices": "(A) negative and distributed uniformly over the surface of the sphere\n(B) negative and appears only at the point on the sphere closest to the point charge\n(C) negative and distributed non-uniformly over the entire surface of the sphere\n(D) zero", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is", "response_choices": "(A) 0\n(B) 54 \u03bcC\n(C) 27 \u03bcC\n(D) 81 \u03bcC", "answer": "C", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "A ray of light traveling in water is incident on its surface open to air. The angle of incidence is \u03b8, which is less than the critical angle. Then there will be", "response_choices": "(A) only a reflected ray and no refracted ray\n(B) only a refracted ray and no reflected ray\n(C) a reflected ray and a refracted ray and the angle between them would be less than 180\u00b0\u2013 2\u03b8\n(D) a reflected ray and a refracted ray and the angle between them would be greater than 180\u00b0\u2013 2\u03b8", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is", "response_choices": "(A) E(92U) > E(137I) + E(97Y) + 2E(n)\n(B) E(92U) < E(137I) + E(97Y) + 2E(n)\n(C) E(92U) < E(140Ba) + E(94Kr) + 2E(n)\n(D) E(92U) = E(140Ba) + E(94Kr) + 2E(n)", "answer": "A", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is", "response_choices": "(A) 802 nm\t(B) 823 nm\t(C) 1882 nm\t(D) 1648 nm", "answer": "B", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "STATEMENT-1\nA block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30\u00b0 with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.\n\nbecause\n\nSTATEMENT-2\nThe coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\n(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\n(C) Statement-1 is True, Statement-2 is False\n(D) Statement-1 is False, Statement-2 is True", "answer": "C", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "STATEMENT-1\nIn an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.\n\nbecause\n\nSTATEMENT-2\nIn an elastic collision, the linear momentum of the system is conserved.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\n(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\n(C) Statement-1 is True, Statement-2 is False\n(D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. because STATEMENT-2 Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.", "response_choices": "A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 C) Statement-1 is True, Statement-2 is False D) Statement-1 is False, Statement-2 is True", "answer": "C", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "STATEMENT-1 If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change. because STATEMENT-2 When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.", "response_choices": "A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 C) Statement-1 is True, Statement-2 is False D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "The ratio x1 / x2 is", "response_choices": "(A) 2, (B) 1/2, (C) \u221a2, (D) 1/\u221a2", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is", "response_choices": "(A) 2I\u03c9/3t, (B) 9I\u03c9/2t, (C) 9I\u03c9/4t, (D) 3I\u03c9/2t", "answer": "A", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "The loss of kinetic energy during the above process is", "response_choices": "(A) I\u03c9\u00b2/2, (B) I\u03c9\u00b2/3, (C) I\u03c9\u00b2/4, (D) I\u03c9\u00b2/6", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be", "response_choices": "(A) Po, (B) Po/2, (C) Po/2 + Mg/\u03c0R\u00b2), (D) Po/2 - Mg/\u03c0R\u00b2", "answer": "A", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is", "response_choices": "(A) (2P\u2080\u03c0R\u2074)/(\u03c0R\u00b2P\u2080 + Mg) (2L), (B) (P\u2080\u03c0R\u00b2-Mg)/(\u03c0R\u00b2P\u2080) (2L), (C) (P\u2080\u03c0R\u00b2 + Mg)/(\u03c0R\u00b2P\u2080) (2L), (D) (P\u2080\u03c0R\u00b2)/(\u03c0R\u00b2P\u2080 - Mg) (2L)", "answer": "D", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is \u03c1. In equilibrium, the height H of the water column in the cylinder satisfies", "response_choices": "(A) \u03c1g(L\u2080 - H)\u00b2 + P\u2080(L\u2080 - H) + L\u2080P\u2080 = 0, (B) \u03c1g(L\u2080 - H)\u00b2 - P\u2080(L\u2080 - H) - L\u2080P\u2080 = 0, (C) \u03c1g(L\u2080 - H)\u00b2 + P\u2080(L\u2080 - H) - L\u2080P\u2080 = 0, (D) \u03c1g(L\u2080 - H)\u00b2 - P\u2080(L\u2080 - H) + L\u2080P\u2080 = 0", "answer": "C", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 20, "question": "Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) GMeMe, G - universal gravitational constant, Me - mass of the earth, Ms - mass of the Sun\n(B) 3RT/M, R - universal gas constant, T - absolute temperature, M - molar mass\n(C) F^2/q^2B^2, F - force, q - charge, B - magnetic field\n(D) GMe/Re, G - universal gravitational constant, Me - mass of the earth, Re - radius of the earth\n\nColumn II: (p) (volt) (coulomb) (metre)\n(q) (kilogram) (metre)^3 (second)^-2\n(r) (metre)^2 (second)^-2\n(s) (farad) (volt)^2 (kg)^-1", "answer": "A:pq, B:qr, C:rr, D:ss", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 21, "question": "Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4x4 matrix given in the ORS.", "response_choices": "(A) A charged capacitor is connected to the ends of the wire, (B) The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion, (C) The wire is placed in a constant electric field that has a direction along the length of the wire, (D) A battery of constant emf is connected to the ends of the wire, (p) A constant current flows through the wire, (q) Thermal energy is generated in the wire, (r) A constant potential difference develops between the ends of the wire, (s) Charges of constant magnitude appear at the ends of the wire", "answer": "D, p, q; B, q, r; C, r; A, s", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 22, "question": "Some laws / processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) Transition between two atomic energy levels, (B) Electron emission from a material, (C) Mosley's law, (D) Change of photon energy into kinetic energy of electrons, (p) Characteristic X-rays, (q) Photoelectric effect, (r) Hydrogen spectrum, (s) \u03b2-decay", "answer": "A(p,b,c), B(a,d), C(r), D(s)", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 23, "question": "The species having bond order different from that in CO is", "response_choices": "(A) NO-, (B) NO+, (C) CN-, (D) N2", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "Among the following, the paramagnetic compound is", "response_choices": "(A) Na2O2, (B) O3, (C) N2O, (D) KO2", "answer": "D", "page_number": 10, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "Extraction of zinc from zinc blende is achieved by", "response_choices": "(A) electrolytic reduction, (B) roasting followed by reduction with carbon, (C) roasting followed by reduction with another metal, (D) roasting followed by self-reduction", "answer": "B", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "In the following reaction, conc. HNO3/conc. H2SO4 -> X the structure of the major product 'X' is", "response_choices": "(A) Structure A, (B) Structure B, (C) Structure C, (D) Structure D", "answer": "B", "page_number": 11, "image_available": "yes", "question_subject": "chemistry"} +{"id": 27, "question": "The reagent(s) for the following conversion, [image showing chemical conversion]", "response_choices": "(A) alcoholic KOH, (B) alcoholic KOH followed by NaNH2, (C) aqueous KOH followed by NaNH2, (D) Zn/CH3OH", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 28, "question": "The number of structural isomers for C6H14 is", "response_choices": "(A) 3, (B) 4, (C) 5, (D) 6", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "The percentage of p-character in the orbitals forming P\u2013P bonds in P4 is", "response_choices": "A) 25, B) 33, C) 50, D) 75", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "When 20 g of naphthoic acid (C11H8O2) is dissolved in 50 g of benzene (Kf = 1.72 K kg mol^-1), a freezing point depression of 2 K is observed. The van't Hoff factor (i) is", "response_choices": "A) 0.5, B) 1, C) 2, D) 3", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "The value of log10K for a reaction A \u21cc B is (Given : \u0394rH\u00b0298K = \u221254.07 kJ mol^-1, \u0394rS\u00b0298K = 10 JK^-1 mol^-1 and R = 8.314 JK^-1 mol^-1, 2.303 \u00d7 8.314 \u00d7 298 = 5705)", "response_choices": "A) 5, B) 10, C) 95, D) 100", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "STATEMENT-1 : Boron always forms covalent bond. because STATEMENT-2 : The small size of B3+ favours formation of covalent bond.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "A", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "STATEMENT-1 : In water, orthoboric acid behaves as a weak monobasic acid. because STATEMENT-2 : In water, orthoboric acid acts as a proton donor.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "STATEMENT-1 : p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid. because STATEMENT-2 : o-Hydroxybenzoic acid has intramolecular hydrogen bonding.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "D", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "STATEMENT-1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC). because STATEMENT-2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 36, "question": "Argon is used in arc welding because of its", "response_choices": "(A) low reactivity with metal\n(B) ability to lower the melting point of metal\n(C) flammability\n(D) high calorific value", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 37, "question": "The structure of XeO3 is", "response_choices": "(A) linear\t(B) planar\t(C) pyramidal\t(D) T-shaped", "answer": "C", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 38, "question": "XeF4 and XeF6 are expected to be", "response_choices": "(A) oxidizing\t(B) reducing\t(C) unreactive\t(D) strongly basic", "answer": "A,B", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "The total number of moles of chlorine gas evolved is", "response_choices": "A) 0.5, B) 1.0, C) 2.0, D) 3.0", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is", "response_choices": "(A) 200 (B) 225 (C) 400 (D) 446", "answer": "D", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "The total charge (coulombs) required for complete electrolysis is", "response_choices": "(A) 24125, (B) 48250, (C) 96500, (D) 193000", "answer": "D", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 42, "question": "Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) [Co(NH3)4(H2O)2]Cl2, (B) [Pt(NH3)2Cl2], (C) [Co(H2O)6]Cl]Cl, (D) [Ni(H2O)6]Cl2 \n Column II: (p) geometrical isomers, (q) paramagnetic, (r) diamagnetic, (s) metal ion with +2 oxidation state", "answer": "A: pq, B: qr, C: rs, D: ps", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 43, "question": "Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) cellulose, (B) nylon-6, 6, (C) protein, (D) sucrose \n Column II: (p) natural polymer, (q) synthetic polymer, (r) amide linkage, (s) glycoside linkage", "answer": "A: p, s; B: q, q; C: r, r; D: s", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 44, "question": "Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) hydrogen gas (P = 200 atm, T = 273 K), (B) hydrogen gas (P = 0, T= 273 K), (C) CO2 (P = 1 atm, T = 273 K), (D) real gas with very large molar volume \n Column II: (p) compressibility factor \u2260 1, (q) attractive forces are dominant, (r) PV = nRT, (s) P(V-nb)=nRT", "answer": "A: p, s; B: q; C: r, r; D: s", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 45, "question": "Let \u03b1, \u03b2 be the roots of the equation x^2 - px + r = 0 and \u03b1/2, 2\u03b2 be the roots of the equation x^2 - qx + r = 0. Then the value of r is", "response_choices": "(A) 2/9 (p - q)(2q - p) (B) 2/9 (q - p)(2p - q) (C) 2/9 (q - 2p)(2q - p) (D) 2/9 (2p - q)(2q - p)", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "Let f(x) be differentiable on the interval (0, \u221e) such that f(1) = 1, and lim (t^2 f(t) - x^2 f(x) / t^2 - x^2) = 1 for each x > 0. Then f(x) is", "response_choices": "(A) 1/3x + 2x^2/3 (B) -1/x + 4x^2/3 (C) -1/x + 2/x^2 (D) 1/x", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is", "response_choices": "(A) 1/2 (B) 1/3 (C) 2/5 (D) 1/5", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c -1, e^(c-1)) and (c + 1, e^(c+1))", "response_choices": "(A) on the left of x = c (B) on the right of x = c (C) at no point (D) at all points", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "lim \u222b f(t) dt equals", "response_choices": "(A) 8/\u03c0 f(2), (B) 2/\u03c0 f(2), (C) 2/\u03c0 (1/2), (D) 4 f(2)", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "A hyperbola, having the transverse axis of length 2 sin \u03b8, is confocal with the ellipse 3x^2 + 4y^2 = 12. Then its equation is", "response_choices": "(A) x^2 cosec^2 \u03b8 - y^2 sec^2 \u03b8 = 1, (B) x^2 sec^2 \u03b8 - y^2 cosec^2 \u03b8 = 1, (C) x^2 sin^2 \u03b8 - y^2 cos^2 \u03b8 = 1, (D) x^2 cos^2 \u03b8 - y^2 sin^2 \u03b8 = 1", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "The number of distinct real values of \u03bb, for which the vectors - \u03bb^2 i + j + k, i - \u03bb^2 j + k and i + j - \u03bb^2 k are coplanar, is", "response_choices": "(A) zero, (B) one, (C) two, (D) three", "answer": "C", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "A man walks a distance of 3 units from the origin towards the north-east (N 45\u00b0E) direction. From there, he walks a distance of 4 units towards the north-west (N 45\u00b0W) direction to reach a point P. Then the position of P in the Argand plane is", "response_choices": "(A) 3e^(i/4) + 4i, (B) (3 - 4i)e^(i/4), (C) (4 + 3i)e^(i/4), (D) (3 + 4i)e^(i/4)", "answer": "D", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "The number of solutions of the pair of equations 2sin^2 \u03b8 - cos 2\u03b8 = 0, 2cos^2 \u03b8 - 3sin \u03b8 = 0 in the interval [0,2\u03c0] is", "response_choices": "(A) zero, (B) one, (C) two, (D) four", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Let H1, H2, ..., Hn be mutually exclusive and exhaustive events with P(Hi) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1. STATEMENT-1 : P(Hi | E) > P(E | Hi). P(Hi) for i = 1, 2, ..., n. because STATEMENT-2 : \u03a3P(Hi) = 1.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, (C) Statement-1 is True, Statement-2 is False, (D) Statement-1 is False, Statement-2 is True", "answer": "D", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169 . STATEMENT-1 : The tangents are mutually perpendicular. because STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338 . (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "response_choices": "A, B, C, D", "answer": "A", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let the vectors PQ , QR , RS , ST , TU and UP represent the sides of a regular hexagon. STATEMENT-1 : PQ \u00d7 (RS + ST) \u2260 0 . because STATEMENT-2 : PQ \u00d7 RS = 0 and PQ \u00d7 ST \u2260 0 . (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "response_choices": "A, B, C, D", "answer": "C", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Let F(x) be an indefinite integral of sin^2 x. STATEMENT-1 : The function F(x) satisfies F(x + \u03c0) = F(x) for all real x. because STATEMENT-2 : sin^2(x + \u03c0) = sin^2 x for all real x. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "response_choices": "A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, C) Statement-1 is True, Statement-2 is False, D) Statement-1 is False, Statement-2 is True", "answer": "D", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Let Vr denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r - 1). Let Tr = Vr+1 - Vr - 2 and Qr = Tr+1 - Tr for r = 1, 2,... The sum V1 + V2 + ... + Vn is (A) 1/12 n(n + 1)(3n^2 - n + 1) (B) 1/12 n(n + 1)(3n^2 + n + 2) (C) 1/2 n(2n^2 - n + 1) (D) 1/3 (2n^3 - 2n + 3)", "response_choices": "A) 1/12 n(n + 1)(3n^2 - n + 1), B) 1/12 n(n + 1)(3n^2 + n + 2), C) 1/2 n(2n^2 - n + 1), D) 1/3 (2n^3 - 2n + 3)", "answer": "B", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "T. is always", "response_choices": "(A) an odd number, (B) an even number, (C) a prime number, (D) a composite number", "answer": "D", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Which one of the following is a correct statement? (A) Q1, Q2, Q3,... are in A.P. with common difference 5 (B) Q1, Q2, Q3,... are in A.P. with common difference 6 (C) Q1, Q2, Q3,... are in A.P. with common difference 11 (D) Q1 - Q2 = Q3 - ...", "response_choices": "(A) Q1, Q2, Q3,... are in A.P. with common difference 5, (B) Q1, Q2, Q3,... are in A.P. with common difference 6, (C) Q1, Q2, Q3,... are in A.P. with common difference 11, (D) Q1 - Q2 = Q3 - ...", "answer": "B", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 61, "question": "The ratio of the areas of the triangles PQS and PQR is", "response_choices": "(A) 1 : \u221a2, (B) 1 : 2, (C) 1 : 4, (D) 1 : 8", "answer": "C", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 62, "question": "The radius of the circumcircle of the triangle PRS is", "response_choices": "(A) 5, (B) 3\u221a3, (C) 3\u221a2, (D) 2\u221a3", "answer": "B", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 63, "question": "The radius of the incircle of the triangle PQR is", "response_choices": "(A) 4, (B) 3, (C) 8/3, (D) 2", "answer": "(D)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 64, "question": "Consider the following linear equations ax + by + cz = 0 bx + cy + az = 0 cx + ay + bz = 0 Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) a + b + c \u2260 0 and a^2 + b^2 + c^2 = ab + bc + ca (B) a + b + c = 0 and a^2 + b^2 + c^2 \u2260 ab + bc + ca (C) a + b + c \u2260 0 and a^2 + b^2 + c^2 \u2260 ab + bc + ca (D) a + b + c = 0 and a^2 + b^2 + c^2 = ab + bc + ca Column II: (p) the equations represent planes meeting only at a single point. (q) the equations represent the line x = y = z. (r) the equations represent identical planes. (s) the equations represent the whole of the three dimensional space.", "answer": "C-r, B-q, A-p, D-s", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 65, "question": "Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 \u00d7 4 matrix given in the ORS.", "response_choices": "Column I: (A) x\u230ax\u230b, (B) \u221ax, (C) x+\u230ax\u230b, (D) \u230ax-1\u230b+\u230ax+1\u230b \n Column II: (p) continuous in (-1, 1), (q) differentiable in (-1, 1), (r) strictly increasing in (-1, 1), (s) not differentiable at least at one point in (-1, 1)", "answer": "A: pqr, B: qs, C: rs, D: pq", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 66, "question": "Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "A: [p, s], B: [s], C: [q], D: [r, s]", "answer": "A: [s], B: [s], C: [q], D: [r]", "page_number": 30, "image_available": "yes", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2007_2.jsonl b/JEE_papers/JSON/JEE_2007_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..3923d43eeabf39ab988deb92c73daf9e83aaed09 --- /dev/null +++ b/JEE_papers/JSON/JEE_2007_2.jsonl @@ -0,0 +1,63 @@ +{"id": 4, "question": "A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 3v^2/4g with respect to the initial position. The object is", "response_choices": "(A) ring (B) solid sphere (C) hollow sphere (D) disc", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is \u03c1, the surface tension of water is T and the atmospheric pressure is P0. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude", "response_choices": "(A) | 2P0 Rh + \u03c0R^2 \u03c1gh - 2RT | (B) | 2P0 Rh + R \u03c1gh^2 - 2RT | (C) | P0 \u03c0R^2 +R \u03c1gh^2 - 2RT | (D) | P0 \u03c0R^2 + R \u03c1gh^2 +2RT |", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is", "response_choices": "(A) zero everywhere, (B) non-zero and uniform, (C) non-uniform, (D) zero only at its center", "answer": "B", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "Positive and negative point charges of equal magnitude are kept at (0, 0, a/2) and (0, 0, -a/2), respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is", "response_choices": "(A) positive, (B) negative, (C) zero, (D) depends on the path connecting the initial and final positions", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A magnetic field B = B0j exists in the region. a < x < 2a and B = -B0j, in the region 2a < x < 3a, where B0 is a positive constant. A positive point charge moving with a velocity v = v0i, where v0 is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,", "response_choices": "(A) (B) (C) (D)", "answer": "(A)", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "Electrons with de-Broglie wavelength \u03bb fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is", "response_choices": "(A) \u03bb0 = 2mc^2/h (B) \u03bb0 = 2h/mc (C) \u03bb0 = 2m^2c^523/h^2 (D) \u03bb0 = \u03bb", "answer": "(A)", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "STATEMENT-1\n\nIf there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.\n\nbecause\n\nSTATEMENT-2\n\nThe linear momentum of an isolated system remains constant.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\n(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\n(C) Statement-1 is True, Statement-2 is False\n(D) Statement-1 is False, Statement-2 is True", "answer": "D", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "STATEMENT-1\n\nA cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.\n\nbecause\n\nSTATEMENT-2\n\nFor every action there is an equal and opposite reaction.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\n(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\n(C) Statement-1 is True, Statement-2 is False\n(D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "STATEMENT-1\n\nA vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.\n\nbecause\n\nSTATEMENT-2\n\nIn the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\n\n(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\n\n(C) Statement-1 is True, Statement-2 is False\n\n(D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "STATEMENT-1\n\nThe total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.\n\nbecause\n\nSTATEMENT-2\n\nThe molecules of a gas collide with each other and the velocities of the molecules change due to the collision.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1\n\n(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1\n\n(C) Statement-1 is True, Statement-2 is False\n\n(D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "The speed of sound of the whistle is", "response_choices": "(A) 340 m/s for passengers in A and 310 m/s for passengers in B, (B) 360 m/s for passengers in A and 310 m/s for passengers in B, (C) 310 m/s for passengers in A and 360 m/s for passengers in B, (D) 340 m/s for passengers in both the trains", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by", "response_choices": "(A), (B), (C), (D)", "answer": "A", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "The spread of frequency as observed by the passengers in train B is", "response_choices": "(A) 310 Hz, (B) 330 Hz, (C) 350 Hz, (D) 290 Hz", "answer": "A", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Light travels as a", "response_choices": "(A) parallel beam in each medium, (B) convergent beam in each medium, (C) divergent beam in each medium, (D) divergent beam in one medium and convergent beam in the other medium", "answer": "A", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "The phases of the light wave at c, d, e and f are \u03c6c, \u03c6d, \u03c6e and \u03c6f respectively. It is given that \u03c6e \u2260 \u03c6f.", "response_choices": "(A) \u03c6c cannot be equal to \u03c6d, (B) \u03c6d can be equal to \u03c6c, (C) (\u03c6d - \u03c6f) is equal to (\u03c6c - \u03c6e), (D) (\u03c6d - \u03c6e) is not equal to (\u03c6f - \u03c6c)", "answer": "C", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "Speed of light is", "response_choices": "(A) the same in medium-1 and medium-2, (B) larger in medium-1 than in medium-2, (C) larger in medium-2 than in medium-1, (D) different at b and d", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 20, "question": "Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "A) The object moves on the x-axis under a conservative force in such a way that its \"speed\" and \"position\" satisfy v = c\u2081\u221a(c\u2082 - x\u00b2), where c\u2081 and c\u2082 are positive constants. (B) The object moves on the x-axis in such a way that its velocity and its displacement from the origin satisfy v = -kx, where k is a positive constant. (C) The object is attached to one end of a mass-less spring of a given spring constant. The other end of the spring is attached to the ceiling of an elevator. Initially everything is at rest. The elevator starts going upwards with a constant acceleration a. The motion of the object is observed from the elevator during the period it maintains this acceleration. (D) The object is projected from the earth's surface vertically upwards with a speed 2\u221a(GM/R), where, M is the mass of the earth and R is the radius of the earth. Neglect forces from objects other than the earth.", "answer": "First option: p,c\nSecond option: d", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 21, "question": "Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) Point P is situated midway between the wires. (B) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. (C) Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii. (D) Point P is situated at the common center of the wires.", "answer": "ACBCBDAD or ACBCBDDA", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 22, "question": "Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) Bimetallic strip, (B) Steam engine, (C) Incandescent lamp, (D) Electric fuse / (p) Radiation from a hot body, (q) Energy conversion, (r) Melting, (s) Thermal expansion of solids", "answer": "A - 's, q' OR 's' alone, B - 'q', C - 'p, q' OR 'p' alone, D - 'q, r' OR 'r' alone", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 23, "question": "Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is", "response_choices": "(A) 3, (B) 4, (C) 5, (D) 6", "answer": "D", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "Among the following metal carbonyls, the C-O bond order is lowest in", "response_choices": "(A) [Mn(CO)6]+, (B) [Fe(CO)5], (C) [Cr(CO)6], (D) [V(CO)6]\u2013", "answer": "D", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is", "response_choices": "(A) Pb2+, (B) Hg2+, (C) Cu2+, (D) Co2+", "answer": "B", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is", "response_choices": "(A) CHO, (B) CHO, (C) COOH, (D) CO2H, CO2H", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 27, "question": "The number of stereoisomers obtained by bromination of trans-2-butene is", "response_choices": "(A) 1, (B) 2, (C) 3, (D) 4", "answer": "A", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "Among the following, the least stable resonance structure is", "response_choices": "(A) [Resonance structure A], (B) [Resonance structure B], (C) [Resonance structure C], (D) [Resonance structure D]", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 29, "question": "A positron is emitted from 2311Na. The ratio of the atomic mass and atomic number of the resulting nuclide is", "response_choices": "A) 22/10, B) 22/11, C) 23/10, D) 23/12", "answer": "C", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "For the process H2O(l) (1 bar, 373 K) \u2192 H2O(g) (1 bar, 373 K), the correct set of thermodynamic parameters is", "response_choices": "A) \u0394G = 0, \u0394S = +ve, B) \u0394G = 0, \u0394S = -ve, C) \u0394G = +ve, \u0394S = 0, D) \u0394G = -ve, \u0394S = +ve", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "Consider a reaction aG + bH \u2192 Products. When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is", "response_choices": "A) 0, B) 1, C) 2, D) 3", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "STATEMENT-1 : Alkali metals dissolve in liquid ammonia to give blue solutions. because STATEMENT-2 : Alkali metals in liquid ammonia give solvated species of the type [M(NH3)x]+ (M = alkali metals).", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True; Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "STATEMENT-1 : Glucose gives a reddish-brown precipitate with Fehling's solution. because STATEMENT-2 : Reaction of glucose with Fehling's solution gives CuO and gluconic acid.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "STATEMENT-1 : Molecules that are not superimposable on their mirror images are chiral. because STATEMENT-2 : All chiral molecules have chiral centres.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "C", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "STATEMENT-1 : Band gap in germanium is small. because STATEMENT-2 : The energy spread of each germanium atomic energy level is infinitesimally small.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 36, "question": "Among the following, identify the correct statement.", "response_choices": "(A) Chloride ion is oxidised by O\u2082 (B) Fe\u00b2\u207a is oxidised by iodine (C) Iodide ion is oxidised by chlorine (D) Mn\u00b2\u207a is oxidised by chlorine", "answer": "C", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 37, "question": "While Fe\u00b3\u207a is stable, Mn\u00b3\u207a is not stable in acid solution because", "response_choices": "(A) O\u2082 oxidises Mn\u00b2\u207a to Mn\u00b3\u207a (B) O\u2082 oxidises both Mn\u00b2\u207a to Mn\u00b3\u207a and Fe\u00b2\u207a to Fe\u00b3\u207a (C) Fe\u00b3\u207a oxidises H\u2082O to O\u2082 (D) Mn\u00b3\u207a oxidises H\u2082O to O\u2082", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 38, "question": "Sodium fusion extract, obtained from aniline, on treatment with iron(II) sulphate and H\u2082SO\u2084 in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of", "response_choices": "(A) Fe\u2084[Fe(CN)\u2086]\u2083 (B) Fe\u2083[Fe(CN)\u2086]\u2082 (C) Fe\u2082[Fe(CN)\u2086]\u2082 (D) Fe\u2083[Fe(CN)\u2086]\u2083", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "Which one of the following reagents is used in the above reaction?", "response_choices": "(A) aq.NaOH + CH\u2083Cl (B) aq.NaOH + CH\u2082Cl\u2082 (C) aq.NaOH + CHCl\u2083 (D) aq.NaOH + CCl\u2084", "answer": "C", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "The electrophile in this reaction is", "response_choices": "(A) :CHCl (B) +CHCl\u2082 (C) :CCl\u2082 (D) -CCl\u2083", "answer": "C", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "The structure of the intermediate I is", "response_choices": "(A) [Structure A] (B) [Structure B] (C) [Structure C] (D) [Structure D]", "answer": "B", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 42, "question": "Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) O\u2083 \u2192 O\u2082 + O\u2082, (B) CrO\u2084\u00b2\u207b + H\u207a \u2192, (C) MnO\u2084\u207b +NO\u2082 + H\u207a \u2192, (D) NO\u2082 + H\u2082SO\u2084 + Fe\u00b2\u207a \u2192\nColumn II: (p) redox reaction, (q) one of the products has trigonal planar structure, (r) dimeric bridged tetrahedral metal ion, (s) disproportionation", "answer": "(A, p), (B, r), (C, r), (D, s)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 43, "question": "Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) C\u2086H\u2085CHO, (B) CH\u2083C\u2261CH, (C) CN\u207b, (D) I\u207b\nColumn II: (p) gives precipitate with 2,4-dinitrophenylhydrazine, (q) gives precipitate with AgNO\u2083, (r) is a nucleophile, (s) is involved in cyanohydrin formation", "answer": "(A, p), (B, q), (C, r), (D, s)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 44, "question": "Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "(A) simple cubic and face-centred cubic, (B) cubic and rhombohedral, (C) cubic and tetragonal, (D) hexagonal and monoclinic, (p) have these cell parameters a =b=c and \u03b1 = \u03b2 = \u03b3, (q) are two crystal systems, (r) have only two crystallographic angles of 90\u00b0, (s) belong to same crystal system", "answer": "p: A, D; q: B; r: C; s: D", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 45, "question": "Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are", "response_choices": "(A) (4/3, 3), (B) (3, 2/3), (C) (3, 4/3), (D) (4/3, 2/3)", "answer": "C", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "If |z|=1 and z \u2260 \u00b11, then all the values of z/(1-z^2) lie on", "response_choices": "(A) a line not passing through the origin\n(B) |z|=\u221a2\n(C) the x-axis\n(D) the y-axis", "answer": "D", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let E^c denote the complement of an event E. Let E, F, G be pairwise independent events with P(G)>0 and P(E \u2229 F \u2229 G)=0. Then P[E^c \u2229 F^c | G] equals", "response_choices": "(A) P(E^c)+ P(F^c)\n(B) P(E^c)- P(F^c)\n(C) P(E^c)- P(F)\n(D) P(E)- P(F^c)", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "(d^2x)/(dy^2) equals", "response_choices": "(A) (d^2y/dx^2)^-1\n(B) -(d^2y/dx^2)^-1(dy/dx)^-3\n(C) (d^2y/dx^2)(dy/dx)^2\n(D) -(d^2y/dx^2)(dy/dx)^3", "answer": "D", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "The differential equation dy/dx = \u221a(1-y^2)/y determines a family of circles with", "response_choices": "(A) variable radii and a fixed centre at (0, 1) (B) variable radii and a fixed centre at (0, -1) (C) fixed radius 1 and variable centres along the x-axis (D) fixed radius 1 and variable centres along the y-axis", "answer": "C", "page_number": 21, "image_available": "yes", "question_subject": "mathematics"} +{"id": 50, "question": "Let a, b, c be unit vectors such that a + b + c = 0. Which one of the following is correct?", "response_choices": "(A) a \u00d7 b = b \u00d7 c = c \u00d7 a = 0 (B) a \u00d7 b = b \u00d7 c = c \u00d7 a \u2260 0 (C) a \u00d7 b = b \u00d7 c = a \u00d7 c \u2260 0 (D) a \u00d7 b, b \u00d7 c, c \u00d7 a are mutually perpendicular", "answer": "B", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2 CD . Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is", "response_choices": "(A) 3 (B) 2 (C) 3/2 (D) 1", "answer": "B", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Let f(x) = (x)/(1 + x^n)^(n) for n >= 2 and g(x) = (f \u2218 f \u2218 ... \u2218 f) (x). Then [x^(-2)g(x) dx] equals", "response_choices": "(A) (1)/((n(n-1))(1 + nx^n)^(1/n) + K), (B) (1)/(n-1)(1 + nx^n)^(-1/n) + K, (C) (1)/((n(n+1))(1 + nx^n)^(1/n) + K), (D) (1)/(n+1)(1 + nx^n)^(1/n) + K", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is", "response_choices": "(A) 360, (B) 192, (C) 96, (D) 48", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Consider the planes 3x - 6y - 2z = 15 and 2x + y - 2z = 5. STATEMENT-1 : The parametric equations of the line of intersection of the given planes are x = 3 + 14t, y = 1 + 2t, z = 15t. because STATEMENT-2 : The vector 14i + 2j + 15k is parallel to the line of intersection of given planes.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, (C) Statement-1 is True, Statement-2 is False, (D) Statement-1 is False, Statement-2 is True", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "STATEMENT-1 : The curve y = -x^2/2 + x + 1 is symmetric with respect to the line x = 1. because STATEMENT-2 : A parabola is symmetric about its axis.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let f(x) = 2 + cos x for all real x. STATEMENT-1 : For each real t, there exists a point c in [t, t + \u03c0] such that f'(c) = 0. because STATEMENT-2 : f(t) = f(t + 2\u03c0) for each real t.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "B", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Lines L1: y - x = 0 and L2: 2x + y = 0 intersect the line L3: y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R. STATEMENT-1: The ratio PR: RQ equals 2\u221a2: \u221a5. because STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.", "response_choices": "(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Which one of the following statements is correct? (A) G1 > G2 > G3 > ... (B) G1 < G2 < G3 < ... (C) G2 = G1 = G3 = ... (D) G1 < G3 < G5 < ... and G2 > G4 > G6 > ...", "response_choices": "(A) G1 > G2 > G3 > ... (B) G1 < G2 < G3 < ... (C) G2 = G1 = G3 = ... (D) G1 < G3 < G5 < ... and G2 > G4 > G6 > ...", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "Which one of the following statements is correct? (A) A1 > A2 > A3 > ... (B) A1 < A2 < A3 < ... (C) A1 > A3 > A5 > ... and A2 < A4 < A6 < ... (D) A1 < A3 < A5 < ... and A2 > A4 > A6 > ...", "response_choices": "(A) A1 > A2 > A3 > ... (B) A1 < A2 < A3 < ... (C) A1 > A3 > A5 > ... and A2 < A4 < A6 < ... (D) A1 < A3 < A5 < ... and A2 > A4 > A6 > ...", "answer": "A", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Which one of the following statements is correct?", "response_choices": "(A) H\u2081 > H\u2082 > H\u2083 > \u22ef\n(B) H\u2081 < H\u2082 < H\u2083 < \u22ef\n(C) H\u2081 > H\u2082 > H\u2083 > \u22ef and H\u2083 < H\u2084 < H\u2086 < \u22ef\n(D) H\u2081 < H\u2083 < H\u2085 < \u22ef and H\u2082 > H\u2084 > H\u2086 > \u22ef", "answer": "B", "page_number": 25, "image_available": "no", "question_subject": "physics"} +{"id": 61, "question": "The line y = x meets y = ke^x for k \u2264 0 at", "response_choices": "(A) no point\n(B) one point\n(C) two points\n(D) more than two points", "answer": "B", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 62, "question": "The positive value of k for which ke^x - x = 0 has only one root is", "response_choices": "(A) 1/e\n(B) 1\n(C) e\n(D) log\u2085 2", "answer": "A", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 63, "question": "For k > 0, the set of all values of k for which ke^x - x = 0 has two distinct roots is", "response_choices": "(A) (0, 1/e)\n(B) (1/e, 1)\n(C) (1/e, \u221e)\n(D) (0, 1)", "answer": "A", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 64, "question": "Let f(x) = (x^2 - 6x + 5) / (x^3 - 5x + 6). Match the expressions/statements in Column I with expressions/statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) If -1 < x < 1, then f(x) satisfies (B) If 1 < x < 2, then f(x) satisfies (C) If 3 < x < 5, then f(x) satisfies (D) If x > 5, then f(x) satisfies\nColumn II: (p) 0 < f(x) < 1 (q) f(x) < 0 (r) f(x) > 0 (s) f(x) < 1", "answer": "p: not selected, q: A, r: C and D, s: A and D", "page_number": 26, "image_available": "yes", "question_subject": "mathematics"} +{"id": 65, "question": "Let (x, y) be such that sin\u207b\u00b9(a x) + cos\u207b\u00b9(y) + cos\u207b\u00b9(b x y) = \u03c0/2. Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "Column I: (A) If a = 1 and b = 0, then (x, y), (B) If a = 1 and b = 1, then (x, y), (C) If a = 1 and b = 2, then (x, y), (D) If a = 2 and b = 2, then (x, y) \n Column II: (p) lies on the circle x\u00b2 + y\u00b2 = 1, (q) lies on (x\u00b2 - 1)(y\u00b2 - 1) = 0, (r) lies on y = x, (s) lies on (4x\u00b2 - 1)(y\u00b2 - 1) = 0", "answer": "p, q, r, s", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 66, "question": "Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 \u00d7 4 matrix given in the ORS.", "response_choices": "(A) Two intersecting circles, (B) Two mutually external circles, (C) Two circles, one strictly inside the other, (D) Two branches of a hyperbola, (p) have a common tangent, (q) have a common normal, (r) do not have a common tangent, (s) do not have a common normal", "answer": "A: pq, B: pq, C: rs, D: rs", "page_number": 28, "image_available": "yes", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2008_1.jsonl b/JEE_papers/JSON/JEE_2008_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..81232ec8716623b18e2cb98d7462198d7f0149f9 --- /dev/null +++ b/JEE_papers/JSON/JEE_2008_1.jsonl @@ -0,0 +1,69 @@ +{"id": 1, "question": "Consider the two curves C1 : y^2 = 4x, C2 : x^2 + y^2 - 6x + 1 = 0. Then,", "response_choices": "(A) C1 and C2 touch each other only at one point, (B) C1 and C2 touch each other exactly at two points, (C) C1 and C2 intersect (but do not touch) at exactly two points, (D) C1 and C2 neither intersect nor touch each other", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "If 0 < x < 1, then sqrt(1 + x^2) ( [x cos (cot^-1 x) + sin (cot^-1 x)]^2 - 1 )^2 =", "response_choices": "(A) x/sqrt(1+x^2), (B) x, (C) x*sqrt(1+x^2), (D) sqrt(1+x^2)", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors \u00e2, b\u0302, \u0109 such that \u00e2.b\u0302 = b\u0302.\u0109 = \u0109.\u00e2 = 1/2. Then, the volume of the parallelopiped is", "response_choices": "(A) 1/sqrt(2), (B) 1/2sqrt(2), (C) sqrt(3)/2, (D) 1/sqrt(3)", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let a and b be non-zero real numbers. Then, the equation (a x^2 + b y^2 + c) (x^2 - 5 x y + 6 y^2) = 0 represents", "response_choices": "(A) four straight lines, when c = 0 and a, b are of the same sign, (B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a, (C) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a, (D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let g(x) = (x-1)^n/(log cos^m (x-1)), 00, and let p be the left hand derivative of |x-1| at x=1. If lim g(x)=p, then", "response_choices": "(A) n=1, m=1 (B) n=1, m=-1 (C) n=2, m=2 (D) n>2, m=n", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "The total number of local maxima and local minima of the function f(x)={(2+x)^3, -3 2/\u221aQS\u00d7SR (C) 1/PS + 1/ST < 4/QR (D) 1/PS + 1/ST > 4/QR", "answer": "B, D", "page_number": 2, "image_available": "yes", "question_subject": "mathematics"} +{"id": 8, "question": "Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The equations of parabolas with latus rectum PQ are", "response_choices": "(A) x^2 + 2\u221a3 y = 3 + \u221a3, (B) x^2 - 2\u221a3 y = 3 + \u221a3, (C) x^2 + 2\u221a3 y = 3 - \u221a3, (D) x^2 - 2\u221a3 y = 3 - \u221a3", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let S_n = \u03a3(n/(n^2 + kn + k^2)) and T_n = \u03a3((n-1)/(n^2 + kn + k^2)), for n = 1, 2, 3, .... Then,", "response_choices": "(A) S_n < \u03c0/3\u221a3, (B) S_n > \u03c0/3\u221a3, (C) T_n < \u03c0/3\u221a3, (D) T_n > \u03c0/3\u221a3", "answer": "A,D", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let f(x) be a non-constant twice differentiable function defined on (-\u221e, \u221e) such that f(x) = f(1 - x) and f''(1/4) = 0. Then,", "response_choices": "(A) f''(x) vanishes at least twice on [0, 1], (B) f'(1/2) = 0, (C) \u222b(1/2)(-1/2) f(x + 1/2) sin x dx = 0, (D) \u222b(1/2)(0) f(t) e^sin \u03c0t dt = \u222b(1/2)(0) f(1 - t) e^sin \u03c0t dt", "answer": "A,B,C,D", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let f and g be real valued functions defined on interval (- 1, 1) such that g''(x) is continuous, g(0) \u2260 0, g'(0) = 0, g''(0) \u2260 0, and f(x) = g(x)sin x. STATEMENT-1 : lim [g(x) cot x - g(0) cosec x] = f''(0) . and STATEMENT-2 : f'(0) = g(0) .", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Consider three planes P1 :x - y + z = 1 P2 : x + y - z = -1 P3 :x - 3y + 3z = 2. Let L1, L2, L3 be the lines of intersection of the planes P2 and P3, P3 and P1, and P1 and P2, respectively. STATEMENT-1 : At least two of the lines L1, L2 and L3 are non-parallel. and STATEMENT-2 : The three planes do not have a common point.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "D", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Consider the system of equations x - 2y + 3z = -1 -x + y - 2z = k x - 3y + 4z = 1 STATEMENT-1 : The system of equations has no solution for k \u2260 3 and STATEMENT-2 : The determinant | 1 3 -1| |-1 -2 k| \u2260 0, for k \u2260 3. |1 4 1|", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Consider the system of equations ax + b y = 0 , c x + d y = 0 , where a, b, c, d \u03f5 {0, 1} . STATEMENT-1 : The probability that the system of equations has a unique solution is 3/8 . and STATEMENT-2 : The probability that the system of equations has a solution is 1 .", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "The equation of circle C is", "response_choices": "(A) (x - 2\u221a3)^2 + (y - 1)^2 = 1, (B) (x - 2\u221a3)^2 + (y + 1/2)^2 = 1, (C) (x - \u221a3)^2 + (y + 1)^2 = 1, (D) (x - \u221a3)^2 + (y - 1)^2 = 1", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 16, "question": "Points E and F are given by", "response_choices": "(A) (\u221a3/2 , 2), (\u221a3, 0), (B) (\u221a3/2 , 1/2), (\u221a3, 0), (C) (\u221a3/2 , 2), (\u221a3/2 , 1/2), (D) (3/2, \u221a3/2), (\u221a3/2 , 1/2)", "answer": "A", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 17, "question": "Equations of the sides QR , RP are", "response_choices": "(A) y = -2/\u221a3 x + 1, y = -2/\u221a3 x - 1, (B) y = 1/\u221a3 x, y = 0, (C) y = \u221a3/2 x + 1, y = -\u221a3/2 x - 1, (D) y = \u221a3 x, y = 0", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 18, "question": "If f (-10\u221a2) = 2\u221a2 , then f''(-10\u221a2) =", "response_choices": "(A) 4\u221a2/7*32, (B) -4\u221a2/7*32, (C) 4\u221a2/7*3, (D) -4\u221a2/7*3", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 19, "question": "The area of the region bounded by the curve y = f(x), the x-axis, and the lines x = a and x = b, where -\u221e < a < b < -2, is", "response_choices": "(A) \u222b\u2090^b [x / (3((f(x))\u00b2 - 1))] dx + b f(b) - a f(a), (B) -\u222b\u2090^b [x / (3((f(x))\u00b2 - 1))] dx + b f(b) - a f(a), (C) \u222b\u2090^b [x / (3((f(x))\u00b2 - 1))] dx - b f(b) + a f(a), (D) -\u222b\u2090^b [x / (3((f(x))\u00b2 - 1))] dx - b f(b) + a f(a)", "answer": "A", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 20, "question": "\u222b\u208b\u2081^1 g'(x) dx =", "response_choices": "(A) 2g(-1), (B) 0, (C) -2g(1), (D) 2g(1)", "answer": "D", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 21, "question": "The number of elements in the set A \u2229 B \u2229 C is", "response_choices": "(A) 0, (B) 1, (C) 2, (D) \u221e", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 22, "question": "Let z be any point in A \u2229 B \u2229 C. Then, |z + 1 - i|\u00b2 + |z - 5 - i|\u00b2 lies between", "response_choices": "(A) 25 and 29, (B) 30 and 34, (C) 35 and 39, (D) 40 and 44", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 23, "question": "Let z be any point in A\u2229B\u2229C and let w be any point satisfying |w-2-\u03b5|<3 Then, |z|-|w|+3 lies between", "response_choices": "(A) -6 and 3, (B) -3 and 6, (C) -6 and 6, (D) -3 and 9", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 24, "question": "Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table. Least count for length = 0.1 cm Least count for time = 0.1 s [Table with data for Student, Length of the pendulum (cm), Number of oscillations (n), Total time for (n) oscillations (s), Time period (s)] If E1, EII and EIII are the percentage errors in g, i.e., (\u0394g/g\u00d7100) for students I, II and III, respectively,", "response_choices": "(A) EI = 0, (B) EI is minimum, (C) EI = EII, (D) EII is maximum", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 25, "question": "Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then", "response_choices": "(A) P1 > P2 > P3, (B) P1 > P3 > P2, (C) P2 > P1 > P3, (D) P3 > P2 > P1", "answer": "C", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 26, "question": "Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?", "response_choices": "(A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases, (B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target, (C) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube, (D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube", "answer": "B", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 27, "question": "Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60\u00b0). In the position of minimum deviation, the angle of refraction will be", "response_choices": "(A) 30\u00b0 for both the colours, (B) greater for the violet colour, (C) greater for the red colour, (D) equal but not 30\u00b0 for both the colours", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 28, "question": "An ideal gas is expanding such that PV^\u03b3 = constant. The coefficient of volume expansion of the gas is", "response_choices": "(A) 1/T (B) 2/T (C) 3/T (D) 4/T", "answer": "C", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 29, "question": "A spherically symmetric gravitational system of particles has a mass density \u03c1=\u03c10 for r\u2264R, 0 for r>R where \u03c10 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r (0 q*B/m, (B) The particle enters Region III only if its velocity V < q*B/m, (C) Path length of the particle in Region II is maximum when velocity V = q*B/m, (D) Time spent in Region II is same for any velocity V as long as the particle returns to Region I", "answer": "B,C", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 33, "question": "In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is \u03bb. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).", "response_choices": "(A) If d = \u03bb, the screen will contain only one maximum\n(B) If \u03bb < d < 2\u03bb, at least one more maximum (besides the central maximum) will be observed on the screen\n(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase\n(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 34, "question": "STATEMENT-1\nIn a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.\nand\nSTATEMENT-2\nResistance of a metal increases with increase in temperature.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "D", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 35, "question": "STATEMENT-1\nAn astronaut in an orbiting space station above the Earth experiences weightlessness.\nand\nSTATEMENT-2\nAn object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 36, "question": "STATEMENT-1\nTwo cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.\n\nand\n\nSTATEMENT-2\nBy the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 37, "question": "STATEMENT-1\nThe stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.\n\nand\n\nSTATEMENT-2\nIn any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 38, "question": "As the bubble moves upwards, besides the buoyancy force the following forces are acting on it", "response_choices": "(A) Only the force of gravity\n(B) The force due to gravity and the force due to the pressure of the liquid\n(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid\n(D) The force due to gravity and the force due to viscosity of the liquid", "answer": "D", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 39, "question": "When the gas bubble is at a height y from the bottom, its temperature is", "response_choices": "(A) T0 ( P0 + \u03c1 \u22c5 g \u22c5 H ) ^ (2/5) / ( P0 + \u03c1i \u22c5 g \u22c5 y )\n(B) T0 ( P0 + \u03c1 \u22c5 g \u22c5 (H - y) ) ^ (2/5) / ( P0 + \u03c1 \u22c5 g \u22c5 H )\n(C) T0 ( P0 + \u03c1 \u22c5 g \u22c5 H ) ^ (3/5) / ( P0 + \u03c1i \u22c5 g \u22c5 y )\n(D) T0 ( P0 + \u03c1 \u22c5 g \u22c5 (H - y) ) ^ (3/5) / ( P0 + \u03c1 \u22c5 g \u22c5 H )", "answer": "B", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 40, "question": "The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)", "response_choices": "(A) \u03c1 \u2099 R g T\u2092 [(P\u2092 + \u03c1 \u2090 g H )\u00b2\u2044\u2085] / [(P\u2092 + \u03c1 \u2090 g y)\u00b9\u2044\u2085], (B) [\u03c1 \u2099 R g T\u2092] / [(P\u2092 + \u03c1 \u2090 g H )\u00b2\u2044\u2085 [(P\u2092 + \u03c1 \u2090 g (H - y))\u00b3\u2044\u2085]], (C) \u03c1 \u2099 R g T\u2092 [(P\u2092 + \u03c1 \u2090 g H )\u00b3\u2044\u2085] / [(P\u2092 + \u03c1 \u2090 g y)\u2075\u2044\u2083], (D) [\u03c1 \u2099 R g T\u2092] / [(P\u2092 + \u03c1 \u2090 g H )\u00b3\u2044\u2085 [(P\u2092 + \u03c1 \u2090 g (H - y))\u00b2\u2044\u2085]]", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 41, "question": "The quantum number n of the state finally populated in He\u207a ions is", "response_choices": "(A) 2, (B) 3, (C) 4, (D) 5", "answer": "C", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 42, "question": "The wavelength of light emitted in the visible region by He\u207a ions after collisions with H atoms is", "response_choices": "(A) 6.5 x 10\u207b\u2077 m, (B) 5.6 x 10\u207b\u2077 m, (C) 4.8 x 10\u207b\u2077 m, (D) 4.0 x 10\u207b\u2077 m", "answer": "C", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 43, "question": "The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He\u207a ion is", "response_choices": "(A) 1/4, (B) 1/2, (C) 1, (D) 2", "answer": "A", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 44, "question": "The speed of the block at point B immediately after it strikes the second incline is", "response_choices": "(A) \u221a60 m/s, (B) \u221a45 m/s, (C) \u221a30 m/s, (D) \u221a15 m/s", "answer": "B", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 45, "question": "The speed of the block at point C, immediately before it leaves the second incline is", "response_choices": "(A) \u221a120 m/s, (B) \u221a105 m/s, (C) \u221a90 m/s, (D) \u221a75 m/s", "answer": "B", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 46, "question": "If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is", "response_choices": "(A) \u221a30 m/s, (B) \u221a15 m/s, (C) 0, (D) -\u221a15 m/s", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 47, "question": "Hyperconjugation involves overlap of the following orbitals", "response_choices": "(A) \u03c3-\u03c3, (B) \u03c3-p, (C) p-p, (D) \u03c0-\u03c0", "answer": "B", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 48, "question": "The major product of the following reaction is", "response_choices": "(A) (B) (C) (D)", "answer": "A", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 49, "question": "Aqueous solution of Na2S2O3 on reaction with Cl2 gives", "response_choices": "(A) Na2S4O6 (B) NaHSO4 (C) NaCl (D) NaOH", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 50, "question": "Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of", "response_choices": "(A) nitrogen (B) oxygen (C) carbon dioxide (D) argon", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 51, "question": "Under the same reaction conditions, initial concentration of 1.386 mol dm^3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio (k1/k0) of the rate constants for first order (k1) and zero order (k0) of the reactions is", "response_choices": "(A) 0.5 mol^-1 dm^3 (B) 1.0 mol dm^-3 (C) 1.5 mol dm^-3 (D) 2.0 mol^-1 dm^3", "answer": "A", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 52, "question": "2.5 mL of 2/5 M weak monoacidic base (Kb = 1 x 10^-12 at 25\u00b0C) is titrated with 2/15 M HCl in water at 25\u00b0C. The concentration of H+ at equivalence point is (Kw = 1 x 10^-14 at 25\u00b0C)", "response_choices": "(A) 3.7 x 10^-13 M, (B) 3.2 x 10^-7 M, (C) 3.2 x 10^-2 M, (D) 2.7 x 10^-2 M", "answer": "D", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 53, "question": "The correct statement(s) about the compound given below is (are)", "response_choices": "(A) The compound is optically active, (B) The compound possesses centre of symmetry, (C) The compound possesses plane of symmetry, (D) The compound possesses axis of symmetry", "answer": "A,D", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 54, "question": "The correct statement(s) concerning the structures E, F and G is (are)", "response_choices": "(A) E, F and G are resonance structures, (B) E, F and E, G are tautomers, (C) F and G are geometrical isomers, (D) F and G are diastereomers", "answer": "B,C,D", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 55, "question": "A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is (are)", "response_choices": "(A) NH4NO3, (B) NH4NO2, (C) NH4Cl, (D) (NH4)2SO4", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 56, "question": "A gas described by van der Waals equation (A) behaves similar to an ideal gas in the limit of large molar volumes (B) behaves similar to an ideal gas in the limit of large pressures (C) is characterised by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature (D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally", "response_choices": "(A), (C) OR (A), (C), (D)", "answer": "(A), (C)", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 57, "question": "STATEMENT-1 : Bromobenzene upon reaction with Br2/Fe gives 1,4-dibromobenzene as the major product. and STATEMENT-2 : In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "response_choices": "(A), (B), (C), (D)", "answer": "C", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 58, "question": "STATEMENT-1 : Pb\u207a\u207a compounds are stronger oxidizing agents than Sn\u207a\u207a compounds. and STATEMENT-2 : The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 59, "question": "STATEMENT-1 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45\u00b0 slope as the atomic number is increased. and STATEMENT-2 : Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 60, "question": "STATEMENT-1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero. and STATEMENT-2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "D", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 61, "question": "The structure of the product I is", "response_choices": "(A) Me/\\/\\/\\/\\Br, (B) Me\\/\\/\\/Br, (C) Me/\\/\\/\\/Br, (D) Me\\/\\/Br", "answer": "D", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 62, "question": "The structures of compounds J and K, respectively, are", "response_choices": "(A) Me\\/\\/COOH and SOCl2, (B) Me/\\/\\/\\/OH and SO2Cl2, (C) Me\\/\\/COOH and SOCl2, (D) Me\\/\\/COOH and CH3SO2Cl", "answer": "A", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 63, "question": "The structure of product L is", "response_choices": "(A) Me\u2014CHO, (B) Me~CHO, (C) Me/\\CHO, (D) Me~CHO", "answer": "C", "page_number": 22, "image_available": "yes", "question_subject": "chemistry"} +{"id": 64, "question": "Among the following, the correct statement is (A) Phosphates have no biological significance in humans (B) Between nitrates and phosphates, phosphates are less abundant in earth's crust (C) Between nitrates and phosphates, nitrates are less abundant in earth's crust (D) Oxidation of nitrates is possible in soil", "response_choices": "(A) Phosphates have no biological significance in humans, (B) Between nitrates and phosphates, phosphates are less abundant in earth's crust, (C) Between nitrates and phosphates, nitrates are less abundant in earth's crust, (D) Oxidation of nitrates is possible in soil", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 65, "question": "Among the following, the correct statement is (A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional (B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional (C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional (D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional", "response_choices": "(A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional, (B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional, (C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional, (D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 66, "question": "White phosphorus on reaction with NaOH gives PH3 as one of the products. This is a", "response_choices": "(A) dimerization reaction, (B) disproportionation reaction, (C) condensation reaction, (D) precipitation reaction", "answer": "B", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 67, "question": "The freezing point of the solution M is", "response_choices": "(A) 268.7 K, (B) 268.5 K, (C) 234.2 K, (D) 150.9 K", "answer": "C", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 68, "question": "The vapour pressure of the solution M is", "response_choices": "(A) 39.3 mm Hg, (B) 36.0 mm Hg, (C) 29.5 mm Hg, (D) 28.8 mm Hg", "answer": "B", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 69, "question": "Water is added to the solution M such that the mole fraction of water in the solution becomes 0.9. The boiling point of this solution is", "response_choices": "(A) 380.4 K, (B) 376.2 K, (C) 375.5 K, (D) 354.7 K", "answer": "B", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} diff --git a/JEE_papers/JSON/JEE_2008_2.jsonl b/JEE_papers/JSON/JEE_2008_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..7b2eb1d06eb6a40edcf01168c1dc7baa8abcde49 --- /dev/null +++ b/JEE_papers/JSON/JEE_2008_2.jsonl @@ -0,0 +1,66 @@ +{"id": 1, "question": "A particle P starts from the point z\u2080 = 1 + 2i, where i = \u221a-1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z\u2081. From z\u2081 the particle moves \u221a2 units in the direction of the vector i + j and then it moves through an angle \u03c0/2 in anticlockwise direction on a circle with centre at origin, to reach a point z\u2082. The point z\u2082 is given by", "response_choices": "(A) 6 + 7i, (B) -7 + 6i, (C) 7 + 6i, (D) -6 + 7i", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Let the function g : (-\u221e, \u221e) \u2192 (\u03c0/2, \u03c0/2) be given by g(u) = 2tan\u207b\u00b9(e\u1d58) - \u03c0/2. Then, g is", "response_choices": "(A) even and is strictly increasing in (0, \u221e), (B) odd and is strictly decreasing in (-\u221e, \u221e), (C) odd and is strictly increasing in (-\u221e, \u221e), (D) neither even nor odd, but is strictly increasing in (-\u221e, \u221e)", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Consider a branch of the hyperbola x\u00b2 - 2y\u00b2 - 2\u221a2x - 4\u221a2y - 6 = 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is", "response_choices": "(A) 1 - 2/\u221a3, (B) \u221a(3/2) - 1, (C) 1 + 2/\u221a3, (D) 3/\u221a2 + 1", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "The area of the region between the curves y = \u221a(1+sinx/cosx) and y = \u221a(1-sinx/cosx) bounded by the lines x = 0 and x = \u03c0/4 is", "response_choices": "(A) \u222b\u2080^(\u03c0/2\u221a1+t\u00b2)dt/(1+t\u00b2\u221a1-t\u00b2), (B) \u222b\u2080^(\u03c0/2\u221a1-t\u00b2)4t/(1+t\u00b2\u221a1-t\u00b2) dt, (C) \u222b\u2080^(\u03c0/4\u221a1+t\u00b2)4t/(1+t\u00b2\u221a1-t\u00b2) dt, (D) \u222b\u2080^(\u03c0/1\u221a1-t\u00b2)t/(1+t\u00b2\u221a1-t\u00b2) dt", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "mathematics"} +{"id": 5, "question": "Consider three points P = (- sin(\u03b2 - \u03b1), - cos \u03b2), Q = (cos(\u03b2 - \u03b1), sin \u03b2) and R = (cos(\u03b2 - \u03b1 + \u03b8), sin(\u03b2 - \u03b8)), where 0 < \u03b1 , \u03b2 , \u03b8 < \u03c0/4. Then,", "response_choices": "(A) P lies on the line segment RQ\n(B) Q lies on the line segment PR\n(C) R lies on the line segment QP\n(D) P, Q, R are non-collinear", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is", "response_choices": "(A) 2, 4 or 8\t(B) 3, 6 or 9\t(C) 4 or 8\t(D) 5 or 10", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let two non-collinear unit vectors \u00e2 and b\u0302 form an acute angle. A point P moves so that at any time t the position vector OP\u20d7 (where O is the origin) is given by \u00e2 cost + b\u0302 sin t. When P is farthest from origin O , let M be the length of OP\u20d7 and \u00fb be the unit vector along OP\u20d7 . Then,", "response_choices": "(A) \u00fb = (\u00e2 + b\u0302) / |\u00e2 + b\u0302| and M = (1 + \u00e2 . b\u0302)^(1/2)\t(B) \u00fb = (\u00e2 - b\u0302) / |\u00e2 - b\u0302| and M = (1 + \u00e2 . b\u0302)^(1/2)\n(C) \u00fb = (\u00e2 + b\u0302) / |\u00e2 + b\u0302| and M = (1 + 2\u00e2 . b\u0302)^(1/2)\t(D) \u00fb = (\u00e2 - b\u0302) / |\u00e2 - b\u0302| and M = (1 + 2\u00e2 . b\u0302)^(1/2)", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let I = \u222b(e^x / e^4x + e^2x + 1) dx, J = \u222b(e^-x / e^-4x + e^-2x + 1) dx. Then, for an arbitrary constant C, the value of J - I equals", "response_choices": "(A) (1/2) log[((e^4x - e^2x + 1) / (e^4x + e^2x + 1))] + C\t(B) (1/2) log[((e^2x + e^x + 1) / (e^2x - e^x + 1))] + C\n(C) (1/2) log[((e^2x - e^x + 1) / (e^2x + e^x + 1))] + C\t(D) (1/2) log[((e^4x + e^2x + 1) / (e^4x - e^2x + 1))] + C", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let g(x) = log f(x) where f(x) is a twice differentiable positive function on (0, \u221e) such that f(x + 1) = x f(x). Then, for N = 1, 2, 3,..., g'(N + 1/2) - g'(1/2) =", "response_choices": "(A) -4{1 + 1/9 + 1/25 + ... + 1/(2N - 1)^2}, (B) 4{1 + 1/9 + 1/25 + ... + 1/(2N - 1)^2}, (C) -4{1 + 1/9 + 1/25 + ... + 1/(2N + 1)^2}, (D) 4{1 + 1/9 + 1/25 + ... + 1/(2N + 1)^2}", "answer": "(A)", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3 and b4 = b3 + a4. STATEMENT-1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P. and STATEMENT-2 : The numbers b1, b2, b3, b4 are in H.P.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "(C)", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let a, b, c, p, q be real numbers. Suppose \u03b1, \u03b2 are the roots of the equation x^2 + 2px + q = 0 and \u03b1, 1/\u03b2 are the roots of the equation ax^2 + 2bx + c = 0, where \u03b2^2 \u2208 {-1, 0, 1}. STATEMENT-1 : (p^2 - q)(b^2 - ac) \u2265 0 and STATEMENT-2 : b \u2260 pa or c \u2260 qa", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "(B)", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Consider L1 : 2x + 3y + p - 3 = 0, L2 : 2x + 3y + p + 3 = 0, where p is a real number, and C : x^2 + y^2 + 6x - 10y + 30 = 0. STATEMENT-1 : If line L1 is a chord of circle C, then line L2 is not always a diameter of circle C. and STATEMENT-2 : If line L1 is a diameter of circle C, then line L2 is not a chord of circle C.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let a solution y = y(x) of the differential equation x\u221a(x^2 - 1) dy - y\u221a(y^2 - 1) dx = 0 satisfy y(2) = 2/\u221a3. STATEMENT-1 : y(x) = sec(sec^-1 x - \u03c0/6) and STATEMENT-2 : y(x) is given by 1/(2\u221a3 - \u221a(1 - x^2))", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Which of the following is true?", "response_choices": "(A) (2 + a)^2 f''(1) + (2 - a)^2 f''(-1) = 0 (B) (2 - a)^2 f''(1) - (2 + a)^2 f''(-1) = 0 (C) f'(1) f'(-1) = (2 - a)^2 (D) f'(1) f'(-1) = -(2 + a)^2", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Which of the following is true?", "response_choices": "(A) f(x) is decreasing on (-1, 1) and has a local minimum at x = 1 (B) f(x) is increasing on (-1, 1) and has a local maximum at x = 1 (C) f(x) is increasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1 (D) f(x) is decreasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let g(x) = \u222b(0 to x) f'(t) / (1 + t^2) dt. Which of the following is true?", "response_choices": "(A) g'(x) is positive on (- \u221e, 0) and negative on (0, \u221e) (B) g'(x) is negative on (- \u221e, 0) and positive on (0, \u221e) (C) g'(x) changes sign on both (- \u221e, 0) and (0, \u221e) (D) g'(x) does not change sign on (- \u221e, \u221e)", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "The unit vector perpendicular to both L1 and L2 is", "response_choices": "A) -i + 7j + 7k/\u221a99, B) -i - 7j + 5k/5\u221a3, C) -i + 7j + 5k/5\u221a3, D) 7i - 7j - k/\u221a99", "answer": "B", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 18, "question": "The shortest distance between L1 and L2 is", "response_choices": "A) 0, B) 17/\u221a3, C) 41/5\u221a3, D) 17/5\u221a3", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 19, "question": "The distance of the point (1, 1, 1) from the plane passing through the point (-1, -2, -1) and whose normal is perpendicular to both the lines L1 and L2 is", "response_choices": "A) 2/\u221a75, B) 7/\u221a75, C) 13/\u221a75, D) 23/\u221a75", "answer": "C", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 20, "question": "Consider the lines given by L1 : x + 3y - 5 = 0 L2 : 3x - ky - 1 = 0 L3 : 5x + 2y - 12 = 0 Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) L1, L2, L3 are concurrent, if (B) One of L1, L2, L3 is parallel to at least one of the other two, if (C) L1, L2, L3 form a triangle, if (D) L1, L2, L3 do not form a triangle, if (p) k = -9 (q) k = - 6/5 (r) k = 5/6 (s) k = 5", "answer": "p:O, q:O, r:O, s:*, A:O, B:*, C:O, D:*", "page_number": 7, "image_available": "yes", "question_subject": "mathematics"} +{"id": 21, "question": "Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) The minimum value of x^2 + 2x + 4/x + 2 is (B) Let A and B be 3 x 3 matrices of real numbers, where A is symmetric, B is skew-symmetric, and (A + B) (A - B) = (A - B) (A + B). If (AB)' = (-1)^k AB, where (AB)' is the transpose of the matrix AB, then the possible values of k are (C) Let a = log\u2083 2, log\u2082 2. An integer k satisfying 1 < 2^(-k + 3 - a) < 2, must be less than (D) If sin \u03b8 = cos \u03c6, then the possible values of 1/\u03c0 (\u03b8 + \u03c6 - \u03c0/2) are (p) 0 (q) 1 (r) 2 (s) 3", "answer": "p:O, q:*, r:*, s:O, A:O, B:O, C:*, D:*", "page_number": 7, "image_available": "yes", "question_subject": "mathematics"} +{"id": 22, "question": "Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 \u00d7 4 matrix given in the ORS.", "response_choices": "Column I: (A) The number of permutations containing the word ENDEA is, (B) The number of permutations in which the letter E occurs in the first and the last positions is, (C) The number of permutations in which none of the letters D, L, N occurs in the last five positions is, (D) The number of permutations in which the letters A, E, O occur only in odd positions is\nColumn II: (p) 5!, (q) 2 \u00d7 5!, (r) 7 \u00d7 5!, (s) 21 \u00d7 5!", "answer": "A: p, B: s, C: r, D: q", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 23, "question": "Consider a system of three charges q, q and 2q/3 placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60\u00b0\n\nFigure:\n\n(A) The electric field at point O is q/8\u03c0\u03b5\u2080R\u00b2 directed along the negative x-axis\n(B) The potential energy of the system is zero\n(C) The magnitude of the force between the charges at C and B is q\u00b2/54\u03c0\u03b5\u2080R\u00b2\n(D) The potential at point O is q/12\u03c0\u03b5\u2080R", "response_choices": "(A), (B), (C), (D)", "answer": "(C)", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 24, "question": "A radioactive sample S1 having an activity of 5 \u03bcCi has twice the number of nuclei as another sample S2 which has an activity of 10 \u03bcCi. The half lives of S1 and S2 can be", "response_choices": "(A) 20 years and 5 years, respectively\n(B) 20 years and 10 years, respectively\n(C) 10 years each\n(D) 5 years each", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 25, "question": "A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is", "response_choices": "(A) \u221a(3\u03c0\u00f750) m/s\n(B) -\u221a(3\u03c0\u00f750) m/s\n(C) \u221a(3\u03c0\u00f750) m/s\n(D) -\u221a(3\u03c0\u00f750) m/s", "answer": "A", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 26, "question": "A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4 k, respectively (see figure 1). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is", "response_choices": "A) 4, B) 2, C) 1/2, D) 1/4", "answer": "C", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 27, "question": "A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle \u03b8 at which the speed of the bob is half of that at A, satisfies", "response_choices": "A) \u03b8 = \u03c0/4, B) \u03c0/4 < \u03b8 < \u03c0/2, C) \u03c0/2 < \u03b8 < 3\u03c0/4, D) 3\u03c0/4 < \u03b8 < \u03c0", "answer": "D", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 28, "question": "A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,", "response_choices": "(A) air from end 1 flows towards end 2. No change in the volume of the soap bubbles\n(B) air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases\n(C) no change occurs\n(D) air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases", "answer": "B", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 29, "question": "A vibrating string of certain length \u2113 under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is", "response_choices": "(A) 344\t(B) 336\t(C) 117.3\t(D) 109.3", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 30, "question": "A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is", "response_choices": "(A) 6\u03b5oR / 5d+3Vt, (B) (15d+9Vt)\u03b5oR / 2d^2-3dVt-9V^2t^2, (C) 6\u03b5oR / 5d-3Vt, (D) (15d-9Vt)\u03b5oR / 2d^2+3dVt-9V^2t^2", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 31, "question": "A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are no, no/2, no/6 and no/8, respectively. The angle of incidence \u03b8 for which the beam just misses entering Region IV is", "response_choices": "(A) sin^-1(3/4), (B) sin^-1(1/5), (C) sin^-1(1/4), (D) sin^-1(1/3)", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 32, "question": "STATEMENT-1\nFor an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.\nand\nSTATEMENT-2\nIf the observer and the object are moving at velocities V1 and V2 respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is V2 - V1.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 33, "question": "STATEMENT-1\nIt is easier to pull a heavy object than to push it on a level ground.\nand\nSTATEMENT-2\nThe magnitude of frictional force depends on the nature of the two surfaces in contact.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 34, "question": "STATEMENT-1\n\nFor practical purposes, the earth is used as a reference at zero potential in electrical circuits.\n\nand\n\nSTATEMENT-2\n\nThe electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by Q/4\u03c0\u03b50R.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 35, "question": "STATEMENT-1\n\nThe sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.\n\nand\n\nSTATEMENT-2\n\nSoft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 36, "question": "The electric field at r = R is", "response_choices": "(A) independent of a, (B) directly proportional to a, (C) directly proportional to a^2, (D) inversely proportional to a", "answer": "A", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 37, "question": "For a = 0, the value of d (maximum value of \u03c1 as shown in the figure) is", "response_choices": "(A) 3Ze/(4\u03c0R^3), (B) 3Ze/(\u03c0R^3), (C) 4Ze/(3\u03c0R^3), (D) Ze/(3\u03c0R^3)", "answer": "B", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 38, "question": "The electric field within the nucleus is generally observed to be linearly dependent on r. This implies", "response_choices": "(A) a = 0, (B) a = R/2, (C) a = R, (D) a = 2R/3", "answer": "C", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 39, "question": "The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is", "response_choices": "(A) -kx, (B) -2kx, (C) -2kx/3, (D) 4kx/3", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 40, "question": "The centre of mass of the disk undergoes simple harmonic motion with angular frequency \u03c9 equal to", "response_choices": "(A) \u221a(k/M), (B) \u221a(2k/M), (C) \u221a(2k/3M), (D) \u221a(4k/3M)", "answer": "D", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 41, "question": "The maximum value of V0 for which the disk will roll without slipping is", "response_choices": "(A) \u03bcg\u221a(k/M), (B) \u03bcg\u221a(2k/M), (C) \u03bcg\u221a(3M/k), (D) \u03bcg\u221a(5M/2k)", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 42, "question": "Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4x4 matrix given in the ORS.", "response_choices": "A) Potential energy of a simple pendulum (y axis) as a function of displacement (x axis), B) Displacement (y axis) as a function of time (x axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x-direction, C) Range of a projectile (y axis) as a function of its velocity (x axis) when projected at a fixed angle, D) The square of the time period (y axis) of a simple pendulum as a function of its length (x axis)", "answer": "B, C, D", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 43, "question": "An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "A, B, C, D. Matrix response with options p, q, r, s", "answer": "p, q, r, s", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 44, "question": "Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "A) ... B) ... C) ... D) ...", "answer": "A: q, B: r and q, C: p and s, D: s", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 45, "question": "The correct stability order for the following species is", "response_choices": "(A) (II) > (IV) > (I) > (III), (B) (I) > (II) > (III) > (IV), (C) (II) > (I) > (IV) > (III), (D) (I) > (III) > (II) > (IV)", "answer": "D", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 46, "question": "Cellulose upon acetylation with excess acetic anhydride/H\u2082SO\u2084 (catalytic) gives cellulose triacetate whose structure is", "response_choices": "Options shown as molecular structure diagrams (A), (B), (C), and (D)", "answer": "A", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 47, "question": "In the following reaction sequence, the correct structures of E, F and G are", "response_choices": "(A) E = Ph* CH3, F = Ph* O Na, G = CH3; (B) E = Ph* CH3, F = Ph* ONa, G = CH3; (C) E = Ph* CH3, F = Ph* O Na, G = CH3; (D) E = Ph* CH3, F = Ph* ONa, G = CH3I", "answer": "C", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 48, "question": "Among the following, the coloured compound is", "response_choices": "(A) CuCl; (B) K3 [Cu(CN)4]; (C) CuF2; (D) [Cu(CH3CN)4]BF4", "answer": "C", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 49, "question": "Both [Ni(CO)4] and [Ni(CN)4]2- are diamagnetic. The hybridisations of nickel in these complexes, respectively, are", "response_choices": "(A) sp3, sp3; (B) sp3, dsp2; (C) dsp2, sp3; (D) dsp2, dsp2", "answer": "B", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 50, "question": "The IUPAC name of [Ni(NH3)4] [NiCl4] is", "response_choices": "(A) Tetrachloronickel (II) - tetraammineniickel (II), (B) Tetraammineniickel (II) - tetrachloronickel (II), (C) Tetraammineniickel (II) - tetrachloronickelate (II), (D) Tetrachloronickel (II) - tetraammineniickelate (I)", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 51, "question": "Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of H2 gas at the cathode is (1 Faraday = 96500 C mol^-1)", "response_choices": "(A) 9.65 \u00d7 10^4 sec, (B) 19.3 \u00d7 10^4 sec, (C) 28.95 \u00d7 10^4 sec, (D) 38.6 \u00d7 10^4 sec", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 52, "question": "Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is", "response_choices": "(A) CH3(CH2)15 N^+(CH3)3 Br^-, (B) CH3(CH2)11 OSO3^- Na^+, (C) CH3(CH2)9 COO^- Na^+, (D) CH3(CH2)11 N^+(CH3)3 Br^-", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 53, "question": "Solubility product constants (Ksp) of salts of types MX, MX2 and M3X at temperature 'T' are 4.0 x 10^-8, 3.2 x 10^-14 and 2.7 x 10^-16, respectively. Solubilities (mol dm^-3) of the salts at temperature 'T' are in the order", "response_choices": "(A) MX > MX2 > M3X, (B) M3X > MX2 > MX, (C) MX2 > M3X > MX, (D) MX > M3X > MX2", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 54, "question": "STATEMENT-1 : Aniline on reaction with NaNO2/HCl at 0 \u00b0C followed by coupling with \u03b2-napththol gives a dark blue coloured precipitate. and STATEMENT-2 : The colour of the compound formed in the reaction of aniline with NaNO2/HCl at 0 \u00b0C followed by coupling with \u03b2-napththol is due to the extended conjugation.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "D", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 55, "question": "STATEMENT-1 : [Fe(H2O)6NO]SO4 is paramagnetic. and STATEMENT-2 : The Fe in [Fe(H2O)6 NO]SO4 has three unpaired electrons.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 56, "question": "STATEMENT-1 : The geometrical isomers of the complex [M(NH3)4Cl2] are optically inactive. and STATEMENT-2 : Both geometrical isomers of the complex [M(NH3)4Cl2] possess axis of symmetry.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 57, "question": "STATEMENT-1 : There is a natural asymmetry between converting work to heat and converting heat to work. and STATEMENT-2 : No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "(A)", "page_number": 24, "image_available": "no", "question_subject": "physics"} +{"id": 58, "question": "Compound H is formed by the reaction of", "response_choices": "(A) Ph CH3 + PhMgBr, (B) Ph CH3 + PhCH2 MgBr, (C) Ph H + PhCH2MgBr, (D) Ph H + Ph MgBr", "answer": "(B)", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 59, "question": "The structure of compound I is", "response_choices": "(A) Ph CH3, (B) H3C Ph, (C) Ph CH3, (D) H3C CH3", "answer": "A", "page_number": 25, "image_available": "yes", "question_subject": "chemistry"} +{"id": 60, "question": "The structures of compounds J, K and L, respectively, are", "response_choices": "(A) PhCOCH3, PhCH2COCH3 and PhCH2COO-K+, (B) PhCHO, PhCH2CHO and PhCOO-K+, (C) PhCOCH3, PhCH2CHO and CH3COO-K+, (D) PhCHO, PhCOCH3 and PhCOO-K+", "answer": "D", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 61, "question": "The number of atoms in this HCP unit cell is", "response_choices": "(A) 4, (B) 6, (C) 12, (D) 17", "answer": "B", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 62, "question": "The volume of this HCP unit cell is", "response_choices": "(A) 24\u221a2 r^3, (B) 16\u221a2 r^3, (C) 12\u221a2 r^3, (D) (64)/(3\u221a3) r^3", "answer": "A", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 63, "question": "The empty space in this HCP unit cell is", "response_choices": "(A) 74%, (B) 47.6%, (C) 32%, (D) 26%", "answer": "D", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 64, "question": "Match the compounds in Column I with their characteristic test(s)/reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "A, B, C, D - Matrix Response", "answer": "B: C, D; C: A, B, C; D: A, B, D OR A: B, C; B: A, B; C: A, B, C; D: A", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"} +{"id": 65, "question": "Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS", "response_choices": "(A) PbS -> PbO, (B) CaCO3 -> CaO, (C) ZnS -> Zn, (D) Cu2S -> Cu, (p) roasting, (q) calcination, (r) carbon reduction, (s) self reduction", "answer": "A:p, B:q, C:r,s, D:s", "page_number": 28, "image_available": "yes", "question_subject": "chemistry"} +{"id": 66, "question": "Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS", "response_choices": "(A) Orbital angular momentum of the electron in a hydrogen-like atomic orbital, (B) A hydrogen-like one-electron wave function obeying Pauli principle, (C) Shape, size and orientation of hydrogen-like atomic orbitals, (D) Probability density of electron at the nucleus in hydrogen-like atom, (p) Principal quantum number, (q) Azimuthal quantum number, (r) Magnetic quantum number, (s) Electron spin quantum number", "answer": "A:q,r, B:p,q,r,s, C:p,q,r, D:p,s", "page_number": 28, "image_available": "yes", "question_subject": "physics"} diff --git a/JEE_papers/JSON/JEE_2009_1.jsonl b/JEE_papers/JSON/JEE_2009_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..f37db39b4a174cb48bdb38a7fdc4588916a99d25 --- /dev/null +++ b/JEE_papers/JSON/JEE_2009_1.jsonl @@ -0,0 +1,59 @@ +{"id": 1, "question": "Given that the abundances of isotopes 54Fe, 56Fe and 57Fe are 5%, 90% and 5%, respectively, the atomic mass of Fe is", "response_choices": "(A) 55.85 (B) 55.95 (C) 55.75 (D) 56.05", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The term that corrects for the attractive forces present in a real gas in the van der Waals equation is", "response_choices": "(A) nb (B) an^2/V^2 (C) an^2/V (D) - nb", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Among the electrolytes Na2SO4, CaCl2, Al2(SO4)3 and NH4Cl, the most effective coagulating agent for Sb2S3 sol is", "response_choices": "(A) Na2SO4 (B) CaCl2 (C) Al2(SO4)3 (D) NH4Cl", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "The Henry's law constant for the solubility of N2 gas in water at 298 K is 1.0 x 10^4 atm. The mole fraction of N2 in air is 0.8. The number of moles of N2 from air dissolved in 10 moles of water at 298 K and 5 atm pressure is", "response_choices": "(A) 4.0 x 10^4 (B) 4.0 x 10^5 (C) 5.0 x 10^4 (D) 4.0 x 10^6", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "The reaction of P4 with X leads selectively to P4O6. The X is", "response_choices": "(A) Dry O2 (B) A mixture of O2 and N2 (C) Moist O2 (D) O2 in the presence of aqueous NaOH", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "The correct acidity order of the following is", "response_choices": "(A) (III) > (IV) > (II) > (I) (B) (IV) > (III) > (I) > (II) (C) (III) > (II) > (IV) > (I) (D) (II) > (III) > (IV) > (I)", "answer": "A", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest is", "response_choices": "(A) Nylon (B) Poly(vinyl chloride) (C) Cellulose (D) Natural Rubber", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "The IUPAC name of the following compound is", "response_choices": "(A) 4-Bromo-3-cyanophenol (B) 2-Bromo-5-hydroxybenzonitrile (C) 2-Cyano-4-hydroxybromobenzene (D) 6-Bromo-3-hydroxybenzonitrile", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "The correct statement(s) regarding defects in solids is(are)", "response_choices": "(A) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion (B) Frenkel defect is a dislocation defect (C) Trapping of an electron in the lattice leads to the formation of F-center (D) Schottky defects have no effect on the physical properties of solids", "answer": "B C", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "The compound(s) that exhibit(s) geometrical isomerism is(are)", "response_choices": "(A) [Pt(en)Cl2] (B) [Pt(en)2]Cl2 (C) [Pt(en)2Cl2]Cl2 (D) [Pt(NH3)2Cl2]", "answer": "C D", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "The compound(s) formed upon combustion of sodium metal in excess air is(are)", "response_choices": "(A) Na2O2 (B) Na2O (C) NaO2 (D) NaOH", "answer": "A OR B D", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "The correct statement(s) about the compound H3C(HO)HC-CH-CH-CH(OH)CH3 (X) is(are)", "response_choices": "(A) The total number of stereoisomers possible for X is 6 (B) The total number of diastereomers possible for X is 3 (C) If the stereochemistry about the double bond in X is trans, the number of enantiomers possible for X is 4 (D) If the stereochemistry about the double bond in X is cis, the number of enantiomers possible for X is 2", "answer": "A D", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "The compound X is", "response_choices": "(A) Na3NO3 (B) NaCl (C) Na2SO4 (D) Na2S", "answer": "D", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "The compound Y is", "response_choices": "(A) MgCl2 (B) FeCl2 (C) FeCl3 (D) ZnCl2", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "The compound Z is", "response_choices": "(A) Mg2[Fe(CN)6] (B) Fe[Fe(CN)6] (C) Fe3[Fe(CN)6]4 (D) K2Zn3[Fe(CN)6]4", "answer": "B", "page_number": 4, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "The structure of the carbonyl compound P is", "response_choices": "(A) (image A) (B) (image B) (C) (image C) (D) (image D)", "answer": "B", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "The structures of the products Q and R, respectively, are", "response_choices": "(A) (image A) (B) (image B) (C) (image C) (D) (image D)", "answer": "A", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"} +{"id": 18, "question": "The structure of the product S is", "response_choices": "(A) (B) (C) (D)", "answer": "B", "page_number": 5, "image_available": "yes", "question_subject": "chemistry"} +{"id": 19, "question": "Match each of the diatomic molecules in Column I with its property/properties in Column II.", "response_choices": "Column I: (A) B\u2082 (B) N\u2082 (C) O\u2082\u207b (D) O\u2082 Column II: (p) Paramagnetic (q) Undergoes oxidation (r) Undergoes reduction (s) Bond order > 2 (t) Mixing of 's' and 'p' orbitals", "answer": "p q r s t, p q r s t, p q r s t, p q r s t", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "Match each of the compounds in Column I with its characteristic reaction(s) in Column II.", "response_choices": "A) CH\u2083CH\u2082CH\u2082CN, (B) CH\u2083CH\u2082OCOCH\u2083, (C) CH\u2083 \u2013 CH = CH \u2013 CH\u2082OH, (D) CH\u2083CH\u2082CH\u2082CH\u2082NH\u2082", "answer": "A) p, q, r, s, t, B) p, q, r, s, t, C) p, q, r, s, t, D) p, q, r, s, t", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 21, "question": "Let P(3, 2, 6) be a point in space and Q be a point on the line r = (j - j + 2k) + \u03bc(-3i + j + 5k). Then the value of \u03bc for which the vector PQ is parallel to the plane x - 4y + 3z = 1 is", "response_choices": "(A) 1/4, (B) -1/4, (C) 1/8, (D) -1/8", "answer": "A", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 22, "question": "Tangents drawn from the point P(1, 8) to the circle x\u00b2 + y\u00b2 - 6x - 4y - 11 = 0 touch the circle at the points A and B. The equation of the circumcircle of the triangle PAB is", "response_choices": "(A) x\u00b2 + y\u00b2 + 4x - 6y + 19 = 0, (B) x\u00b2 + y\u00b2 - 4x - 10y +19 = 0, (C) x\u00b2 + y\u00b2 - 2x + 6y - 29 = 0, (D) x\u00b2 + y\u00b2 - 6x - 4y +19 = 0", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 23, "question": "Let f be a non-negative function defined on the interval [0, 1]. If \u222b[0, 1] (f(t))^2 dt = \u222b[0, 1] f(t) dt, 0 \u2264 x \u2264 1, and f(0) = 0, then", "response_choices": "(A) f(1/2) < 1/2 and f(1/3) > 1/3, (B) f(1/2) > 1/2 and f(1/3) < 1/3, (C) f(1/2) < 1/2 and f(1/3) < 1/3, (D) f(1/2) > 1/2 and f(1/3) > 1/3", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 24, "question": "Let z = x + iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the equation z^2 + z^3 = 350 is", "response_choices": "(A) 48, (B) 32, (C) 40, (D) 80", "answer": "A", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 25, "question": "The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x^2 + 9y^2 = 9 meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin O is", "response_choices": "(A) 31/10, (B) 29/10, (C) 21/10, (D) 27/10", "answer": "D", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 26, "question": "If a, b, c and d are unit vectors such that |a \u00d7 b| |c \u00d7 d| = 1 and a.c = 1/2, then", "response_choices": "(A) a, b, c are non-coplanar, (B) b, c, d are non-coplanar, (C) b, d are non-parallel, (D) a, d are parallel and b, c are parallel", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 27, "question": "Let z = cos \u03b8 + i sin \u03b8. Then the value of \u03a3[n=1 to 18] Im(z^2n+1) at \u03b8 = 2\u00b0 is", "response_choices": "(A) 1/sin 2\u00b0, (B) 1/3 sin 2\u00b0, (C) 1/2 sin 2\u00b0, (D) 1/4 sin 2\u00b0", "answer": "D", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 28, "question": "The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is", "response_choices": "(A) 55 (B) 66 (C) 77 (D) 88", "answer": "C", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 29, "question": "Area of the region bounded by the curve y = e^x and lines x = 0 and y = e is", "response_choices": "(A) e - 1 (B) \\int_{1}^{e} (e + 1 - y) dy (C) e - \\int_{e}^{1} e^x dx (D) \\int_{1}^{e} \\ln y dy", "answer": "B C D", "page_number": 8, "image_available": "yes", "question_subject": "mathematics"} +{"id": 30, "question": "Let L = \\lim_{x \\to 0} \\frac{a - \\sqrt{a^2 - x^2} - \\frac{x^2}{4}}{x^4}, a > 0. If L is finite, then", "response_choices": "(A) a = 2 (B) a = 1 (C) L = \\frac{1}{64} (D) L = \\frac{1}{32}", "answer": "A C", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 31, "question": "In a triangle ABC with fixed base BC, the vertex A moves such that cos B + cos C = 4 sin^2 \\frac{A}{2}. If a, b and c denote the lengths of the sides of the triangle opposite to the angles A, B and C, respectively, then", "response_choices": "(A) b + c = 4a (B) b + c = 2a (C) locus of point A is an ellipse (D) locus of point A is a pair of straight lines", "answer": "B C", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 32, "question": "If (sin^4 x)/2 + (cos^4 x)/3 = 1/5, then", "response_choices": "(A) tan^2 x = 2/3, (B) (sin^8 x)/(8) + (cos^8 x)/(27) = 1/125, (C) tan^2 x = 1/3, (D) (sin^8 x)/(8) + (cos^8 x)/(27) = 2/125", "answer": "A, B", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 33, "question": "Let M be the set of all 3\u00d73 symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0. The number of matrices in M is", "response_choices": "(A) 12, (B) 6, (C) 9, (D) 3", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 34, "question": "The number of matrices A in M for which the system of linear equations [x 1 A] [y 0 z 0] has a unique solution, is", "response_choices": "(A) less than 4, (B) at least 4 but less than 7, (C) at least 7 but less than 10, (D) at least 10", "answer": "C", "page_number": 9, "image_available": "yes", "question_subject": "mathematics"} +{"id": 35, "question": "The number of matrices A in M for which the system of linear equations [x 1 A] [y 0 z 0] is inconsistent, is", "response_choices": "(A) 0, (B) more than 2, (C) 2, (D) 1", "answer": "B", "page_number": 9, "image_available": "yes", "question_subject": "mathematics"} +{"id": 36, "question": "The probability that X \u22653 equals", "response_choices": "(A) 25/216 (B) 25/36 (C) 5/36 (D) 125/216", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 37, "question": "The probability that X \u22653 equals", "response_choices": "(A) 125/216 (B) 25/36 (C) 5/36 (D) 25/216", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "The conditional probability that X \u22656 given X \u22653 equals", "response_choices": "(A) 125/216 (B) 25/216 (C) 5/36 (D) 25/36", "answer": "D", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 41, "question": "Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1, Q2, Q3, respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q1 : Q2 : Q3, is", "response_choices": "A) 1 : 2 : 3 , (B) 1 : 3 : 5 , (C) 1 : 4 : 9 , (D) 1 : 8 : 18", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 42, "question": "A block of base 10 cm \u00d7 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is \u221a3. The inclination \u03b8 of this inclined plane from the horizontal plane is gradually increased from 0\u00b0. Then", "response_choices": "(A) at \u03b8 = 30\u00b0, the block will start sliding down the plane (B) the block will remain at rest on the plane up to certain \u03b8 and then it will topple (C) at \u03b8 = 60\u00b0, the block will start sliding down the plane and continue to do so at higher angles (D) at \u03b8 = 60\u00b0, the block will start sliding down the plane and on further increasing \u03b8, it will topple at certain \u03b8", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 43, "question": "A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as", "response_choices": "(A) 9 m/s , (B) 12 m/s , (C) 16 m/s , (D) 21.33 m/s", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 44, "question": "Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is m. The mass of the ink used to draw the outer circle is 5m. The coordinates of the centres of the different parts are: outer circle (0, 0), left inner circle (-a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, -a). The y-coordinate of the centre of mass of the ink in this drawing is", "response_choices": "(A) a/10 , (B) a/8 , (C) a/12 , (D) a/3", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 45, "question": "Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other than that at A, these two particles will again reach the point A?", "response_choices": "(A) 4, (B) 3, (C) 2, (D) 1", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 46, "question": "The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. If and Ia are the currents in the segments ab and cd. Then,", "response_choices": "(A) I1 > I2, (B) I1 < I2, (C) Ia is in the direction ba and Ic is in the direction cd, (D) I1 is in the direction ab and I2 is in the direction dc", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 47, "question": "A disk of radius a/4 having a uniformly distributed charge 6 C is placed in the x-y plane with its centre at (-a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8 C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges \u20137 C and 3 C are placed at (a/4, -a/4, 0) and (-5a/4, 3a/4, 0), respectively. Consider a cubical surface formed by six surfaces x = +a/2, y = +a/2, z = +a/2. The electric flux through this cubical surface is", "response_choices": "(A) -2 C/\u03b50, (B) 2 C/\u03b50, (C) 10 C/\u03b50, (D) 12 C/\u03b50", "answer": "A", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 48, "question": "The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4/3 s is", "response_choices": "(A) \u221a3 \u03c02 cm/s2 / 32, (B) \u2013 \u03c02 cm/s2 / 32, (C) \u03c02 cm/s2 / 32, (D) \u221a5 \u03c02 cm/s2 / 32", "answer": "D", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 49, "question": "If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one can surely say that", "response_choices": "(A) linear momentum of the system does not change in time, (B) kinetic energy of the system does not change in time, (C) angular momentum of the system does not change in time, (D) potential energy of the system does not change in time", "answer": "A", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 50, "question": "A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are: (42, 56), (48, 48), (60, 40), (66, 33), (73, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)", "response_choices": "(A) (42, 56), (B) (48, 48), (C) (66, 33), (D) (73, 39)", "answer": "CD", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 51, "question": "For the circuit shown in the figure", "response_choices": "(A) the current I through the battery is 7.5 mA, (B) the potential difference across R1 is 18 V, (C) ratio of powers dissipated in R1 and R2 is 3, (D) if R1 and R2 are interchanged, magnitude of the power dissipated in R2 will decrease by a factor of 9", "answer": "D", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 52, "question": "Cv and Cp denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then", "response_choices": "(A) Cp - Cv is larger for a diatomic ideal gas than for a monatomic ideal gas, (B) Cp + Cv is larger for a diatomic ideal gas than for a monatomic ideal gas, (C) Cp/Cv is larger for a diatomic ideal gas than for a monatomic ideal gas, (D) Cp \u00b7 Cv is larger for a diatomic ideal gas than for a monatomic ideal gas", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 53, "question": "In the core of nuclear fusion reactor, the gas becomes plasma because of", "response_choices": "(A) strong nuclear force acting between the deuterons (B) Coulomb force acting between the deuterons (C) Coulomb force acting between deuteron-electron pairs (D) the high temperature maintained inside the reactor core", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 54, "question": "Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with kinetic energy 1.5 eT, when the separation between them is large enough to neglect Coulomb potential energy. Also neglect any interaction from other particles in the core. The minimum temperature T required for them to reach a separation of 4 \u00d7 10^(-14) m is in the range", "response_choices": "(A) 1.0\u00d710^9 K \u2264 T < 2.0\u00d710^9 K (B) 2.0\u00d710^9 K \u2264 T < 3.0\u00d710^9 K (C) 3.0\u00d710^9 K \u2264 T < 4.0\u00d710^9 K (D) 4.0\u00d710^9 K \u2264 T < 5.0\u00d710^9 K", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 55, "question": "Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of these is most promising based on Lawson criterion?", "response_choices": "(A) deuteron density = 2.0\u00d710^(14) cm^(-3), confinement time = 5.0\u00d710^(-8) s (B) deuteron density = 8.0\u00d710^(14) cm^(-3), confinement time = 9.0\u00d710^(-8) s (C) deuteron density = 4.0\u00d710^(13) cm^(-3), confinement time = 1.0\u00d710^(-11) s (D) deuteron density = 1.0\u00d710^(21) cm^(-3), confinement time = 4.0\u00d710^(-12) s", "answer": "B", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 56, "question": "The allowed energy for the particle for a particular value of n is proportional to", "response_choices": "(A) n^4 (B) n^(1/2) (C) n^(-1) (D) n^2", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "If the mass of the particle is m = 1.0 x 10^-30 kg and a = 6.6 nm, the energy of the particle in its ground state is closest to", "response_choices": "(A) 0.8 meV, (B) 8 meV, (C) 80 meV, (D) 800 meV", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 58, "question": "The speed of the particle, that can take discrete values, is proportional to", "response_choices": "(A) n^-1/2, (B) n^-1, (C) n^1/2, (D) n", "answer": "D", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 59, "question": "Matrix - Match Type", "response_choices": "", "answer": "p-q, r-s, t", "page_number": 17, "image_available": "yes", "question_subject": "mathematics"} +{"id": 59, "question": "Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case, a point M and a line PQ passing through M are shown. Let E be the electric field and V be the electric potential at M (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line PQ. Let B be the magnetic field at M and \u03bc be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.", "response_choices": "Column I: (A) E = 0, (B) V \u2260 0, (C) B = 0, (D) \u03bc \u2260 0", "answer": "p q r s t", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 60, "question": "Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column I gives some statements about X and/or Y. Match these statements to the appropriate system(s) from Column II.", "response_choices": "A) The force exerted by X on Y has a magnitude Mg.\nB) The gravitational potential energy of X is continuously increasing.\nC) Mechanical energy of the system X + Y is continuously decreasing.\nD) The torque of the weight of Y about point P is zero.", "answer": "p\nq\nr\ns\nt", "page_number": 19, "image_available": "yes", "question_subject": "physics"} diff --git a/JEE_papers/JSON/JEE_2009_2.jsonl b/JEE_papers/JSON/JEE_2009_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..049defb98e794127eabe9129dd170f3b117e0bf2 --- /dev/null +++ b/JEE_papers/JSON/JEE_2009_2.jsonl @@ -0,0 +1,51 @@ +{"id": 1, "question": "For a first order reaction A\u2192P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = -(2000)/T + 6.0. The pre-exponential factor A and the activation energy Ea, respectively, are", "response_choices": "(A) 1.0 \u00d7 10\u2076 s\u207b\u00b9 and 9.2 kJ mol\u207b\u00b9 (B) 6.0 s\u207b\u00b9 and 16.6 kJ mol\u207b\u00b9 (C) 1.0 \u00d7 10\u2076 s\u207b\u00b9 and 16.6 kJ mol\u207b\u00b9 (D) 1.0 \u00d7 10\u2076 s\u207b\u00b9 and 38.3 kJ mol\u207b\u00b9", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)\u2086 is", "response_choices": "(A) 0 (B) 2.84 (C) 4.90 (D) 5.92", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "In the following carbocation, H\u2083CH\u2083 that is most likely to migrate to the positively charged carbon is", "response_choices": "(A) CH\u2083 at C-4 (B) H at C-4 (C) CH\u2083 at C-2 (D) H at C-2", "answer": "D", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The correct stability order of the following resonance structures is", "response_choices": "(A) (I) > (II) > (IV) > (III) (B) (I) > (III) > (II) > (IV) (C) (II) > (I) > (III) > (IV) (D) (III) > (I) > (IV) > (II)", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "For the reduction of NO3- ion in an aqueous solution, E0 is +0.96 V. Values of E0 for some metal ions are given below \n\nV2+(aq) + 2e- \u2192 V \t\t\t\t\t\tE0 = -1.19 V\nFe3+(aq) + 3e- \u2192 Fe \t\t\t\t\t\tE0 = -0.04 V\nAu3+(aq) + 3e- \u2192 Au \t\t\t\t\t\tE0 = +1.40 V\nHg2+(aq) + 2e- \u2192 Hg \t\t\t\t\t\tE0 = +0.86 V\n\nThe pair(s) of metals that is(are) oxidized by NO3- in aqueous solution is(are)", "response_choices": "(A) V and Hg\t\t\t\t\t\t(B) Hg and Fe\n(C) Fe and Au\t\t\t\t\t\t(D) Fe and V", "answer": "AC", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "Among the following, the state function(s) is(are)", "response_choices": "(A) Internal energy\t\t\t\t\t\t(B) Irreversible expansion work\n(C) Reversible expansion work\t\t\t\t(D) Molar enthalpy", "answer": "AD", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "In the reaction\n\n2X + B2H6 \u2192 [BH2(X)2]2+ [BH4]-\n\nthe amine(s) X is(are)", "response_choices": "(A) NH3\t\t\t\t\t\t\t(B) CH3NH2\n(C) (CH3)2NH\t\t\t\t\t\t(D) (CH3)3N", "answer": "ABC", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)", "response_choices": "(A) N2O\t\t\t\t\t\t\t(B) N2O4\n(C) N2O3\t\t\t\t\t\t\t(D) N2O5", "answer": "BC", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The correct statement(s) about the following sugars X and Y is(are)", "response_choices": "(A) X is a reducing sugar and Y is a non-reducing sugar\n(B) X is a non-reducing sugar and Y is a reducing sugar\n(C) The glucosidic linkages in X and Y are \u03b1 and \u03b2, respectively\n(D) The glucosidic linkages in X and Y are \u03b2 and \u03b1, respectively", "answer": "C", "page_number": 3, "image_available": "yes", "question_subject": "chemistry"} +{"id": 10, "question": "Match each of the reactions given in Column I with the corresponding product(s) given in Column II", "response_choices": "Column I: (A) Cu + dil HNO3, (B) Cu + conc HNO3, (C) Zn + dil HNO3, (D) Zn + conc HNO3\nColumn II: (p) NO, (q) NO2, (r) N2O, (s) Cu(NO3)2, (t) Zn(NO3)2", "answer": "p:q:r:s:t", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "4", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "The dissociation constant of a substituted benzoic acid at 25\u00b0C is 1.0 \u00d7 10\u207b\u2074. The pH of a 0.01 M solution of its sodium salt is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "8", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "The total number of \u03b1 and \u03b2 particles emitted in the nuclear reaction \u00b2\u00b3\u00b2U \u2192 \u00b2\u00b9\u2074Pb is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "8", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "The oxidation number of Mn in the product of alkaline oxidative fusion of MnO\u2082 is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "6", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The number of water molecule(s) directly bonded to the metal centre in CuSO\u2084\u00b75H\u2082O is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "5", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "The coordination number of Al in the crystalline state of AlCl\u2083 is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "6", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 19, "question": "The total number of cyclic structural as well as stereo isomers possible for a compound with the molecular formula C\u2085H\u2081\u2080 is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "7", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "If the sum of first n terms of an A.P. is cn\u00b2, then the sum of squares of these n terms is", "response_choices": "(A) n(4n\u00b2 - 1)c\u00b2 / 6, (B) n(4n\u00b2 + 1)c\u00b2 / 3, (C) n(4n\u00b2 - 1)c\u00b2 / 3, (D) n(4n\u00b2 + 1)c\u00b2 / 6", "answer": "C", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 21, "question": "A line with positive direction cosines passes through the point P(2, -1,2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals", "response_choices": "(A) 1 (B) \u221a2 (C) \u221a3 (D) 2", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 22, "question": "The normal at a point P on the ellipse x^2 + 4y^2 = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points", "response_choices": "(A) (-3\u221a5/2 , 2/7) (B) (3\u221a5/2 , \u221a19/4) (C) (-2\u221a3, -1/7) (D) (+2\u221a3, + 4\u221a3/7)", "answer": "C", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 23, "question": "The locus of the orthocentre of the triangle formed by the lines (1 + p)x - py + p(1 + p) = 0, (1 + q)x - qy + q(1 + q) = 0, and y = 0, where p \u2260 q, is", "response_choices": "(A) a hyperbola (B) a parabola (C) an ellipse (D) a straight line", "answer": "D", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 24, "question": "If In = \u222b (sin nx / (1 + x^8))sin x dx, n = 0, 1, 2, ..., then", "response_choices": "(A) In = In-2 (B) \u2211I2n+1 = 10\u03c0 (C) \u2211In = 0 (D) In = In+1", "answer": "A,B,C", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 25, "question": "An ellipse intersects the hyperbola 2x^2 - 2y^2 - 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then", "response_choices": "(A) Equation of ellipse is x^2 + 2y^2 = 2 (B) The foci of ellipse are (\u00b11, 0) (C) Equation of ellipse is x^2 - 2y^2 = 4 (D) The foci of ellipse are (\u00b1\u221a2, 0)", "answer": "A, B", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 26, "question": "For the function f(x) = x cos ^1/x, x \u2265 1,", "response_choices": "(A) for at least one x in the interval [1, \u221e), f(x + 2) - f(x) < 2 (B) lim f'(x) = 1 x\u2192\u221e (C) for all x in the interval [1, \u221e), f(x + 2) - f(x) > 2 (D) f'(x) is strictly decreasing in the interval [1, \u221e)", "answer": "B, C, D", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 27, "question": "The tangent PT and the normal PN to the parabola y^2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose", "response_choices": "(A) vertex is (2a/3, 0) (B) directrix is x = 0 (C) latus rectum is 2a/3 (D) focus is (a, 0)", "answer": "A, D", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 28, "question": "For 0 < \u03b8 < \u03c0/2 , the solution(s) of \u03a3cosec\u2061(\u03b8 + (m - 1)\u03c0/4)cosec\u2061(\u03b8 + m\u03c0/4) = 4\u221a2 m = 1 5 is(are)", "response_choices": "(A) \u03c0/4 (B) \u03c0/6 (C) \u03c0/12 (D) 5\u03c0/12", "answer": "C, D", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 29, "question": "Match the statements/expressions given in Column I with the values given in Column II.", "response_choices": "A: p, B: q, C: r, D: s, AND t", "answer": "A: p, q, r, s, t; B: p, q, r, s, t; C: p, q, r, s, t; D: p, q, r, s, t", "page_number": 8, "image_available": "yes", "question_subject": "mathematics"} +{"id": 30, "question": "Match the statements/expressions given in Column I with the values given in Column II.", "response_choices": "A) The number of solutions of the equation x^(5/3) - cos x = 0 in the interval (0, \u03c0/2); B) Value(s) of k for which the planes kx + 4y + z = 0, 4x + ky + 2z = 0 and 2x + 2y + z = 0 intersect in a straight line; C) Value(s) of k for which |x - 1| + |x - 2| + |x + 1| + |x + 2| = 4k has integer solution(s); D) If y' = y + 1 and y(0) = 1, then value(s) of y(ln 2)", "answer": "p: 1, q: 2, r: 3, s: 4, t: 5", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 31, "question": "The maximum value of the function f(x) = 2x^3 - 15x^2 + 36x - 48 on the set A = {x | x^2 + 20 \u2264 9x} is", "response_choices": "", "answer": "7", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 32, "question": "Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations: 3x - y - z = 0, -3x + z = 0, -3x + 2y + z = 0. Then the number of such points for which x^2 + y^2 + z^2 \u2264 100 is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "7", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 33, "question": "Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2\u221a2 and angle B = 30\u00b0. The absolute value of the difference between the areas of these triangles is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "4", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 34, "question": "Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and lim [1 + p(x)/x^2] = 2. Then the value of p(2) is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "6", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 35, "question": "Let f: R \u2192 R be a continuous function which satisfies f(x) = \u222b[f(t)/t]dt. Then the value of f(ln 5) is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "4", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 36, "question": "The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "8", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 37, "question": "The smallest value of k, for which both the roots of the equation x^2 - 5kx + 16 (k^2 - k + 1) = 0 are real, distinct and have values at least 4, is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "2", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "If the function f(x) = x^4 + e^2 and g(x) = f'^-1(x), then the value of g'(1) is", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "2", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is", "response_choices": "(A) k1A/k2, (B) k2A/k1, (C) k1A/k1 + k2, (D) k2A/k1 + k2", "answer": "D", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 40, "question": "A piece of wire is bent in the shape of a parabola y = kx^2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is", "response_choices": "(A) a/gk, (B) a/2gk, (C) 2a/gk, (D) a/4gk", "answer": "B", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 41, "question": "Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions ξp = 2.0 eV, ξq = 2.5 eV and ξr = 3.0 eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is", "response_choices": "(A), (B), (C), (D) [Graph options]", "answer": "A", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 42, "question": "A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle \u03b8 in one direction and released. The frequency of oscillation is", "response_choices": "1 \u2044 \u221a(2k \u2044 M), 1 \u2044 \u221a(k \u2044 M), 1 \u2044 \u221a(6k \u2044 M), 1 \u2044 \u221a(24k \u2044 M)", "answer": "C", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 43, "question": "Two metallic rings A and B, identical in shape and size but having different resistivities \u03c1A and \u03c1B, are kept on top of two identical solenoids as shown in the figure. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights hA and hB, respectively, with hA > hB. The possible relation(s) between their resistivities and their masses mA and mB is(are)", "response_choices": "\u03c1A > \u03c1B and mA = mB, \u03c1A < \u03c1B and mA = mB, \u03c1A > \u03c1B and mA > mB, \u03c1A < \u03c1B and mA < mB", "answer": "BC", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 44, "question": "A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,", "response_choices": "the intensity of the sound heard at the first resonance was more than that at the second resonance, the prongs of the tuning fork were kept in a horizontal plane above the resonance tube, the amplitude of vibration of the ends of the prongs is typically around 1 cm, the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air", "answer": "AD", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 45, "question": "The figure shows the P-V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then,", "response_choices": "(A) the process during the path A \u2192 B is isothermal\n(B) heat flows out of the gas during the path B \u2192 C \u2192 D\n(C) work done during the path A \u2192 B \u2192 C is zero\n(D) positive work is done by the gas in the cycle ABCDA", "answer": "BD", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 46, "question": "Under the influence of the Coulomb field of charge +Q, a charge \u2013q is moving around it in an elliptical orbit. Find out the correct statement(s).", "response_choices": "(A) The angular momentum of the charge \u2013q is constant\n(B) The linear momentum of the charge \u2013q is constant\n(C) The angular velocity of the charge \u2013q is constant\n(D) The linear speed of the charge \u2013q is constant", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 47, "question": "A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,", "response_choices": "(A) \u20d7VC - \u20d7VA = 2(\u20d7VB - \u20d7VC)\t(B) \u20d7VC - \u20d7VB = \u20d7VB - \u20d7VA\n(C) |\u20d7VC - \u20d7VA| = 2|\u20d7VB - \u20d7VC|\t(D) |\u20d7VC - \u20d7VA| = 4|\u20d7VB|", "answer": "BC", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 48, "question": "Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II", "response_choices": "A. The energy of the system is increased\nB. Mechanical energy is provided to the system, which is converted into energy of random motion of its parts\nC. Internal energy of the system is converted into its mechanical energy\nD. Mass of the system is decreased", "answer": "A: p q r s t\nB: p q r s l\nC: p q r s l\nD: p q r s l", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 49, "question": "Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits S1 and S2. In each of these cases S1P1 - S2P1 = \u03bb/4 and S1P2 - S2P2 = \u03bb/3, where \u03bb is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index \u03bc and thickness t is pasted on slit S2. The thicknesses of the sheets are different in different cases. The phase difference between the light waves reaching a point P on the screen from the two slits is denoted by \u03b4(P) and the intensity by I(P). Match each situation given in Column I with the statement(s) in Column II valid for that situation.", "response_choices": "p) \u03b4(P1) = 0, q) \u03b4(P2) = 0, r) I(P1) = 0, s) I(P1) > I(P2), t) I(P2) > I(P1)", "answer": "A: p,q,r,s,t\nB: p,q,r,s,t\nC: p,q,r,s,f\nD: p,q,f,s,t", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 54, "question": "A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k(\u03bc\u2080I / 48\u03c0x), find the value of k.", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "7", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 55, "question": "A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s\u00b2, find the work done (in Joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "8", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 56, "question": "A solid sphere of radius R has a charge Q distributed in its volume with a charge density \u03c1 = kr\u2074, where k and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 3 times that at r = R, find the value of a.", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "2", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 57, "question": "A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.", "response_choices": "0, 1, 2, 3, 4, 5, 6, 7, 8, 9", "answer": "5", "page_number": 17, "image_available": "no", "question_subject": "physics"} diff --git a/JEE_papers/JSON/JEE_2010_1.jsonl b/JEE_papers/JSON/JEE_2010_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..b132437f1e5d264071c9b7de57fd2239ccf661d1 --- /dev/null +++ b/JEE_papers/JSON/JEE_2010_1.jsonl @@ -0,0 +1,84 @@ +{"id": 1, "question": "The correct structure of ethylenediaminetetraacetic acid (EDTA) is", "response_choices": "A) HOOC-CH2 | N-CH=CH-N | CH2-COOH, B) HOOC | N-CH2-CH2-N | COOH, C) HOOC-CH2 | N-CH2-CH2-N | CH2-COOH, D) HOOC-CH2 | CH2 | N-CH-CH-N | CH2-COOH", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"} +{"id": 2, "question": "The ionization isomer of [Cr(H2O)4Cl(NO2)]Cl is", "response_choices": "A) [Cr(H2O)4(O2N)]Cl2, B) [Cr(H2O)4Cl2](NO2), C) [Cr(H2O)4Cl(ONO)]Cl, D) [Cr(H2O)4Cl2(NO2)]\u00b7H2O", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are", "response_choices": "A) BrCH2CH2CH2CH2CH3 and CH3CH2C\u2261CH, B) BrCH2CH2CH3 and CH3CH2CH2C\u2261CH, C) BrCH2CH2CH2CH2CH3 and CH3C\u2261CH, D) BrCH2CH2CH2CH3 and CH3CH2C\u2261CH", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "The correct statement about the following disaccharide is", "response_choices": "A) Ring (a) is pyranose with \u03b1-glycosidic link\nB) Ring (a) is furanose with \u03b1-glycosidic link\nC) Ring (b) is furanose with \u03b1-glycosidic link\nD) Ring (b) is pyranose with \u03b2-glycosidic link", "answer": "A", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "In the reaction the products are", "response_choices": "A) Br-OCH3 and H2\nB) Br and CH3Br\nC) Br and CH3OH\nD) OH and CH3Br", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is", "response_choices": "A) K, B) k, C) k, D) k", "answer": "A", "page_number": 3, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The species which by definition has ZERO standard molar enthalpy of formation at 298 K is", "response_choices": "A) Br2 (g), B) Cl2 (g), C) H2O (g), D) CH4 (g)", "answer": "B", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "The bond energy (in kcal mol^-1) of a C-C single bond is approximately", "response_choices": "A) 1, B) 10, C) 100, D) 1000", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The reagent(s) used for softening the temporary hardness of water is(are)", "response_choices": "A) Ca3(PO4)2 B) Ca(OH)2 C) Na2CO3 D) NaOCl", "answer": "B", "page_number": 4, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "In the reaction the intermediate(s) is(are)", "response_choices": "A) B) C) D)", "answer": "A and C", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"} +{"id": 11, "question": "In the Newman projection for 2,2-dimethylbutane X and Y can respectively be", "response_choices": "A) H and H B) H and C2H5 C) C2H5 and H D) CH3 and CH3", "answer": "B and D", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"} +{"id": 12, "question": "Among the following, the intensive property is (properties are)", "response_choices": "A) molar conductivity B) electromotive force C) resistance D) heat capacity", "answer": "A and B", "page_number": 4, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "Aqueous solutions of HNO3, KOH, CH3COOH, and CH3COONa of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)", "response_choices": "A) HNO3 and CH3COOH, B) KOH and CH3COONa, C) HNO3 and CH3COONa, D) CH3COOH and CH3COONa", "answer": "C and D", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "Partial roasting of chalcopyrite produces", "response_choices": "A) Cu2S and FeO, B) Cu2O and FeO, C) CuS and Fe2O3, D) Cu2O and Fe2O3", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "Iron is removed from chalcopyrite as", "response_choices": "A) FeO, B) FeS, C) Fe2O3, D) FeSiO3", "answer": "D", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "In self-reduction, the reducing species is", "response_choices": "A) S, B) O\u00b2\u207b, C) S\u00b2\u207b, D) SO\u2082", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "For the above cell", "response_choices": "A) Ecell < 0; \u0394G > 0, B) Ecell > 0; \u0394G < 0, C) Ecell < 0; \u0394G\u00b2 > 0, D) Ecell > 0; \u0394G\u00b2 < 0", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "If the 0.05 molar solution of M+ is replaced by a 0.0025 molar M+ solution, then the magnitude of the cell potential would be", "response_choices": "A) 35 mV, B) 70 mV, C) 140 mV, D) 700 mV", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 19, "question": "The total number of basic groups in the following form of lysine is", "response_choices": "", "answer": "2", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 20, "question": "The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C\u2087H\u2088 is", "response_choices": "", "answer": "5", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} +{"id": 21, "question": "In the product given, the stoichiometric ratio for the molecular aldol condensation reaction is", "response_choices": "", "answer": "1", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 22, "question": "Amongst the following, the total number of compounds soluble in aqueous NaOH is", "response_choices": "", "answer": "4", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 23, "question": "Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is", "response_choices": "KCN, K\u2082SO\u2084, (NH\u2084)\u2082C\u2082O\u2084, NaCl, Zn(NO\u2083)\u2082, FeCl\u2083, K\u2082CO\u2083, NH\u2084NO\u2083, LiCN", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF\u2085 is", "response_choices": "", "answer": "either 0 or 8", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "The value of n in the molecular formula Be\u2084Al\u2082Si\u2085O\u2081\u2088 is", "response_choices": "", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is", "response_choices": "", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "The concentration of R in the reaction R \u2192 P was measured as a function of time and the following data is obtained:", "response_choices": "", "answer": "[R] (molar): 1.0, 0.75, 0.40, 0.10; t(min.): 0.0, 0.05, 0.12, 0.18", "page_number": 8, "image_available": "yes", "question_subject": "chemistry"} +{"id": 28, "question": "The number of neutrons emitted when \u00b2\u00b3\u2075\u2089\u2082U undergoes controlled nuclear fission to \u00b9\u2074\u00b2\u2085\u2084Xe and \u2079\u2070\u2083\u2088Sr is", "response_choices": "", "answer": "4", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 29, "question": "If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a sin 2C + c sin 2A) / c is", "response_choices": "A) 1/2, B) \u221a3/2, C) 1, D) \u221a3", "answer": "D", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 30, "question": "Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is", "response_choices": "A) x + 2y - 2z = 0, B) 3x + 2y - 2z = 0, C) x - 2y + z = 0, D) 5x + 2y - 4z = 0", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 31, "question": "Let \u03c9 be a complex cube root of unity with \u03c9\u22601. A fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that \u03c9\u00b9\u02e1 +\u03c9\u00b9\u00b2+\u03c9\u00b9\u00b3=0 is", "response_choices": "A) 1/18, B) 1/9, C) 2/9, D) 1/36", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 32, "question": "Let P, Q, R and S be the points on the plane with position vectors \u22122i\u2212j, 4i, 3i+3j and \u22123i+2j respectively. The quadrilateral PQRS must be a", "response_choices": "A) parallelogram, which is neither a rhombus nor a rectangle, B) square, C) rectangle, but not a square, D) rhombus, but not a square", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 33, "question": "The number of 3x3 matrices A whose entries are either 0 or 1 and for which the system A[x y z]^T = [1 0 0]^T has exactly two distinct solutions, is", "response_choices": "A) 0, B) 2^9 - 1, C) 168, D) 2", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 34, "question": "The value of lim [x->0] (1/x^3) \u222b(0 to 1) (x t \u03b8n (1+t))/(t^4 + 4) dt is", "response_choices": "A) 0, B) 1/12, C) 1/24, D) 1/64", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 35, "question": "Let p and q be real numbers such that p \u2260 0, p^3 \u2260 q and p^3 \u2260 -q . If \u03b1 and \u03b2 are nonzero complex numbers satisfying \u03b1 + \u03b2 = - p and \u03b1^2 + \u03b2^2 = q , then a quadratic equation having (\u03b1/\u03b2) and (\u03b1/\u03b1) as its roots is", "response_choices": "A) (p^3 + q) x^2 - (p^3 + 2q)x + (p^3 + q) = 0, B) (p^3 + q) x^2 - (p^3 - 2q)x + (p^3 + q) = 0, C) (p^3 - q) x^2 - (5p^3 - 2q) x + (p^3 - q) = 0, D) (p^3 - q) x^2 - (5p^3 + 2q) x + (p^3 - q) = 0", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 36, "question": "Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^x + e^-x, g(x) = xe^x + e^-x and h(x) = x^2 e^x + e^-x. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then", "response_choices": "A) a = b and c \u2260 b, B) a = c and a \u2260 b, C) a \u2260 b and c \u2260 b, D) a = b = c", "answer": "D", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 37, "question": "Let A and B be two distinct points on the parabola y^2 = 4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be", "response_choices": "A) -1/r, B) 1/r, C) 2/r, D) -2/r", "answer": "C and D", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "Let ABC be a triangle such that \u2220ACB = \u03c0/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x^2 + x + 1, b = x^2 - 1 and c = 2x + 1 is (are)", "response_choices": "A) -(-2+\u221a3), B) 1+\u221a3, C) 2+\u221a3, D) 4\u221a3", "answer": "B", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "Let z\u2081 and z\u2082 be two distinct complex numbers and let z = (1 - t) z\u2081 + tz\u2082 for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then", "response_choices": "A) |z - z\u2081| + |z - z\u2082| = |z\u2081 - z\u2082|, B) Arg (z - z\u2081) = Arg (z - z\u2082), C) |z-z\u2081 z-z\u2082| = 0, D) Arg (z - z\u2081) = Arg(z\u2082 - z\u2081)|z\u2082-z\u2081 z\u2081-z\u2082|", "answer": "A and C and D", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 40, "question": "Let f be a real-valued function defined on the interval (0, \u221e) by f(x) = \u222b(0 to x) t + sin t dt. Then which of the following statement(s) is (are) true?", "response_choices": "A) f'(x) exists for all x\u2208(0,\u221e) B) f'(x) exists for all x\u2208(0,\u221e) and f' is continuous on (0,\u221e), but not differentiable on (0,\u221e) C) there exists \u03b1 > 1 such that |f'(x)|<|f(x)| for all x\u2208(\u03b1,\u221e) D) there exists \u03b2 > 0 such that |f(x)|+|f'(x)|\u2264\u03b2 for all x\u2208(0,\u221e)", "answer": "B and C", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} +{"id": 41, "question": "The value(s) of \u222b(0 to 1) x^4(1-x)^4/(1+x^2) dx is (are)", "response_choices": "A) 22/7 - \u03c0 B) 2/105 C) 0 D) 71/15 - 3\u03c0/2", "answer": "A", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Let p be an odd prime number and Tp be the following set of 2x2 matrices : Tp = {A= [a b] : a,b,c \u2208 {0, 1, 2, ..., p-1}} The number of A in Tp such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is", "response_choices": "A) (p - 1)\u00b2 B) 2 (p - 1) C) (p - 1)\u00b2 + 1 D) 2p - 1", "answer": "D", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is [Note : The trace of a matrix is the sum of its diagonal entries.]", "response_choices": "A) (p - 1) (p\u00b2 - p + 1) B) p\u00b3 - (p - 1)\u00b2 C) (p - 1)\u00b2 D) (p - 1) (p\u00b2 - 2)", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "The number of A in Tp such that det (A) is not divisible by p is", "response_choices": "A) 2p^2 B) p^3 - 5p C) p^3 - 3p D) p^3 - p^2", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "Equation of a common tangent with positive slope to the circle as well as to the hyperbola is", "response_choices": "A) 2x-\u221a5y-20=0 B) 2x-\u221a5y+4=0 C) 3x-4y+8=0 D) 4x-3y+4=0", "answer": "B", "page_number": 13, "image_available": "yes", "question_subject": "mathematics"} +{"id": 46, "question": "Equation of the circle with AB as its diameter is", "response_choices": "A) x^2+y^2-12x+24=0 B) x^2+y^2+12x+24=0 C) x^2+y^2+24x-12=0 D) x^2+y^2-24x-12=0", "answer": "A", "page_number": 13, "image_available": "yes", "question_subject": "mathematics"} +{"id": 47, "question": "The number of values of \u03b8 in the interval (-(\u03c0/2),(\u03c0/2)) such that \u03b8 \u2260 l\u03c0/5 for n=0,\u00b11,\u00b12 and tan\u03b8=cot\u03b8 as well as sin2\u03b8=cos4\u03b8 is", "response_choices": "No explicit options given", "answer": "3", "page_number": 13, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "The maximum value of the expression 1 / (sin^2 \u03b8 + 3 sin \u03b8 cos \u03b8 + 5cos^2 \u03b8) is", "response_choices": "", "answer": "2", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "If \u0101 and b\u0304 are vectors in space given by \u0101 = i\u22122j\u0304/\u221a5 and b\u0304 = 2i\u0304 + j\u0304 + 3k\u0304/\u221a14, then the value of (2\u0101 + b\u0304) \u22c5 (\u0101 \u00d7 b\u0304) \u00d7 (\u0101 \u22122 b\u0304) is", "response_choices": "", "answer": "5", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "The line 2x + y = 1 is tangent to the hyperbola x^2/a^2 - y^2/b^2 = 1. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is", "response_choices": "", "answer": "2", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "If the distance between the plane Ax - 2y + z = d and the plane containing the lines x-1/2 = y-2/3 = z-3/4 and x-2/3 = y-3/4 = z-4/5 is \u221a6, then |d| is", "response_choices": "", "answer": "6", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = { x - [x] if [x] is odd, 1 + [x] - x if [x] is even}. Then the value of \u222b(10/-10) \u03c0^2 * 10 f(x) cos \u03c0x dx is", "response_choices": "", "answer": "4", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let \u03c9 be the complex number cos 2\u03c0/3 + i sin 2\u03c0/3. Then the number of distinct complex numbers z satisfying |z+1 \u03c9 \u03c9^2; \u03c9 z+\u03c9^2 1; \u03c9^2 1 z+\u03c9| = 0 is equal to", "response_choices": "", "answer": "1", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Let Sk, k = 1, 2, ..., 100, denote the sum of the infinite geometric series whose first term is (k-1)/k! and the common ratio is 1/k. Then the value of 100^2 + (\u03a3 from k=1 to 100) [(k^2 - 3k + 1) Sk] is", "response_choices": "", "answer": "3", "page_number": 15, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "The number of all possible values of \u03b8 , where 0 < \u03b8 < \u03c0, for which the system of equations (y + z) cos 3 \u03b8 = (xyz) sin 3 \u03b8, x sin 3\u03b8 = (2 cos 3\u03b8) / y, 2 sin 3\u03b8 / z, (xyz) sin 3 \u03b8 = (y + 2z) cos 3 \u03b8 + y sin 3 \u03b8 have a solution (x0, y0, z0) with y0 \u2260 0, is", "response_choices": "", "answer": "3", "page_number": 15, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(-3) is equal to", "response_choices": "", "answer": "9", "page_number": 15, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Consider a thin square sheet of side L and thickness t, made of a material of resistivity \u03c1. The resistance between two opposite faces, shown by the shaded areas in the figure is", "response_choices": "A) directly proportional to L, B) directly proportional to t, C) independent of L, D) independent of t", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 58, "question": "A real gas behaves like an ideal gas if its", "response_choices": "A) pressure and temperature are both high, B) pressure and temperature are both low, C) pressure is high and temperature is low, D) pressure is low and temperature is high", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 59, "question": "Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R\u2081\u2080\u2080, R\u2086\u2080 and R\u2084\u2080, respectively, the relation between these resistances is", "response_choices": "A) 1/R\u2081\u2080\u2080 = 1/R\u2086\u2080 + 1/R\u2084\u2080, B) R\u2081\u2080\u2080 = R\u2086\u2080 + R\u2084\u2080, C) R\u2081\u2080\u2080 > R\u2086\u2080 > R\u2084\u2080, D) 1/R\u2081\u2080\u2080 > 1/R\u2086\u2080 > 1/R\u2084\u2080", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 60, "question": "To verify Ohm's law, a student is provided with a test resistor Rr, a high resistance R, a small resistance Rs, two identical galvanometers G1 and G2, and a variable voltage source V. The correct circuit to carry out the experiment is", "response_choices": "A) B) C) D)", "answer": "C", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 61, "question": "An AC voltage source of variable angular frequency \u03c9 and fixed amplitude Vo is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When \u03c9 is increased", "response_choices": "A) the bulb glows dimmer B) the bulb glows brighter C) total impedance of the circuit is unchanged D) total impedance of the circuit increases", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 62, "question": "A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is", "response_choices": "A) IBL, B) IBL/\u03c0, C) IBL/2\u03c0, D) IBL/4\u03c0", "answer": "C", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 63, "question": "A block of mass m is on an inclined plane of angle \u03b8. The coefficient of friction between the block and the plane is \u03bc and tan\u03b8>\u03bc. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P\u2081= mg(sin\u03b8 - \u03bc cos\u03b8) to P\u2082= mg(sin\u03b8 + \u03bc cos\u03b8), the frictional force f versus P graph will look like", "response_choices": "A) [Graph A], B) [Graph B], C) [Graph C], D) [Graph D]", "answer": "A", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 64, "question": "A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is", "response_choices": "A) 2GM(4\u221a2-5)/7R B) -2GM(4\u221a2-5)/7R C) GM/4R D) 2GM(\u221a2-1)/5R", "answer": "A", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 65, "question": "A few electric field lines for a system of two charges Q\u2081 and Q\u2082 fixed at two different points on the x-axis are shown in the figure. These lines suggest that", "response_choices": "A) |Q\u2081| > |Q\u2082| B) |Q\u2081| < |Q\u2082| C) at a finite distance to the left of Q\u2081 the electric field is zero D) at a finite distance to the right of Q\u2082 the electric field is zero", "answer": "A and D", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 66, "question": "A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true ?", "response_choices": "A) Error \u0394T in measuring T, the time period, is 0.05 seconds B) Error \u0394T in measuring T, the time period, is 1 second C) Percentage error in the determination of g is 5% D) Percentage error in the determination of g is 2.5%", "answer": "A and C", "page_number": 19, "image_available": "no", "question_subject": "physics"} +{"id": 67, "question": "A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms\u207b\u00b9. Which of the following statement(s) is (are) correct for the system of these two masses ?", "response_choices": "A) Total momentum of the system is 3 kg ms\u207b\u00b9\nB) Momentum of 5 kg mass after collision is 4 kg ms\u207b\u00b9\nC) Kinetic energy of the centre of mass is 0.75 J\nD) Total kinetic energy of the system is 4 J", "answer": "A and C", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 68, "question": "A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60\u00b0 (see figure). If the refractive index of the material of the prism is \u221a5, which of the following is (are) correct ?", "response_choices": "A) The ray gets totally internally reflected at face CD\nB) The ray comes out through face AD\nC) The angle between the incident ray and the emergent ray is 90\u00b0\nD) The angle between the incident ray and the emergent ray is 120\u00b0", "answer": "A and B and C", "page_number": 20, "image_available": "yes", "question_subject": "physics"} +{"id": 69, "question": "One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is PA. Choose the correct option(s) from the following", "response_choices": "A) Internal energies at A and B are the same\nB) Work done by the gas in process AB is PAVB ln 4\nC) Pressure at C is P0/4\nD) Temperature at C is T0/4", "answer": "A and B and C and D", "page_number": 20, "image_available": "yes", "question_subject": "physics"} +{"id": 70, "question": "If the total energy of the particle is E, it will perform periodic motion only if", "response_choices": "A) E < 0, B) E > 0, C) Vo > E > 0, D) E > Vo", "answer": "B or C or (B and C)", "page_number": 21, "image_available": "yes", "question_subject": "physics"} +{"id": 71, "question": "For periodic motion of small amplitude A, the time period T of this particle is proportional to", "response_choices": "A) A\u221a(m/\u03b1), B) 1/A\u221a(\u03b1/m), C) A\u221a(\u03b1/m), D) 1/A\u221a(\u03b1/m)", "answer": "B", "page_number": 21, "image_available": "yes", "question_subject": "physics"} +{"id": 72, "question": "The acceleration of this particle for |x|>Xo is", "response_choices": "B) proportional to (Vo/mXo), A) proportional to Vo, C) proportional to \u221a(Vo/mXo), D) zero", "answer": "D", "page_number": 21, "image_available": "yes", "question_subject": "physics"} +{"id": 73, "question": "In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B2 (dashed line). If B2 is larger than B1, which of the following graphs shows the correct variation of R with T in these fields?", "response_choices": "Options A), B), C), and D) are shown in the image graphs.", "answer": "A", "page_number": 22, "image_available": "yes", "question_subject": "physics"} +{"id": 74, "question": "A superconductor has Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when", "response_choices": "A) B = 5 Tesla, Tc (B) = 80 K, B) B = 5 Tesla, 75 K < Tc (B) < 100 K, C) B = 10 Tesla, 75 K < Tc (B) < 100 K, D) B = 10 Tesla, Tc (B) = 70 K", "answer": "B", "page_number": 22, "image_available": "yes", "question_subject": "physics"} +{"id": 75, "question": "The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes from m25 to m50. The ratio m25/m50 is", "response_choices": "", "answer": "6", "page_number": 23, "image_available": "no", "question_subject": "physics"} +{"id": 76, "question": "An \u03b1-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are \u03bb\u03b1 and \u03bbp respectively. The ratio \u03bbp/\u03bb\u03b1, to the nearest integer, is", "response_choices": "", "answer": "3", "page_number": 23, "image_available": "no", "question_subject": "physics"} +{"id": 77, "question": "When two identical batteries of internal resistance 1\u03a9 each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 2.25 J2, then the value of R in \u03a9 is", "response_choices": "", "answer": "4", "page_number": 23, "image_available": "no", "question_subject": "physics"} +{"id": 78, "question": "Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T1 and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?", "response_choices": "", "answer": "9", "page_number": 23, "image_available": "no", "question_subject": "physics"} +{"id": 79, "question": "When two progressive waves y1 = 4 sin(2x - 6t) and y2 = 3 sin(2x-6t - \u03c0/2) are superimposed, the amplitude of the resultant wave is", "response_choices": "", "answer": "5", "page_number": 23, "image_available": "no", "question_subject": "physics"} +{"id": 80, "question": "A 0.1 kg mass is suspended from a wire of negligble mass. The length of the wire is 1m and its cross-sectional area is 4.9\u00d710^-7m\u00b2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s\u207b\u00b9. If the Young's modulus of the material of the wire is n\u00d710^9Nm\u207b\u00b2, the value of n is", "response_choices": "No response choices provided.", "answer": "4", "page_number": 24, "image_available": "no", "question_subject": "physics"} +{"id": 81, "question": "A binary star consists of two stars A (mass 2.2M_\u29bf) and B (mass 11M_\u29bf), where M_\u29bf is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is", "response_choices": "No response choices provided.", "answer": "6", "page_number": 24, "image_available": "no", "question_subject": "physics"} +{"id": 82, "question": "Gravitational acceleration on the surface of a planet is \u221a(5/11)g , where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms\u207b\u00b9, the escape speed on the surface of the planet in kms\u207b\u00b9 will be", "response_choices": "No response choices provided.", "answer": "3", "page_number": 24, "image_available": "no", "question_subject": "physics"} +{"id": 83, "question": "A piece of ice (heat capacity = 2100 J kg\u207b\u00b9 \u00b0C\u207b\u00b9 and latent heat = 3.36 \u00d7 10\u2075 J kg\u207b\u00b9) of mass m grams is at -5\u00b0C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is", "response_choices": "No response choices provided.", "answer": "8", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 84, "question": "A stationary source is emitting sound at a fixed frequency f\u2080, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f\u2080. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms\u207b\u00b9.", "response_choices": "No response choices provided.", "answer": "7", "page_number": 24, "image_available": "no", "question_subject": "physics"} diff --git a/JEE_papers/JSON/JEE_2010_2.jsonl b/JEE_papers/JSON/JEE_2010_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..e4a31e946fb02f6a7af96ca9d29a88e26e48a7a8 --- /dev/null +++ b/JEE_papers/JSON/JEE_2010_2.jsonl @@ -0,0 +1,57 @@ +{"id": 1, "question": "The complex showing a spin-only magnetic moment of 2.82 B.M. is", "response_choices": "A) Ni(CO)4 B) [NiCl4]2- C) Ni(PPh3)4 D) [Ni(CN)4]2-", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The species having pyramidal shape is", "response_choices": "A) SO3 B) BrF3 C) SiO32- D) OSF2", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "In the reaction H3C-(ring structure)-C-NH2 (1) NaOH/Br2 T (2) (ring structure)-C-Cl the structure of the Product T is", "response_choices": "A) (structure) B) (structure) C) (structure) D) (structure)", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The compounds P, Q and S were separately subjected to nitration using HNO3/H2SO4 mixture. The major product formed in each case respectively, is", "response_choices": "A) HO-NO2, H3C-NO2, O2N-; B) HO-NO2, H3C-NO2, -NO2; C) HO-NO2, H3C-NO2, -NO2; D) HO-NO2, H3C-NO2, O-NO2", "answer": "C", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "The packing efficiency of the two-dimensional square unit cell shown below is", "response_choices": "A) 39.27%; B) 68.02%; C) 74.05%; D) 78.54%", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule B2 is", "response_choices": "A) 1 and diamagnetic, B) 0 and diamagnetic, C) 1 and paramagnetic, D) 0 and paramagnetic", "answer": "A", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "The total number of diprotic acids among the following is H3PO4, H2SO4, H3PO3, H2CO3, H2S2O7, H3BO3, H3PO2, H2CrO4, H2SO3", "response_choices": "", "answer": "6", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "Total number of geometrical isomers for the complex [RhCl(CO)(PPh3)(NH3)] is", "response_choices": "", "answer": "3", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, Na, Ti", "response_choices": "", "answer": "2", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Silver (atomic weight = 108 g mol\u207b\u00b9) has a density of 10.5 g cm\u207b\u00b3. The number of silver atoms on a surface of area 10\u207b\u00b9\u00b2 m\u00b2 can be expressed in scientific notation as y \u00d7 10^x. The value of x is", "response_choices": "", "answer": "7", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is ws and that along the dotted line path is wd, then the integer closest to the ratio wd/ws is", "response_choices": "Not Available", "answer": "2", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "The compounds P and Q respectively are", "response_choices": "A) H3C-CH2-CH-C-H and H3C-C-H, B) H3C-CH-C-H and C-H, C) H3C-CH2-CH-C-H and H3C-C-H, D) H3C-CH2-CH-C-H and H-C-H", "answer": "B", "page_number": 5, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "The compound R is", "response_choices": "A) H3C-C-C-H, B) H3C-C=C-H, CH3, C-CH-CH, CH3, OH, D) H3C-CH-CH-H, CH3, CH2-OH", "answer": "A", "page_number": 6, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "The compound S is", "response_choices": "A) H3C-CH-CH-H, CH2-CN, B) H3C-C-H, CH2-CN, C) H3C-CH-CH-OH, CH3, CN, CH2-OH, D) H3C-CH-OH, CH3-OH", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "chemistry"} +{"id": 15, "question": "The state S1 is", "response_choices": "A) 1s, B) 2s, C) 2p, D) 3s", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "Energy of the state S1 in units of the hydrogen atom ground state energy is", "response_choices": "A) 0.75, B) 1.50, C) 2.25, D) 4.50", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The orbital angular momentum quantum number of the state S2 is", "response_choices": "A) 0, B) 1, C) 2, D) 3", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "Match the reactions in Column I with appropriate options in Column II.", "response_choices": "A) r and s, B) t, C) p and q, D) r", "answer": "A: r and s, B: t, C: p and q, D: r", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 19, "question": "All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.", "response_choices": "Column I: A) (CH3)2SiCl2, B) XeF4, C) Cl2, D) VCl3 \n Column II: p) Hydrogen halide formation, q) Redox reaction, r) Reacts with glass, s) Polymerization, t) O2 formation", "answer": "A: p and s, B: p and q and r and t, C: p and q, D: p", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "For r = 0, 1, ..., 10, let Ar, Br and Cr denote, respectively, the coefficient of xr in the expansions of (1+x)10, (1+x)20 and (1+x)30. Then \n 10 \u2211 Ar (B10Br - C10Ar)\nr=1 \nis equal to", "response_choices": "A) B10 - C10, B) A10 (B102 - C10A10), C) 0, D) C10 - B10", "answer": "D", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 21, "question": "Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to", "response_choices": "A) 25, B) 34, C) 42, D) 41", "answer": "D", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 22, "question": "Let f be a real-valued function defined on the interval (-1, 1) such that e^-x f(x) = 2 + \u222b(\u221a(t^4 + 1 dt), for all x \u2208 (-1, 1), and let f^-1 be the inverse function of f. Then (f^-1)' (2) is equal to", "response_choices": "A) 1, B) 1/3, C) 1/2, D) 1/e", "answer": "B", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 23, "question": "If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = \u03b1 , where \u03b1 > 0, is 5, then the foot of the perpendicular from P to the plane is", "response_choices": "A) (8/3, 4/3, 7/3), B) (4/3, 4/3, 1/3), C) (1/3, 2/3, 10/3), D) (2/3, 1/3, 5/2)", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 24, "question": "Two adjacent sides of a parallelogram ABCD are given by AB = 2i + 10j + 11k and AD = - i + 2j + 2k The side AD is rotated by an acute angle \u03b1 in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle \u03b1 is given by", "response_choices": "A) 8/9, B) \u221a17/9, C) 1/9, D) 4\u221a5/9", "answer": "B", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 25, "question": "A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is", "response_choices": "A) 3/5, B) 6/7, C) 20/23, D) 9/20", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 26, "question": "Two parallel chords of a circle of radius 2 are at a distance \u221a3 + 1 apart. If the chords subtend at the center, angles of \u03c0/k and 2\u03c0/k, where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]", "response_choices": "NA", "answer": "3", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 27, "question": "Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15\u221a3. If \u2220ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r^2 is equal to", "response_choices": "NA", "answer": "3", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 28, "question": "Let f be a function defined on R (the set of all real numbers) such that f(x)=2010(x\u22122009)(x\u22122010)^2(x\u22122011)^3(x\u22122012)^4, for all x \u2208 R. If g is a function defined on R with values in the interval (0, \u221e) such that f(x) = \u2113n (g (x)), for all x \u2208 R, then the number of points in R at which g has a local maximum is", "response_choices": "NA", "answer": "1", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 29, "question": "Let a1, a2, a3, ... , a11 be real numbers satisfying a1 = 15, 27 - 2a2 > 0 and ak = 2ak-1 - ak-2 for k = 3, 4, ..., 11. If (a1^2 + a2^2 + ... + a11^2)/11 = 90, then the value of (a1 + a2 + ... + a11)/11 is equal to", "response_choices": "NA", "answer": "0", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 30, "question": "Let k be a positive real number and let A= [2k-1 \u221a2k 2\u221ak; 2\u221ak 1 -2k; -2\u221ak 2k -1] and B=[0 2k-1 \u221ak; 1-2k 0 2\u221ak; -\u221ak -2\u221ak 0] If det (adj A) + det(adj B) =10^6, then [k] is equal to", "response_choices": "Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to [k].", "answer": "4", "page_number": 11, "image_available": "yes", "question_subject": "mathematics"} +{"id": 31, "question": "The real number s lies in the interval", "response_choices": "A) (-1/4,0) B) (-11,-3/4) C) (-3/4,1/2) D) (0,1/4)", "answer": "C", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 32, "question": "The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval", "response_choices": "A) (3/4,3) B) (21/64,11/16) C) (9,10) D) (0,21/64)", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 33, "question": "The function f(x) is", "response_choices": "A) increasing in (\u2212t, -1/4) and decreasing in (\u22121/4, t)\nB) decreasing in (\u2212t, -1/4) and increasing in (\u22121/4, t)\nC) increasing in (-t, t)\nD) decreasing in (-t, t)", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} +{"id": 34, "question": "The coordinates of A and B are", "response_choices": "A) (3, 0) and (0, 2)\nB) (-8 \u221a161/5, 15) and (-9 8/5, 5)\nC) (-8 \u221a161/5, 15) and (0, 2)\nD) (3, 0) and (-9 8/5, 5)", "answer": "D", "page_number": 12, "image_available": "yes", "question_subject": "mathematics"} +{"id": 35, "question": "The orthocenter of the triangle PAB is", "response_choices": "A) (5, 8/7)\nB) (7, 25/5, 8)\nC) (11, 8/5, 5)\nD) (8, 7/25, 5)", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} +{"id": 36, "question": "The equation of the locus of the point whose distances from the point P and the line AB are equal, is", "response_choices": "A) 9x^2 + y^2 - 6xy - 54x - 62y + 241 = 0, B) x^2 + 9y^2 + 6xy - 54x + 62y - 241 = 0, C) 9x^2 + 9y^2 - 6xy - 54x - 62y - 241 = 0, D) x^2 + y^2 - 2xy + 27x + 31y - 120 = 0", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "mathematics"} +{"id": 37, "question": "Match the statements in Column-I with those in Column-II. [Note: Here z takes values in the complex plane and Im z and Re z denote, respectively, the imaginary part and the real part of z.]", "response_choices": "Column I: A) The set of points z satisfying |z-1|z|=|z+1|z|, B) The set of points z satisfying |z+4|+|z-4|=10, C) If |w|=2, then the set of points z=w-1/w, D) If |w|=1, then the set of points z=w+1/w; Column II: p) an ellipse with eccentricity 4/5, q) the set of points z satisfying Im z=0, r) the set of points z satisfying |Im z|\u22641, s) the set of points z satisfying |Re z|\u22642, t) the set of points z satisfying |z|\u22643", "answer": "A: q and r, B: p, C: p and s and t, D: q and r and s and t", "page_number": 13, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "Match the statements in Column-I with the values in Column-II.", "response_choices": "A) A line from the origin meets the lines x-2=y-1=z+1 and x-8/3=y+3/2=-z-1/1 at P and Q respectively. If length PQ = d, then d^2 is p) - 4\nB) The values of x satisfying tan^-1 (x + 3) - tan^-1 (x - 3) = sin^-1 (3/5) are q) 0\nC) Non-zero vectors \u0101, b\u0304 and c\u0304 satisfy \u0101.b\u0304 = 0, (b\u0304 - \u0101).(b\u0304 + c\u0304) = 0 and 2|b\u0304 + c\u0304| = |b\u0304 - \u0101|. If \u0101 = \u03bcb\u0304 + 4c\u0304, then the possible values of \u03bc are r) 4\nD) Let f be the function on [-\u03c0, \u03c0] given by f(0) = 9 and f(x) = sin((9x/2)/sin(x/2)) for x \u2260 0. The value of (2/\u03c0) \u222b[-\u03c0]^\u03c0 f(x) dx is s) 5\nt) 6", "answer": "A: t\nB: p and r\nC: either q or (q and s)\nD: r", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is", "response_choices": "A) 0.02 mm, B) 0.05 mm, C) 0.1 mm, D) 0.2 mm", "answer": "D", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 40, "question": "A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms^-1, the mass of the string is", "response_choices": "A) 5 grams, B) 10 grams, C) 20 grams, D) 40 grams", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 41, "question": "A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is", "response_choices": "A) virtual and at a distance of 16 cm from the mirror, B) real and at a distance of 16 cm from the mirror, C) virtual and at a distance of 20 cm from the mirror, D) real and at a distance of 20 cm from the mirror", "answer": "B", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 42, "question": "A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is", "response_choices": "A) 4.50 J, B) 7.50 J, C) 5.06 J, D) 14.06 J", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 43, "question": "A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81\u03c0/104 Vm\u22121. When the field is switched off, the drop is observed to fall with terminal velocity 2 \u00d7 10\u22123 m s\u22121. Given g = 9.8 m s\u22122, viscosity of the air = 1.8 \u00d7 10\u22125 Ns m\u22122 and the density of oil = 900 kg m\u22123, the magnitude of q is", "response_choices": "A) 1.6 \u00d7 10\u221219 C, B) 3.2 \u00d7 10\u221219 C, C) 4.8 \u00d7 10\u221219 C, D) 8.0 \u00d7 10\u221219 C", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 44, "question": "A uniformly charged thin spherical shell of radius R carries uniform surface charge density of \u03c3 per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to", "response_choices": "A) (1/\u03b50)*\u03c3^2*R^2, B) (1/\u03b50)*\u03c3*R, C) (1/\u03b50*R)*\u03c3^2, D) (1/\u03b50*R^2)*\u03c3^2", "answer": "A", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 45, "question": "A diatomic ideal gas is compressed adiabatically to (1/32) of its initial volume. In the initial temperature of the gas is T\u2081 (in Kelvin) and the final temperature is \u03b1T\u2081, the value of \u03b1 is", "response_choices": "", "answer": "4", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 46, "question": "At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?", "response_choices": "[Take : \u2113n 5 = 1.6, \u2113n 3 = 1.1]", "answer": "2", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 47, "question": "Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from (25/3) m to (50/7) m in 30 seconds. What is the speed of the object in km per hour ?", "response_choices": "", "answer": "3", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 48, "question": "A large glass slab (\u03bc = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?", "response_choices": "", "answer": "6", "page_number": 18, "image_available": "no", "question_subject": "physics"} +{"id": 49, "question": "To determine the half life of a radioactive element, a student plots a graph of |dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is", "response_choices": "", "answer": "8", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 50, "question": "If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r< \u03bc2, C) \u03bc2 = \u03bc3, D) \u03bc2 > \u03bc3", "answer": "A: p and r, B: q and s and t, C: p and r and t, D: q and s", "page_number": 21, "image_available": "yes", "question_subject": "physics"} +{"id": 57, "question": "You are given many resistances, capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V1 and V2. (indicated in circuits) are related as shown in column I. Match the two", "response_choices": "A) I \u2260 0, V1 is proportional to I\nB) I \u2260 0, V2 > V1\nC) V1 = 0, V2 = V\nD) I \u2260 0, V2 is proportional to I", "answer": "A: r and s and t\nB: q and r and s and t\nC: p and q\nD: q and r and s and t", "page_number": 22, "image_available": "yes", "question_subject": "physics"} diff --git a/JEE_papers/JSON/JEE_2011_1.jsonl b/JEE_papers/JSON/JEE_2011_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..5b2926572e56c36df78cbbf3ccad0cf17f52440b --- /dev/null +++ b/JEE_papers/JSON/JEE_2011_1.jsonl @@ -0,0 +1,72 @@ +{"id": 1, "question": "Extra pure N2 can be obtained by heating", "response_choices": "(A) NH3 with CuO, (B) NH4NO3, (C) (NH4)2Cr2O7, (D) Ba(N3)2", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl-, CN- and H2O, respectively, are", "response_choices": "(A) octahedral, tetrahedral and square planar, (B) tetrahedral, square planar and octahedral, (C) square planar, tetrahedral and octahedral, (D) octahedral, square planar and octahedral", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Bombardment of aluminum by \u03b1-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products X, Y and Z respectively are,", "response_choices": "(A) proton, neutron, positron, (B) neutron, positron, proton, (C) proton, positron, neutron, (D) positron, proton, neutron", "answer": "A", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is", "response_choices": "(A) 1.78 M, (B) 2.00 M, (C) 2.05 M, (D) 2.22 M", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "AgNO3 (aq.) was added to an aqueous KCl solution gradually and the conductivity of the solution was measured. The plot of conductance (\u039b) versus the volume of AgNO3 is", "response_choices": "(A) (P), (B) (Q), (C) (R), (D) (S)", "answer": "S", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "Among the following compounds, the most acidic is", "response_choices": "(A) p-nitrophenol, (B) p-hydroxybenzoic acid, (C) o-hydroxybenzoic acid, (D) p-toluic acid", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "The major product of the following reaction is", "response_choices": "(A), (B), (C), (D)", "answer": "A", "page_number": 3, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "Extraction of metal from the ore cassiterite involves", "response_choices": "(A) carbon reduction of an oxide ore, (B) self-reduction of a sulphide ore, (C) removal of copper impurity, (D) removal of iron impurity", "answer": "AD", "page_number": 4, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)", "response_choices": "(A) Adsorption is always exothermic. (B) Physisorption may transform into chemisorption at high temperature. (C) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature. (D) Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.", "answer": "ABD", "page_number": 4, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "According to kinetic theory of gases", "response_choices": "(A) collisions are always elastic. (B) heavier molecules transfer more momentum to the wall of the container. (C) only a small number of molecules have very high velocity. (D) between collisions, the molecules move in straight lines with constant velocities.", "answer": "ACD", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "Amongst the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any), is (are)", "response_choices": "(A) H2C=C-CH2 (B) H-C\u2261C-CH2 (C) H2C=C=O (D) H2C=C-CH2", "answer": "BC", "page_number": 5, "image_available": "yes", "question_subject": "chemistry"} +{"id": 12, "question": "The metal rod M is", "response_choices": "(A) Fe (B) Cu (C) Ni (D) Co", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "The compound N is", "response_choices": "(A) AgNO3 (B) Zn(NO3)2 (C) Al(NO3)3 (D) Pb(NO3)2", "answer": "A", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "The final solution contains", "response_choices": "(A) [Pb(NH3)4]2+ and [CoCl4]2- (B) [Al(NH3)4]3+ and [Cu(NH3)4]2+ (C) [Ag(NH3)2]+ and [Cu(NH3)4]+ (D) [Ag(NH3)2]+ and [Ni(NH3)6]2+", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "The structure of compound P is", "response_choices": "(A) CH3CH2CH2CH2\u2014C\u2261C\u2014H, (B) H3CH2C\u2014C\u2261C\u2014CH2CH3, (C) H3C\u2014C\u2014C\u2261C\u2014CH3, (D) H3C\u2014C\u2014C\u2261C\u2014H", "answer": "D", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 16, "question": "The structure of the compound Q is", "response_choices": "(A) H3C\u2014OH\u2014C\u2014CH2CH3, (B) H3C\u2014C\u2014C\u2014CH3, (C) H3C\u2014OH\u2014CH2CHCH3, (D) CH3CH2CH2CHCH2CH3", "answer": "B", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "The difference in the oxidation numbers of the two types of sulphur atoms in Na\u2082S\u2082O\u2086 is", "response_choices": "", "answer": "5", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "Reaction of Br\u2082 with Na\u2082CO\u2083 in aqueous solution gives sodium bromide and sodium bromate with evolution of CO\u2082 gas. The number of sodium bromide molecules involved in the balanced chemical equation is", "response_choices": "", "answer": "5", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 19, "question": "The maximum number of electrons that can have principal quantum number, n = 3, and spin quantum number, m_s = \u20131/2, is", "response_choices": "", "answer": "9", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "The work function (\u03a6) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is", "response_choices": "Metal: Li, Na, K, Mg, Cu, Ag, Fe, Pt, W; \u03a6 (eV): 2.4, 2.3, 2.2, 3.7, 4.8, 4.3, 4.7, 6.3, 4.75", "answer": "4", "page_number": 9, "image_available": "no", "question_subject": "chemistry"} +{"id": 21, "question": "To an evacuated vessel with movable piston under external pressure of 1 atm., 0.1 mol of He and 1.0 mol of an unknown compound (vapour pressure 0.68 atm. at 0 \u00b0C) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at 0 \u00b0C is close to", "response_choices": "", "answer": "7", "page_number": 9, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "The total number of alkenes possible by dehydrobromination of 3-bromo-3-cyclopentyihexane using alcoholic KOH is", "response_choices": "", "answer": "5", "page_number": 9, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "A decapeptide (Mol. Wt. 796) on complete hydrolysis gives glycine (Mol. Wt. 75), alanine and phenylalanine. Glycine contributes 47.0 % to the total weight of the hydrolysed products. The number of glycine units present in the decapeptide is", "response_choices": "", "answer": "6", "page_number": 9, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is", "response_choices": "(A) 8.50 kHz (B) 8.25 kHz (C) 7.75 kHz (D) 7.50 kHz", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 25, "question": "5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T\u2081, the work done in the process is", "response_choices": "(A) (9/8) R T\u2081 (B) (3/2) R T\u2081 (C) (15/8) R T\u2081 (D) (9/2) R T\u2081", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 26, "question": "Consider an electric field E = E\u2080 x, where E\u2080 is a constant. The flux through the shaded area (as shown in the figure) due to this field is", "response_choices": "(A) 2E\u2080a\u00b2 (B) \u221a(2E\u2080a\u00b2) (C) E\u2080a\u00b2 (D) (E\u2080a\u00b2/\u221a2)", "answer": "C", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 27, "question": "The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 \u00c5. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is", "response_choices": "(A) 1215 \u00c5, (B) 1640 \u00c5, (C) 2430 \u00c5, (D) 4687 \u00c5", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 28, "question": "A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is", "response_choices": "(A) 9, (B) 18, (C) 27, (D) 36", "answer": "D", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 29, "question": "A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is", "response_choices": "(A) 10.2 ohm, (B) 10.6 ohm, (C) 10.8 ohm, (D) 11.1 ohm", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 30, "question": "A 2 \u03bcF capacitor is charged as shown in figure. The percentage of its stored energy dissipated after the switch S is turned to position 2 is", "response_choices": "(A) 0%, (B) 20%, (C) 75%, (D) 80%", "answer": "D", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 31, "question": "A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given charge '+Q'. Now they are connected by a thin metal wire. Then", "response_choices": "(A) Einside = 0, (B) QA > QB, (C) \u03c3A = RB/RA * \u03c3B, (D) Eout surface A < Eout surface B", "answer": "ABCD", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 32, "question": "An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?", "response_choices": "(A) They will never come out of the magnetic field region, (B) They will come out travelling along parallel paths, (C) They will come out at the same time, (D) They will come out at different times.", "answer": "BC, BD, BCD", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 33, "question": "A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat 'Q' flows only from left to right through the blocks. Then in steady state", "response_choices": "A) heat flow through A and E slabs are same.\nB) heat flow through slab E is maximum.\nC) temperature difference across slab E is smallest.\nD) heat flow through C = heat flow through B + heat flow through D.", "answer": "D", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 34, "question": "A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (< L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?", "response_choices": "A) Restoring torque in case A = Restoring torque in case B\nB) Restoring torque in case A < Restoring torque in case B\nC) Angular frequency for case A > Angular frequency for case B.\nD) Angular frequency for case A < Angular frequency for case B.", "answer": "D", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 35, "question": "Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 36, "question": "For such systems, phase space is a plane in which position is plotted along horizontal axis and momentum is plotted along vertical axis.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 37, "question": "For example, the phase space diagram for a particle moving with constant velocity is a straight line as shown in the figure.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 35, "question": "The phase space diagram for a ball thrown vertically up from ground is", "response_choices": "A, B, C, D", "answer": "D", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 36, "question": "The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then", "response_choices": "(A) E1 = \u221a2 E2, (B) E1 = 2 E2, (C) E1 = 4 E2, (D) E1 = 16 E2", "answer": "C", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 37, "question": "Consider the spring-mass system, with the mass submerged in water, as shown in the figure. The phase space diagram for one cycle of this system is", "response_choices": "(A), (B), (C), (D)", "answer": "B", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 38, "question": "Taking the electronic charge as 'e' and the permittivity as '\\epsilon_0', use dimensional analysis to determine the correct expression for \\omega_p.", "response_choices": "(A) \\sqrt{Ne/m\\epsilon_0}, (B) \\sqrt{m\\epsilon_0/Ne}, (C) \\sqrt{Ne^2/m\\epsilon_0}, (D) \\sqrt{m\\epsilon_0/Ne^2}", "answer": "C", "page_number": 18, "image_available": "no", "question_subject": "physics"} +{"id": 39, "question": "Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N = 4 \u00d7 10^27 m^-3. Take \\epsilon_0 = 10^-11 and m = 10^-30, where these quantities are in proper SI units.", "response_choices": "(A) 800 nm, (B) 600 nm, (C) 300 nm, (D) 200 nm", "answer": "B", "page_number": 18, "image_available": "no", "question_subject": "physics"} +{"id": 40, "question": "A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s\u00b2. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is", "response_choices": "", "answer": "4", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 41, "question": "A block is moving on an inclined plane making an angle 45\u00b0 with the horizontal and the coefficient of friction is \u03bc. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 \u03bc, then N is", "response_choices": "", "answer": "5", "page_number": 19, "image_available": "no", "question_subject": "physics"} +{"id": 42, "question": "Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side 'a '. The surface tension of the soap film is \u03b3. The system of charges and planar film are in equilibrium, and \u03b1 = k [a^2/\u03b3]^(1/N), where 'k' is a constant. Then N is", "response_choices": "", "answer": "3", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 43, "question": "Steel wire of length 'L' at 40\u00b0C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40\u00b0C to 30\u00b0C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^(-5) /\u00b0C, Young's modulus of steel is 10^11 N/m^2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly", "response_choices": "", "answer": "3", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 44, "question": "The activity of a freshly prepared radioactive sample is 10^10 disintegrations per second, whose mean life is 10^9 s. The mass of an atom of this radioisotope is 10^(-23) kg. The mass (in mg) of the radioactive sample is", "response_choices": "", "answer": "1", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 45, "question": "A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I0 cos (300 t) where I0 is constant. If the magnetic moment of the loop is N d0 I0 sin (300 t), then 'N' is", "response_choices": "(No response choices provided)", "answer": "6", "page_number": 21, "image_available": "yes", "question_subject": "physics"} +{"id": 46, "question": "Four solid spheres each of diameter \u221a5 cm and mass 0.5 kg are placed with their centers at the corners of a square of side 4cm. The moment of inertia of the system about the diagonal of the square is N \u00d7 10^-4 kg-m^2, then N is", "response_choices": "(No response choices provided)", "answer": "9", "page_number": 21, "image_available": "no", "question_subject": "physics"} +{"id": 47, "question": "Let (x0, y0) be the solution of the following equations (2x)^(ln2) = (3y)^(ln3), 3^(ln x) = 2^(ln y). Then x0 is", "response_choices": "A) 1/6, B) 1/3, C) 1/2, D) 6", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "The value of \u222b(^(3)_(0.5)) (1/sin x^2 + sin (ln 6 - x^2)) dx is", "response_choices": "A) (1/4)ln(3/2), B) (1/2)ln(3/2), C) ln(3/2), D) (1/6)ln(3/2)", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Let a\u20d7=i\u20d7+j\u20d7+k\u20d7, b\u20d7=i\u20d7\u2212j\u20d7+k\u20d7 and c\u20d7=i\u20d7\u2212j\u20d7\u2212k\u20d7 be three vectors. A vector v\u20d7 in the plane of a\u20d7 and b\u20d7, whose projection on c\u20d7 is 1/\u221a3, is given by", "response_choices": "A) i\u20d7\u22123j\u20d7+3k\u20d7, B) \u22123i\u20d7\u22123j\u20d7\u2212k\u20d7, C) 3i\u20d7\u2212j\u20d7+3k\u20d7, D) i\u20d7+3j\u20d7\u22123k\u20d7", "answer": "C", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Let P={\u03b8: sin \u03b8\u2212cos \u03b8=\u221a2 cos \u03b8} and Q={\u03b8: sin \u03b8+cos \u03b8=\u221a2 sin \u03b8} be two sets. Then", "response_choices": "A) P\u2282Q and Q\u2212P\u2260\u2205, B) Q\u2284P, C) P\u2284Q, D) P=Q", "answer": "D", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let the straight line x=b divide the area enclosed by y=(1\u2212x)\u00b2, y=0, and x=0 into two parts R\u2081 (0\u2264x\u2264b) and R\u2082 (b\u2264x\u22641) such that R\u2081\u2212R\u2082=1/4. Then b equals", "response_choices": "A) 3/4, B) 1/2, C) 1/3, D) 1/4", "answer": "B", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Let \u03b1 and \u03b2 be the roots of x^2 - 6x - 2 = 0, with \u03b1 > \u03b2. If a_n = \u03b1^n - \u03b2^n for n\u22651, then the value of (a_0 - 2a_1)/2a_0 is", "response_choices": "(A) 1, (B) 2, (C) 3, (D) 4", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "A straight line L through the point (3,-2) is inclined at an angle 60\u00b0 to the line \u221a3x + y = 1. If L also intersects the x-axis, then the equation of L is", "response_choices": "(A) y + \u221a3x + 2 - 3\u221a3 = 0, (B) y - \u221a3x + 2 + 3\u221a3 = 0, (C) \u221a3y - x + 3 + 2\u221a3 = 0, (D) \u221a3y + x - 3 + 2\u221a3 = 0", "answer": "B", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "The vector(s) which is/are coplanar with vectors \\vec{i} + \\vec{j} + 2\\vec{k} and \\vec{i} + 2\\vec{j} + \\vec{k}, and perpendicular to the vector \\vec{i} + \\vec{j} + \\vec{k} is/are", "response_choices": "(A) \\vec{j} - \\vec{k}, (B) -\\vec{i} + \\vec{j}, (C) \\vec{i} - \\vec{j}, (D) -\\vec{j} + \\vec{k}", "answer": "AD", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN = NM . If P^T denotes the transpose of P, then M^2N^2 (M^TN)^-1 (MN^-1)^T is equal to", "response_choices": "(A) M^2, (B) -N^2, (C) -M^2, (D) MN", "answer": "MARKS TO ALL", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let the eccentricity of the hyperbola x^2/a^2 - y^2/b^2 = 1 be reciprocal to that of the ellipse x^2 + 4y^2 = 4 . If the hyperbola passes through a focus of the ellipse, then", "response_choices": "(A) the equation of the hyperbola is x^2/3 - y^2/2 = 1, (B) a focus of the hyperbola is (2, 0), (C) the eccentricity of the hyperbola is \\sqrt{5}/3, (D) the equation of the hyperbola is x^2 - 3y^2 = 3", "answer": "BD", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Let f : R \u2192 R be a function such that f(x + y) = f(x) + f(y), \u2200x, y \u2208 R. If f(x) is differentiable at x = 0, then", "response_choices": "(A) f(x) is differentiable only in a finite interval containing zero, (B) f(x) is continuous \u2200x \u2208 R, (C) f'(x) is constant \u2200x \u2208 R, (D) f(x) is differentiable except at finitely many points", "answer": "BC,BCD", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "If the point P(a, b, c), with reference to (E), lies on the plane 2x + y + z = 1, then the value of 7a + b + c is", "response_choices": "(A) 0, (B) 12, (C) 7, (D) 6", "answer": "D", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 59, "question": "Let \u03c9 be a solution of x^3 - 1 = 0 with Im(\u03c9) > 0. If a = 2 with b and c satisfying (E), then the value of (3/\u03c9^4) + (1/\u03c9^6) + (3/\u03c9^5) is equal to", "response_choices": "(A) -2, (B) 2, (C) 3, (D) -3", "answer": "A", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 60, "question": "Let b = 6, with a and c satisfying (E). If \u03b1 and \u03b2 are the roots of the quadratic equation ax^2 + bx + c = 0, then \u03a3[(1/\u03b1)^n + (1/\u03b2)^n] is", "response_choices": "(A) 6, (B) 7, (C) 6/7, (D) \u221e", "answer": "B", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 61, "question": "The probability of the drawn ball from U2 being white is", "response_choices": "(A) 13/30 (B) 23/30 (C) 19/30 (D) 11/30", "answer": "B", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 62, "question": "Given that the drawn ball from U2 is white, the probability that head appeared on the coin is", "response_choices": "(A) 17/23 (B) 11/23 (C) 15/23 (D) 12/23", "answer": "D", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 63, "question": "Consider the parabola y\u00b2 = 8x. Let A\u2081 be the area of the triangle formed by the end points of its latus rectum and the point P(1, 2) on the parabola, and A\u2082 be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum. Then A\u2081/A\u2082 is", "response_choices": "", "answer": "2", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 64, "question": "Let a\u2081, a\u2082, a\u2083, ..., a\u2081\u2080\u2080 be an arithmetic progression with a\u2081 = 3 and S\u2085 = \u03a3\u207f\u1d56=\u00b9 a\u1d56 , 1 \u2264 p \u2264 100. For any integer n with 1 \u2264 n \u2264 20, let m = 5n. If S_m/S\u2085 does not depend on n, then a\u2085 is", "response_choices": "", "answer": "3, 9, 3 & 9 BOTH", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 65, "question": "The positive integer value of n > 3 satisfying the equation 1/[sin(\u03c0/n)] = 1/[sin(2\u03c0/n)] + 1/[sin(3\u03c0/n)] is", "response_choices": "", "answer": "7", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 66, "question": "Let f : [1, \u221e) \u2192 [2, \u221e) be a differentiable function such that f(1) = 2. If \u222b(6/1) f(t) dt = 3x f(x) - x5 for all x \u2265 1, then the value of f(2) is", "response_choices": "", "answer": "MARKS TO ALL", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 67, "question": "If z is any complex number satisfying |z - 3 - 2i| \u2264 2, then the minimum value of |2z - 6 + 5i| is", "response_choices": "", "answer": "5", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 68, "question": "The minimum value of the sum of real numbers a^-5, a^-4, 3a^-3, 1, a8 and a^10 with a > 0 is", "response_choices": "", "answer": "8", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 69, "question": "Let f(\u03b8) = sin(tan^-1((sin \u03b8)/\u221a(cos 2\u03b8))), where -\u03c0/4 < \u03b8 < \u03c0/4. Then the value of d/d(tan \u03b8)(f(\u03b8)) is", "response_choices": "", "answer": "1", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2011_2.jsonl b/JEE_papers/JSON/JEE_2011_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..8c9316a0048fe3e260e4f47b5baab05ead6185b4 --- /dev/null +++ b/JEE_papers/JSON/JEE_2011_2.jsonl @@ -0,0 +1,60 @@ +{"id": 1, "question": "Oxidation states of the metal in the minerals haematite and magnetite, respectively, are", "response_choices": "(A) II, III in haematite and III in magnetite\n(B) II, III in haematite and II in magnetite\n(C) II in haematite and II, III in magnetite\n(D) III in haematite and II, III in magnetite", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "Among the following complexes (K\u2013P), \nK3[Fe(CN)6] (K), [Co(NH3)6]Cl3 (L), Na3[Co(oxalate)3] (M), [Ni(H2O)6]Cl2 (N),\nK3[Pt(CN)6] (O) and [Zn(H2O)6](NO3)2 (P)\nthe diamagnetic complexes are", "response_choices": "(A) K, L, M, N\t(B) K, M, O, P\t(C) L, M, O, P\t(D) L, M, N, O", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Passing H2S gas into a mixture of Mn2+, Ni2+, Cu2+ and Hg2+ ions in an acidified aqueous\nsolution precipitates", "response_choices": "(A) CuS and HgS\t\t(B) MnS and CuS\n(C) MnS and NiS\t\t(D) NiS and HgS", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "Consider the following cell reaction:\n2Fe(s) + O2(g) + 4H+(aq) \u2192 2Fe3+(aq) + 2H2O(l)\t\tE\u00b0 = 1.67 V\nAt [Fe3+] = 10\u20133 M, P(O2) = 0.1 atm and pH = 3, the cell potential at 25 \u00b0C is", "response_choices": "(A) 1.47 V\t(B) 1.77 V\t(C) 1.87 V\t(D) 1.57 V", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "The freezing point (in \u00b0C) of a solution containing 0.1 g of K4[Fe(CN)6] (Mol. Wt. 329) in 100 g of water (Kf = 1.86 K kg mol^-1) is", "response_choices": "(A) \u22122.3 \u00d7 10^-2 (B) \u22125.7 \u00d7 10^-2 (C) \u22125.7 \u00d7 10^-3 (D) \u22121.2 \u00d7 10^-2", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "Amongst the compounds given, the one that would form a brilliant colored dye on treatment with NaNO2 in dil. HCl followed by addition to an alkaline solution of \u03b2-naphthol\u0196(CH3)2 \u0194 NH2 \u0194 CH2NH2", "response_choices": "\u03b2CH3 NHCH3 H3C", "answer": "C", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The major product of the following reaction is RCH2OH ------> H\u2295 (anhydrous)", "response_choices": "(A) a hemiacetal (B) an acetal (C) an ether (D) an ester", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "The following carbohydrate is H OH HO HO HO H H", "response_choices": "(A) a ketohexose (B) an aldohexose (C) an \u03b1-furanose (D) an \u03b1-pyranose", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "Reduction of the metal centre in aqueous permanganate ion involves", "response_choices": "(A) 3 electrons in neutral medium, (B) 5 electrons in neutral medium, (C) 3 electrons in alkaline medium, (D) 5 electrons in acidic medium", "answer": "ACD", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "The equilibrium 2 Cu\u207a \u21cc Cu\u00b2\u207a + Cu\u2070 in aqueous medium at 25 \u00b0C shifts towards the left in the presence of", "response_choices": "(A) NO\u2083\u207b, (B) Cl\u207b, (C) SCN\u207b, (D) CN\u207b", "answer": "BCD", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "For the first order reaction \n\n2N2O5(g) \u2192 4NO2(g) + O2(g)", "response_choices": "(A) the concentration of the reactant decreases exponentially with time.\n(B) the half-life of the reaction decreases with increasing temperature.\n(C) the half-life of the reaction depends on the initial concentration of the reactant. \n(D) the reaction proceeds to 99.6 % completion in eight half-life duration.", "answer": "ABD", "page_number": 4, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "The correct functional group X and the reagent/reaction conditions Y in the following scheme are\n\nX\u2014(CH2)4\u2014X (i) Y\n \u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014> condensation polymer\n O O\n (ii) \\C\u2014(CH2)4\u2014C/\n \\ /\n HO OH\n heat", "response_choices": "(A) X = COOCH3 , Y = H2/Ni/heat \n(B) X = CONH2 , Y = H2/Ni/heat\n(C) X = CONH2 , Y = Br2/NaOH\n(D) X = CN , Y = H2/Ni/heat", "answer": "CD", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "Among the following, the number of compounds than can react with PCl5 to give POCl3 is O2, CO2, SO2, H2O, H2SO4, P2O10", "response_choices": "", "answer": "4", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "The volume (in mL) of 0.1 M AgNO3 required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of [Cr(H2O)6]Cl3, as silver chloride is close to", "response_choices": "", "answer": "6", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "In 1 L saturated solution of AgCl [Ksp(AgCl) = 1.6 \u00d7 10^-10], 0.1 mol of CuCl [Ksp(CuCl) = 1.0 \u00d7 10^-6] is added. The resultant concentration of Ag+ in the solution is 1.6 \u00d7 10^-x. The value of \"x\" is", "response_choices": "", "answer": "7", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "The number of hexagonal faces that are present in a truncated octahedron is", "response_choices": "", "answer": "8", "page_number": 5, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The maximum number of isomers (including stereoisomers) that are possible on mono-chlorination of the following compound, is CH3 \\C\\ CH2CH2\\CH2CH3 \\H", "response_choices": "", "answer": "8", "page_number": 5, "image_available": "yes", "question_subject": "chemistry"} +{"id": 18, "question": "The total number of contributing structures showing hyperconjugation (involving C-H bonds) for the following carbocation is H3C-C(+)-CH2CH3 ", "response_choices": "", "answer": "6", "page_number": 5, "image_available": "yes", "question_subject": "chemistry"} +{"id": 19, "question": "Match the transformations in column I with appropriate options in column II", "response_choices": "Column I: (A) CO2(s) \u2192 CO2(g), (B) CaCO3(s) \u2192 CaO(s) + CO2(g), (C) 2 H\u2022 \u2192 H2(g), (D) P(white, solid) \u2192 P(red, solid) \n\nColumn II: (p) phase transition, (q) allotropic change, (r) \u0394H is positive, (s) \u0394S is positive, (t) \u0394S is negative", "answer": "A: p, r and s\nB: r and s\nC: t\nD: p, q and t", "page_number": 6, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II", "response_choices": "A: r, s and t; B: p and s; C: r and s; D: q and r", "answer": "A: r, s and t; B: p and s; C: r and s; D: q and r", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} +{"id": 21, "question": "A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence \u03b8. The reflected ( R ) and transmitted ( T ) intensities, both as function of \u03b8, are plotted. The correct sketch is", "response_choices": "(A), (B), (C) and (D)", "answer": "C", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 22, "question": "A satellite is moving with a constant speed 'V' in a circular orbit about the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is", "response_choices": "(A) 1/2 mV^2, (B) mV^2, (C) 3/2 mV^2, (D) 2mV^2", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 23, "question": "A long insulated copper wire is closely wound as a spiral of 'N' turns. The spiral has inner radius 'a' and outer radius 'b'. The spiral lies in the X-Y plane and a steady current 'I' flows through the wire. The Z-component of the magnetic field at the center of the spiral is", "response_choices": "(A) (\u03bc\u2080N I / 2(b-a)) ln (b/a), (B) (\u03bc\u2080N I / 2(b-a)) ln ((b+a)/(b-a)), (C) (\u03bc\u2080N I / 2b) ln (b/a), (D) (\u03bc\u2080N I / 2b) ln ((b+a)/(b-a))", "answer": "A", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 24, "question": "A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x\u2081(t) = A sin \u03c9t and x\u2082(t) = A sin (\u03c9t + 2\u03c0/3). Adding a third sinusoidal displacement x\u2083(t) = B sin (\u03c9t + \u03d5) brings the mass to a complete rest. The values of B and \u03d5 are", "response_choices": "(A) \u221a2 A, 3\u03c0/4, (B) A, 4\u03c0/3, (C) \u221a3 A, 5\u03c0/6, (D) A, \u03c0/3", "answer": "B", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 25, "question": "Which of the field patterns given below is valid for electric field as well as for magnetic field?", "response_choices": "A, B, C, D", "answer": "C", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 26, "question": "A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is", "response_choices": "(A) 250 m/s, (B) 250\u221a2 m/s, (C) 400 m/s, (D) 500 m/s", "answer": "D", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 27, "question": "The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is", "response_choices": "(A) 0.9%, (B) 2.4%, (C) 3.1%, (D) 4.2%", "answer": "C", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 28, "question": "A wooden block performs SHM on a frictionless surface with frequency, v0. The block carries a charge +Q on its surface. If now a uniform electric field E is switched-on as shown, then the SHM of the block will be", "response_choices": "A) of the same frequency and with shifted mean position. B) of the same frequency and with the same mean position. C) of changed frequency and with shifted mean position. D) of changed frequency and with the same mean position.", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 29, "question": "Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if", "response_choices": "(A) dA < dF, (B) dB > dF, (C) dA > dF, (D) dA + dB = 2 dF", "answer": "ABD", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 30, "question": "A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?", "response_choices": "(A) IRA > IRB, (B) IRA < IRB, (C) VCA > VCB, (D) VCA < VCB", "answer": "BC", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 31, "question": "Which of the following statement(s) is/are correct?", "response_choices": "(A) If the electric field due to a point charge varies as r^-2.5 instead of r^-2, then the Gauss law will still be valid. (B) The Gauss law can be used to calculate the field distribution around an electric dipole. (C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same. (D) The work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB - VA).", "answer": "CD", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 32, "question": "A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision", "response_choices": "(A) the ring has pure rotation about its stationary CM. (B) the ring comes to a complete stop. (C) friction between the ring and the ground is to the left. (D) there is no friction between the ring and the ground.", "answer": "A OR AC", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 33, "question": "A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of 60\u00b0 to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^2, is", "response_choices": "No response choices provided", "answer": "5", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 34, "question": "A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is", "response_choices": "No response choices provided", "answer": "4", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 35, "question": "Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is", "response_choices": "No response choices provided", "answer": "5", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 36, "question": "Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oil to act as a thin lens. An object 'S' is placed 24 cm above water surface. The location of its image is at 'x' cm above the bottom of the tank. Then 'x' is", "response_choices": "No response choices provided", "answer": "2", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 37, "question": "A series R-C combination is connected to an AC voltage of angular frequency \u03c9 = 500 radian/s. If the impedance of the R-C circuit is R\u221a1.25, the time constant (in millisecond) of the circuit is", "response_choices": "No response choices provided", "answer": "4", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 38, "question": "A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A \u00d7 10 (where 1 < A < 10). The value of 'Z' is", "response_choices": "No response choices provided", "answer": "7", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 39, "question": "One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.", "response_choices": "Matrix response", "answer": "A: p, r and t; B: p and r; C: q and s; D: r and t", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 40, "question": "Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as \u03bb1. Match each system with statements given in Column II describing the nature and wavelength of the standing waves.", "response_choices": "(A) Pipe closed at one end, (B) Pipe open at both ends, (C) Stretched wire clamped at both ends, (D) Stretched wire clamped at both ends and at mid-point", "answer": "A : p and t, B : p and s, C : q and s, D : q and r", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 41, "question": "Let P(6,3) be a point on the hyperbola (x^2/a^2) - (y^2/b^2) = 1. If the normal at the point P intersects the x-axis at (9,0), then the eccentricity of the hyperbola is", "response_choices": "(A) \u221a5/2, (B) \u221a3/2, (C) \u221a2, (D) \u221a3", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "A value of b for which the equations x^2 + bx - 1 = 0 and x^2 + x + b = 0, have one root in common is", "response_choices": "(A) -\u221a2, (B) -i\u221a3, (C) i\u221a5, (D) \u221a2", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let \u03c9 \u2260 1 be a cube root of unity and S be the set of all non-singular matrices of the form [1 a b; \u03c9 1 c; \u03c9^2 \u03c9 1], where each of a, b, and c is either \u03c9 or \u03c9^2. Then the number of distinct matrices in the set S is", "response_choices": "(A) 2, (B) 6, (C) 4, (D) 8", "answer": "A", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "The circle passing through the point (-1,0) and touching the y-axis at (0,2) also passes through the point", "response_choices": "(A) (3/2,0), (B) (-5/2,2), (C) (3,5/2), (D) (-4,0)", "answer": "D", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "If lim [1+\ud835\udc65ln(1+\ud835\udc4f\u00b2)] = 2\ud835\udc4fsin\u00b2\ud835\udf03, \ud835\udc4f>0 and \ud835\udf03\u2208(-\ud835\udf0b,\ud835\udf0b], then the value of \ud835\udf03 is", "response_choices": "A) \u00b1\ud835\udf0b/4, B) \u00b1\ud835\udf0b/3, C) \u00b1\ud835\udf0b/6, D) \u00b1\ud835\udf0b/2", "answer": "D", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "Let f:[-1,2]\u2192(0,\u221e) be a continuous function such that f(x)=f(1-x) for all x\u2208[-1,2]. Let R\u2081= \u222bxf(x)dx, and R\u2082 be the area of the region bounded by y=f(x), x=-1, x=2, and the x-axis. Then", "response_choices": "A) R\u2081=2R\u2082, B) R\u2081=3R\u2082, C) 2R\u2081=R\u2082, D) 3R\u2081=R\u2082", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let f(x)=x\u00b3 and g(x)=sinx for all x\u2208R. Then the set of all x satisfying (f\u2218g\u2218g\u2218f)(x)=(g\u2218g\u2218f)(x), where (f\u2218g)(x)=f(g(x)), is", "response_choices": "A) \u00b1\u221an\ud835\udf0b, n\u2208{0,1,2,...}, B) \u00b1\u221an\ud835\udf0b, n\u2208{1,2,...}, C) \ud835\udf0b/2+2n\ud835\udf0b, n\u2208{...,-2,-1,0,1,2,...}, D) 2n\ud835\udf0b, n\u2208{...,-2,-1,0,1,2,...}", "answer": "A", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Let (x,y) be any point on the parabola y\u00b2=4x. Let P be the point that divides the line segment from (0,0) to (x,y) in the ratio 1:3. Then the locus of P is", "response_choices": "A) x\u00b2=y, B) y\u00b2=2x, C) y\u00b2=x, D) x\u00b2=2y", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "If f(x)={ \u2212x, \u03c0/2 \u2264 x\u2264 \u03c0/2; \u2212cos x, \u2212\u03c0/2 < x \u2264 0; x\u22121, 0 < x \u2264 1; ln x, x>1,}, then", "response_choices": "(A) f(x) is continuous at x = \u03c0/2, (B) f(x) is not differentiable at x = 0, (C) f(x) is differentiable at x = 1, (D) f(x) is differentiable at x = 3/2", "answer": "ABCD", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then", "response_choices": "(A) P(E)=4/5, P(F)=3/5, (B) P(E)=1/5, P(F)=2/5, (C) P(E)=2/5, P(F)=1/5, (D) P(E)=3/5, P(F)=4/5", "answer": "AD", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let L be a normal to the parabola y^2 = 4x. If L passes through the point (9, 6), then L is given by", "response_choices": "(A) y - x + 3 = 0, (B) y + 3x - 33 = 0, (C) y + x - 15 = 0, (D) y - 2x + 12 = 0", "answer": "ABD", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Let f : (0,1) \u2192 R be defined by f(x) = (b - x)/(1 - bx), where b is a constant such that 0 < b < 1. Then", "response_choices": "(A) f is not invertible on (0, 1), (B) f \u2260 f^-1 on (0, 1) and f'(b) = 1/f'(0), (C) f = f^-1 on (0, 1) and f'(b) = 1/f'(0), (D) f^-1 is differentiable on (0, 1)", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let \u03c9 = e^(2i/3), and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x, a + b\u03c9 + c\u03c9^2 = y, a + b\u03c9^2 + c\u03c9 = z. Then the value of |x|^2 + |y|^2 + |z|^2 / |a|^2 + |b|^2 + |c|^2 is", "response_choices": "", "answer": "MARKS TO ALL", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "The number of distinct real roots of x^4 - 4x^3 + 12x^2 + x - 1 = 0 is", "response_choices": "", "answer": "2", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x \u2208 \u211d, where f'(x) denotes d f(x)/dx and g(x) is a given non-constant differentiable function on \u211d with g(0) = g(2) = 0. Then the value of y(2) is", "response_choices": "", "answer": "0", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let M be a 3x3 matrix satisfying M = [0 -1; 1 2; 0 3], M^-1 = [1 1; 1 1; 0 -1], and M^T = [1 0; 0 1; 1 12]. Then the sum of the diagonal entries of M is", "response_choices": "", "answer": "9", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Let a = -i - k, b = -i + j and c = i + 2j + 3k be three given vectors. If r is a vector such that r \u00d7 b = c \u00d7 b and r . a = 0, then the value of r.b is", "response_choices": "", "answer": "9", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "The straight line 2x - 3y = 1 divides the circular region x^2 + y^2 \u2264 6 into two parts. If S = {(2, 3), (5, 3), (1, -1), (1, 1)}, then the number of point(s) in S lying inside the smaller part is", "response_choices": "", "answer": "2", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "Match the statements given in Column I with the values given in Column II", "response_choices": "(A) If \u0101 = j + \u221a3 k\u0304 , b\u0304 = - j + \u221a3 k\u0304 and c\u0304 = 2\u221a3 k\u0304 form a triangle, then the internal angle of the triangle between \u0101 and b\u0304 is \n(B) If \u222b_0^\u03c0 (f(x) - 3x)dx = a^2 - b^2, then the value of f(\u03c0/6) is \n(C) The value of \u222b_(\u03c0/3)^(5\u03c0/6) (\u03c0^2/9) sec(\u03c0x) dx is \n(D) The maximum value of |Arg (1/(1-z))| for |z|=1, z\u22601 is given by", "answer": "A : q\nB : p or p, q, r, s and t\nC : s\nD : t", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Match the statements given in Column I with the intervals/union of intervals given in Column II", "response_choices": "(A) The set {Re(2iz / (1-z^2)) : z is a complex number, |z|=1, z != +1} is (p) (-\u221e, -1) \u222a (1, \u221e) \n\n(B) The domain of the function f(x) = sin^-1 (8(3)^(x+3) / (1-3^(x+1))) is (q) (-\u221e, 0) \u222a (0, \u221e)\n\n(C) If f(\u03b8) = [-tan \u03b8 tan \u03b8 1 / -1 -tan \u03b8 1], then the set {f(\u03b8) : 0 \u2264 \u03b8 < \u03c0/2} is (r) [2, \u221e) \n\n(D) If f(x) = x^(2/3) (3x-10), x \u2265 0, then f(x) is increasing in (s) (-\u221e, -1] \u222a [1, \u221e)", "answer": "A: s\nB: t\nC: r\nD: r", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2012_1.jsonl b/JEE_papers/JSON/JEE_2012_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..f83c835960ae7c67f9df15adae5a67a9aba7d0b1 --- /dev/null +++ b/JEE_papers/JSON/JEE_2012_1.jsonl @@ -0,0 +1,60 @@ +{"id": 1, "question": "A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed \u03c9, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains \u03c9 throughout. The magnitude of the torque (|\u03c4|) on the system about O, as a function of time is best represented by which plot?", "response_choices": "A, B, C, D", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures 2T and 3T respectively. The temperature of the middle (i.e. second) plate under steady state condition is", "response_choices": "(A) (65/2)*(1/T) (B) (97/4)*(1/T) (C) (97/2)*(1/T) (D) (97)*(1/T)", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field | E(r)| and the electric potential V(r) with the distance r from the centre, is best represented by which graph ?", "response_choices": "(A) |E(r)| and V(r) graphs (B) |E(r)| and V(r) graphs (C) |E(r)| and V(r) graphs (D) |E(r)| and V(r) graphs", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "In the determination of Young's modulus (Y = 4ML/\u03c0d^3) by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement", "response_choices": "(A) due to the errors in the measurements of d and l are the same. (B) due to the error in the measurement of d is twice that due to the error in the measurement of l. (C) due to the error in the measurement of l is twice that due to the error in the measurement of d. (D) due to the error in the measurement of d is four times that due to the error in the measurement of l.", "answer": "A", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A small block is connected to one end of a massless spring of un-stretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t = 0. It then executes simple harmonic motion with angular frequency \u03c9 = \u03c0/2 rad/s. Simultaneously at t = 0, a small pebble is projected with speed v from point P at an angle of 45\u00b0 as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is (take g = 10 m/s\u00b2)", "response_choices": "(A) \u221a50 m/s, (B) \u221a51 m/s, (C) \u221a52 m/s, (D) \u221a53 m/s", "answer": "A", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "Young's double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe widths recorded are \u03b2G, \u03b2R and \u03b2B, respectively. Then,", "response_choices": "(A) \u03b2G > \u03b2B > \u03b2R, (B) \u03b2B > \u03b2G > \u03b2R, (C) \u03b2R > \u03b2B > \u03b2G, (D) \u03b2R > \u03b2G > \u03b2B", "answer": "D", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed \u03c9. If the angular momentum of the system, calculated about O and P are denoted by Lo and Lp respectively, then", "response_choices": "A) Lo and Lp do not vary with time. B) Lo varies with time while Lp remains constant. C) Lo remains constant while Lp varies with time. D) Lo and Lp both vary with time.", "answer": "C", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the r m s speeds (v_rms(helium))/(v_rms(argon)) is", "response_choices": "(A) 0.32, (B) 0.45, (C) 2.24, (D) 3.16", "answer": "D", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference X. A proton is released at rest midway between the two plates. It is found to move at 45\u00b0 to the vertical JUST after release. Then X is nearly", "response_choices": "(A) 1 x 10^-3 V, (B) 1 x 10^-7 V, (C) 1 x 10^-9 V, (D) 1x 10^-10 V", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature R = 14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be", "response_choices": "(A) - 280.0 cm, (B) 40.0 cm, (C) 21.5 cm, (D) 13.3 cm", "answer": "B", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "A cubical region of side a has its centre at the origin. It encloses three fixed point charges, \u2212q at (0, \u2212a/4,0), +3q at (0,0,0) and \u2212q at (0,+a/4,0). Choose the correct option(s).", "response_choices": "(A) The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the plane x = \u2212 a/2. (B) The net electric flux crossing the plane y = +a/2 is more than the net electric flux crossing the plane y = \u2212 a/2. (C) The net electric flux crossing the entire region is q/\u03b50. (D) The net electric flux crossing the plane z = +a/2 is equal to the net electric flux crossing the plane x = +a/2.", "answer": "ACD", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "For the resistance network shown in the figure, choose the correct option(s).", "response_choices": "(A) The current through P Q is zero. (B) I1 = 3 A. (C) The potential at S is less than that at Q. (D) I2 = 2 A.", "answer": "ABCD", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "A small block of mass of 0.1 kg lies on a fixed inclined plane P Q which makes an angle \u03b8 with the horizontal. A horizontal force of 1 N acts on the block through its center of mass as shown in the figure. The block remains stationary if (take g = 10 m/s\u00b2)", "response_choices": "(A) \u03b8 = 45\u00b0 (B) \u03b8 > 45\u00b0 and a frictional force acts on the block towards P. (C) \u03b8 > 45\u00b0 and a frictional force acts on the block towards Q. (D) \u03b8 < 45\u00b0 and a frictional force acts on the block towards Q.", "answer": "AC", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields E = E0 j and B = B0 i. At time t = 0, this charge has velocity v in the x-y plane, making an angle \u03b8 with the x-axis. Which of the following option(s) is(are) correct for time t > 0?", "response_choices": "(A) If \u03b8 = 0\u00b0, the charge moves in a circular path in the x-z plane. (B) If \u03b8 = 0\u00b0, the charge undergoes helical motion with constant pitch along the y-axis. (C) If \u03b8 = 10\u00b0, the charge undergoes helical motion with its pitch increasing with time, along the y-axis. (D) If \u03b8 = 90\u00b0, the charge undergoes linear but accelerated motion along the y-axis.", "answer": "CD", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,", "response_choices": "(A) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (B) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is open. (C) a low-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed. (D) a high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.", "answer": "BD", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "An infinitely long solid cylinder of radius R has a uniform volume charge density \u03c1. It has a spherical cavity of radius R/2 with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point P, which is at a distance 2R from the axis of the cylinder, is given by the expression 23\u03c1R/16\u03c0\u03b5\u2080. The value of k is", "response_choices": "", "answer": "6", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by N/12 \u03bc\u2080aJ, then the value of N is", "response_choices": "", "answer": "5", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "A lamina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R, as shown in the figure. The moment of inertia of this lamina about axes passing through O and P is Io and Ip, respectively. Both these axes are perpendicular to the plane of the lamina. The ratio Ip/Io to the nearest integer is", "response_choices": "No response choices provided", "answer": "3", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "A circular wire loop of radius R is placed in the x-y plane centered at the origin O. A square loop of side a (a << R) having two turns is placed with its center at z = \u221a3 R along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of 45\u00b0 with respect to the z-axis. If the mutual inductance between the loops is given by \u03bc0a^2/2\u221a2 R, then the value of p is", "response_choices": "No response choices provided", "answer": "7", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 20, "question": "A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is: (take the proton mass, mp = (5/3) x 10^-27 kg; h/e = 4.2 x 10^15 J.s/C; 4\u03c0\u03b50 = 9 x 10^9 m/F; 1 fm = 10^-15 m)", "response_choices": "No response choices provided", "answer": "7", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 21, "question": "In allene (C3H4), the type(s) of hybridisation of the carbon atoms is (are)", "response_choices": "(A) sp and sp\u00b3 (B) sp and sp\u00b2 (C) only sp\u00b2 (D) sp\u00b2 and sp\u00b3", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "For one mole of a van der Waals gas when b = 0 and T = 300 K, the PV vs. 1/V plot is shown below. The value of the van der Waals constant a (atm.liter\u00b2 mol\u207b\u00b2) is", "response_choices": "(A) 1.0 (B) 4.5 (C) 1.5 (D) 3.0", "answer": "C", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 23, "question": "The number of optically active products obtained from the complete ozonolysis of the given compound is", "response_choices": "(A) 0, (B) 1, (C) 2, (D) 4", "answer": "A", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 24, "question": "A compound M\u00a5Xq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown below. The empirical formula of the compound is", "response_choices": "(A) MX, (B) MX\u2082, (C) M\u2082X, (D) M\u2086X\u2081\u2084", "answer": "B", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 25, "question": "The number of aldol reaction(s) that occurs in the given transformation is", "response_choices": "(A) 1, (B) 2, (C) 3, (D) 4", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 26, "question": "The colour of light absorbed by an aqueous solution of CuSO4 is", "response_choices": "(A) orange-red, (B) blue-green, (C) yellow, (D) violet", "answer": "A", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "The carboxyl functional group (\u2013COOH) is present in", "response_choices": "(A) picric acid, (B) barbituric acid, (C) ascorbic acid, (D) aspirin", "answer": "D", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0 is Bohr radius]", "response_choices": "(A) (h^2)/(4\u03c0^2ma0^2), (B) (h^2)/(16\u03c0^2ma0^2), (C) (h^2)/(32\u03c0^2ma0^2), (D) (h^2)/(64\u03c0^2ma0^2)", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "Which ordering of compounds is according to the decreasing order of the oxidation state of nitrogen?", "response_choices": "(A) HNO3, NO, NH4Cl, N2, (B) HNO3, NO, N2, NH4Cl, (C) HNO3, NH4Cl, NO, N2, (D) NO, HNO3, NH4Cl, N2", "answer": "B", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "As per IUPAC nomenclature, the name of the complex [Co(H2O)4(NH3)2]Cl3 is", "response_choices": "(A) Tetraaquadiaminecobalt (III) chloride, (B) Tetraaquadimminecobalt (III) chloride, (C) Diaminetetraaquacobalt (III) chloride, (D) Diamminetraaquacobalt (III) chloride", "answer": "D", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "Identify the binary mixture(s) that can be separated into individual compounds, by differential extraction, as shown in the given scheme.", "response_choices": "(A) C6H5OH and C6H5COOH, (B) C6H5COOH and C6H5CH3OH, (C) C6H5CH2OH and C6H5OH, (D) C6H5CH2OH and C6H5CH2COOH", "answer": "BD", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "Choose the correct reason(s) for the stability of the lyophobic colloidal particles. (A) Preferential adsorption of ions on their surface from the solution, (B) Preferential adsorption of solvent on their surface from the solution, (C) Attraction between different particles having opposite charges on their surface, (D) Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles", "response_choices": "(A) Preferential adsorption of ions on their surface from the solution, (B) Preferential adsorption of solvent on their surface from the solution, (C) Attraction between different particles having opposite charges on their surface, (D) Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles", "answer": "AD", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "Which of the following molecules, in pure form, is (are) unstable at room temperature?", "response_choices": "(A) [Cyclohexane ring], (B) [Benzene ring], (C) [Cycloheptatriene oxide], (D) [Benzene oxide]", "answer": "BC", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 34, "question": "Which of the following hydrogen halides react(s) with AgNO3(aq) to give a precipitate that dissolves in Na2S2O3(aq) ?", "response_choices": "(A) HCl (B) HF (C) HBr (D) HI", "answer": "ACD", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "For an ideal gas, consider only P-V work in going from an initial state X to the final state Z. The final state Z can be reached by either of the two paths shown in the figure. Which of the following choice(s) is (are) correct ? [Take \u2206S as change in entropy and w as work done]", "response_choices": "(A) \u2206Sx\u2192z = \u2206Sx\u2192y + \u2206Sy\u2192z (B) wx\u2192z = wx\u2192y + wy\u2192z (C) wx\u2192y\u2192z = wx\u2192y (D) \u2206Sx\u2192y\u2192z = \u2206Sx\u2192y", "answer": "AC", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 36, "question": "The substituents R1 and R2 for nine peptides are listed in the table given below. How many of these peptides are positively charged at pH = 7.0 ?", "response_choices": "", "answer": "4", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table ?", "response_choices": "", "answer": "8", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 38, "question": "When the following aldohexose exists in its D-configuration, the total number of stereoisomers in its pyranose form is CHO CH2 CHOH CHOH CHOH CH2OH", "response_choices": "No response choices provided", "answer": "8", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "29.2% (w/w) HCl stock solution has a density of 1.25 g mL-1. The molecular weight of HCl is 36.5 g mol-1. The volume (mL) of stock solution required to prepare a 200 mL solution of 0.4 M HCl is", "response_choices": "No response choices provided", "answer": "8", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of [t1/8] / [t1/10] x 10? (take loge2 = 0.3)", "response_choices": "No response choices provided", "answer": "9", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is", "response_choices": "(A) 75, (B) 150, (C) 210, (D) 243", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Let f(x) = { (x^2 cos (\u03c0/x)), x \u2260 0, x \u2208 R, 0, x = 0 } then f is", "response_choices": "(A) differentiable both at x = 0 and at x = 2, (B) differentiable at x = 0 but not differentiable at x = 2, (C) not differentiable at x = 0 but differentiable at x = 2, (D) differentiable neither at x = 0 nor at x = 2", "answer": "B", "page_number": 19, "image_available": "yes", "question_subject": "mathematics"} +{"id": 43, "question": "The function f : [0, 3] \u2192 [1, 29], defined by f(x) = 2x^3 \u2212 15x^2 + 36x + 1, is", "response_choices": "(A) one-one and onto, (B) onto but not one-one, (C) one-one but not onto, (D) neither one-one nor onto", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "If lim (x\u2192\u221e) (x^2 + x + 1 / x + 1) \u2212 ax \u2212 b = 4 , then", "response_choices": "(A) a = 1, b = 4, (B) a = 1, b = \u2212 4, (C) a = 2, b = \u2212 3, (D) a = 2, b = 3", "answer": "B", "page_number": 19, "image_available": "yes", "question_subject": "mathematics"} +{"id": 45, "question": "Let z be a complex number such that the imaginary part of z is nonzero and a = z\u00b2 + z + 1 is real. Then a cannot take the value", "response_choices": "(A) - 1, (B) 1/3, (C) 1/2, (D) 3/4", "answer": "D", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "The ellipse E\u2081 : x\u00b2/9 + y\u00b2/4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E\u2082 passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse E\u2082 is", "response_choices": "(A) \u221a2/2, (B) \u221a3/2, (C) 1/2, (D) 3/4", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let P = [aij] be a 3x3 matrix and let Q = [bij], where bij = 2^(i+j-2)*aij for 1 \u2264 i, j \u2264 3. If the determinant of P is 2, then the determinant of the matrix Q is", "response_choices": "(A) 2\u00b9\u2070, (B) 2\u00b9\u00b9, (C) 2\u00b9\u00b2, (D) 2\u00b9\u00b3", "answer": "D", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "The integral \u222b (sec\u00b2 x / (sec x + tan x)\u00bd) dx equals (for some arbitrary constant K)", "response_choices": "(A) 1 / (sec x + tan x)\u00b9/\u00b2 {[1 / 11 - 1/7 (sec x + tan x)\u00b2] + K}, (B) 1 / (sec x + tan x)\u00b9/\u00b2 {[1 / 11 + 1/7 (sec x + tan x)\u00b2] + K}, (C) 1 / (sec x + tan x)\u00b9/\u00b2 {[1 / 11 - 1/7 (sec x + tan x)\u00b2] + K}, (D) 1 / (sec x + tan x)\u00b9/\u00b2 {[1 / 11 + 1/7 (sec x + tan x)\u00b2] + K}", "answer": "C", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "The point P is the intersection of the straight line joining the points Q(2,3.5) and R(1, -1, 4) with the plane 5x - 4y - z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR, then the length of the line segment PS is", "response_choices": "(A) 1/\u221a2, (B) \u221a2, (C) 2, (D) 2\u221a2", "answer": "A", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line 4x - 5y = 20 to the circle x\u00b2 + y\u00b2 = 9 is", "response_choices": "(A) 20(x\u00b2 + y\u00b2) - 36x + 45y = 0, (B) 20(x\u00b2 + y\u00b2) + 36x - 45y = 0, (C) 36(x\u00b2 + y\u00b2) - 20x + 45y = 0, (D) 36(x\u00b2 + y\u00b2) + 20x - 45y = 0", "answer": "A", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let \u03b8, \u03c6\u2208 [0, 2\u03c0] be such that 2 cos \u03b8 (1\u2212 sin \u03c6) = sin^2 \u03b8 (tan (\u03b8/2) + cot (\u03b8/2)) cos \u03c6 \u2212 1, tan ( 2\u03c0\u2212 \u03b8 ) > 0 and \u22121 < sin \u03b8 < \u2212 \u221a3/2. Then \u03c6 cannot satisfy", "response_choices": "(A) 0 < \u03c6 < \u03c0/2 (B) \u03c0/2 < \u03c6 < 4\u03c0/3 (C) 4\u03c0/3 < \u03c6 < 3\u03c0/2 (D) 3\u03c0/2 < \u03c6 < 2\u03c0", "answer": "ACD", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Let S be the area of the region enclosed by y = e^(x^2), y = 0, x = 0, and x = 1. Then", "response_choices": "(A) S \u2265 1/e (B) S \u2265 1 \u2212 1/e (C) S \u2264 1/4 (1 + 1/\u221ae) (D) S \u2264 1/\u221a2 + 1/e (1 \u2212 1/\u221a2)", "answer": "ABD", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "A ship is fitted with three engines E1, E2 and E3. The engines function independently of each other with respective probabilities 1/2, 1/4 and 1/4. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let X1, X2 and X3 denote respectively the events that the engines E1, E2 and E3 are functioning. Which of the following is (are) true ?", "response_choices": "(A) P [ X1^c | X ] = 3/16, (B) P (Exactly two engines of the ship are functioning | X) = 7/8, (C) P [ X | X2 ] = 5/16, (D) P [ X | X1 ] = 7/16", "answer": "BD", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Tangents are drawn to the hyperbola x^2/9 - y^2/4 = 1, parallel to the straight line 2x - y = 1. The points of contact of the tangents on the hyperbola are", "response_choices": "(A) (9/\u221a(2\u221a2), 1/\u221a2), (B) ( -9/\u221a(2\u221a2), -1/\u221a2), (C) (3\u221a3, -2\u221a2), (D) (-3\u221a3, 2\u221a2)", "answer": "AB", "page_number": 23, "image_available": "yes", "question_subject": "mathematics"} +{"id": 55, "question": "If y (x) satisfies the differential equation y' - y tan x = 2x sec x and y (0) = 0 , then", "response_choices": "(A) y (\u03c0/4) = (\u03c0^2/(8\u221a2)), (B) y' (\u03c0/4) = (\u03c0^2/18), (C) y (\u03c0/3) = (\u03c0^2/9), (D) y' (\u03c0/3) = (4\u03c0 + 2\u03c0^2)/(3\u221a3)", "answer": "AD", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let f : IR \u2192 IR be defined as f(x) = [x] + [x^2 - 1]. The total number of points at which f attains either a local maximum or a local minimum is", "response_choices": "", "answer": "5", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "The value of 6 + log\u2082 ( (1/\u221a2) / (4 - (1/\u221a2)) / (4 - (1/\u221a2)) / (4 - (1/\u221a2)) ... ) is", "response_choices": "", "answer": "4", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p'(0) is", "response_choices": "", "answer": "9", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "If \u0101, b\u0304 and c\u0304 are unit vectors satisfying | \u0101 - b\u0304 |^2 + | b\u0304 - c\u0304 |^2 + | c\u0304 - \u0101 |^2 = 9, then | 2\u0101 + 5b\u0304 + 5c\u0304 | is", "response_choices": "", "answer": "3", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Let S be the focus of the parabola y^2 = 8x and let PQ be the common chord of the circle x^2 +y^2 - 2x - 4y = 0 and the given parabola. The area of the triangle PQS is", "response_choices": "", "answer": "4", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2012_2.jsonl b/JEE_papers/JSON/JEE_2012_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..e3f27b77b082157b50265b1cd31f5680009414bc --- /dev/null +++ b/JEE_papers/JSON/JEE_2012_2.jsonl @@ -0,0 +1,61 @@ +{"id": 1, "question": "A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector k\u0302 is coming out of the plane of the paper. The magnetic moment of the current loop is", "response_choices": "(A) a^2Ik\u0302, (B) (\u03c0+1)/2a^2Ik\u0302, (C) -(\u03c0+1)/2a^2Ik\u0302, (D) (2\u03c0+1)a^2Ik\u0302", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "An infinitely long hollow conducting cylinder with inner radius R/2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, |B| as a function of the radial distance r from the axis is best represented by", "response_choices": "(A), (B), (C), (D) [options represented by graphs]", "answer": "D", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If \u03c1c is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is", "response_choices": "(A) more than half-filled if \u03c1c is less than 0.5. (B) more than half-filled if \u03c1c is more than 1.0. (C) half-filled if \u03c1c is more than 0.5. (D) less than half-filled if \u03c1c is less than 0.5.", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "In the given circuit, a charge of +80 \u03bcC is given to the upper plate of the 4 \u03bcF capacitor. Then in the steady state, the charge on the upper plate of the 3 \u03bcF capacitor is", "response_choices": "(A) +32 \u03bcC (B) +40 \u03bcC (C) +48 \u03bcC (D) +80 \u03bcC", "answer": "C", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "Two moles of ideal helium gas are in a rubber balloon at 30\u00b0C. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to 35\u00b0C. The amount of heat required in raising the temperature is nearly (take R = 8.31 J/mol.K)", "response_choices": "(A) 62 J (B) 104 J (C) 124 J (D) 208 J", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "Consider a disc rotating in the horizontal plane with a constant angular speed \u03c9 about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R. The velocity of projection is in the y-z plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) \u03c9 remains constant throughout. Then", "response_choices": "(A) P lands in the shaded region and Q in the unshaded region.\n(B) P lands in the unshaded region and Q in the shaded region.\n(C) Both P and Q land in the unshaded region.\n(D) Both P and Q land in the shaded region.", "answer": "C or D", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "A student is performing the experiment of Resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38\u00b0C in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is", "response_choices": "(A) 14.0 cm\t\t(B) 15.2 cm\t\t(C) 16.4 cm\t\t(D) 17.6 cm", "answer": "B", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed \u03c9. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is vr. In one time period (T) of rotation of the discs, vr as a function of time is best represented by", "response_choices": "A, B, C, D", "answer": "A", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "For light incident from air on a meta-material, the appropriate ray diagram is", "response_choices": "(A), (B), (C), (D)", "answer": "C", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "Most materials have the refractive index, n > 1. So, when a light ray from air enters a naturally occurring material, then by Snell's law, (sin \u03b81) / (sin \u03b82) = n2 / n1, it is understood that the refracted ray bends towards the normal. But it never emerges on the same side of the normal as the incident ray. According to electromagnetism, the refractive index of the medium is given by the relation, n = (c / v) = \u00b1\u221a(\u03b5r\u03bcr), where c is the speed of electromagnetic waves in vacuum, v its speed in the medium, \u03b5r and \u03bcr are the relative permittivity and permeability of the medium respectively. In normal materials, both \u03b5r and \u03bcr are positive, implying positive n for the medium. When both \u03b5r and \u03bcr are negative, one must choose the negative root of n. Such negative refractive index materials can now be artificially prepared and are called meta-materials. They exhibit significantly different optical behavior, without violating any physical laws. Since n is negative, it results in a change in the direction of propagation of the refracted light. However, similar to normal materials, the frequency of light remains unchanged upon refraction even in meta-materials.", "response_choices": "N/A", "answer": "N/A", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "Choose the correct statement.", "response_choices": "(A) The speed of light in the meta-material is v = c|r|, (B) The speed of light in the meta-material is v = c/|r|, (C) The speed of light in the meta-material is v = c, (D) The wavelength of the light in the meta-material (\u03bbm) is given by \u03bbm = \u03bbair|r|, where \u03bbair is the wavelength of the light in air.", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "What is the maximum energy of the anti-neutrino?", "response_choices": "(A) Zero. (B) Much less than 0.8 \u00d7 10\u2076 eV. (C) Nearly 0.8 \u00d7 10\u2076 eV. (D) Much larger than 0.8 \u00d7 10\u2076 eV.", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "If the anti-neutrino had a mass of 3 eV/c\u00b2 (where c is the speed of light) instead of zero mass, what should be the range of the kinetic energy, K, of the electron?", "response_choices": "(A) 0 \u2264 K \u2264 0.8 \u00d7 10\u2076 eV (B) 3.0 eV \u2264 K \u2264 0.8 \u00d7 10\u2076 eV (C) 3.0 eV \u2264 K < 0.8 \u00d7 10\u2076 eV (D) 0 \u2264 K < 0.8 \u00d7 10\u2076 eV", "answer": "D", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?", "response_choices": "(A) It is vertical for both the cases (a) and (b). (B) It is vertical for case (a); and is at 45\u00b0 to the x-z plane and lies in the plane of the disc for case (b). (C) It is horizontal for case (a); and is at 45\u00b0 to the x-z plane and is normal to the plane of the disc for case (b). (D) It is vertical for case (a); and is at 45\u00b0 to the x-z plane and is normal to the plane of the disc for case (b).", "answer": "A", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?", "response_choices": "(A) It is \u221a2\u03c9 for both the cases. (B) It is \u03c9 for case (a); and \u03c9/\u221a2 for case (b). (C) It is \u03c9 for case (a); and \u221a2\u03c9 for case (b). (D) It is \u03c9 for both the cases.", "answer": "D", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "In the given circuit, the AC source has \u03c9 = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)", "response_choices": "(A) The current through the circuit, I is 0.3 A.\n(B) The current through the circuit, I is 0.3\u221a2 A.\n(C) The voltage across 100 \u03a9 resistor = 10 \u221a2 V.\n(D) The voltage across 50 \u03a9 resistor = 10 V.", "answer": "C or AC", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)", "response_choices": "(A) The emf induced in the loop is zero if the current is constant.\n(B) The emf induced in the loop is finite if the current is constant.\n(C) The emf induced in the loop is zero if the current decreases at a steady rate.\n(D) The emf induced in the loop is finite if the current decreases at a steady rate.", "answer": "AC", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown in the figure. Given that K = 1/(4\u03c0\u03b50 \u00d7 L), which of the following statement(s) is(are) correct?", "response_choices": "(A) The electric field at O is 6K along OD. \n(B) The potential at O is zero. \n(C) The potential at all points on the line PR is same. \n(D) The potential at all points on the line ST is same.", "answer": "ABC", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statement(s) is(are) correct?", "response_choices": "(A) Both cylinders P and Q reach the ground at the same time. \n(B) Cylinder P has larger linear acceleration than cylinder Q. \n(C) Both cylinders reach the ground with same translational kinetic energy. \n(D) Cylinder Q reaches the ground with larger angular speed.", "answer": "D", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "Two spherical planets P and Q have the same uniform density \u03c1, masses Mp and Mq, and surface areas A and 4A, respectively. A spherical planet R also has uniform density \u03c1 and its mass is (Mp + Mq). The escape velocities from the planets P, Q and R, are Vp, Vq and Vr, respectively. Then", "response_choices": "(A) Vq > Vr > Vp \t(B) Vr > Vq > Vp \t(C) Vr/ Vp = 3 \t(D) Vp/ Vq = 1/2", "answer": "BD", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 20, "question": "The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed \u03c9 and (ii) an inner disc of radius 2R rotating anti-clockwise with angular speed \u03c9/2. The ring and disc are separated by frictionless ball bearings. The system is in the x-z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30\u00b0 with the horizontal. Then with respect to the horizontal surface,", "response_choices": "(A) the point O has a linear velocity 3R\u03c9\u03b9\u0302\n(B) the point P has a linear velocity (1/4)R\u03c9\u03b9\u0302 + (\u221a3/4)R\u03c9\u03ba\u0302\n(C) the point P has a linear velocity (3/4)R\u03c9\u03b9\u0302 - (\u221a3/4)R\u03c9\u03ba\u0302\n(D) the point P has a linear velocity |(3 - \u221a3/4)R\u03c9\u03b9\u0302 + (1/4)R\u03c9\u03ba\u0302|", "answer": "AB", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 21, "question": "NiCl2(P(C2H5)3)2(C7H8))2 exhibits temperature dependent magnetic behaviour (paramagnetic / diamagnetic). The coordination geometries of Ni2+ in the paramagnetic and diamagnetic states are respectively", "response_choices": "(A) tetrahedral and tetrahedral, (B) square planar and square planar, (C) tetrahedral and square planar, (D) square planar and tetrahedral", "answer": "C", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "In the cyanide extraction process of silver from argentite ore, the oxidizing and reducing agents used are", "response_choices": "(A) O2 and CO respectively., (B) O2 and Zn dust respectively., (C) HNO3 and Zn dust respectively., (D) HNO3 and CO respectively.", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "The reaction of white phosphorus with aqueous NaOH gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively", "response_choices": "(A) redox reaction; \u2013 3 and \u2013 5, (B) redox reaction; + 3 and + 5, (C) disproportionation reaction; \u2013 3 and + 5, (D) disproportionation reaction; \u2013 3 and + 3", "answer": "Zero Marks to all", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "The shape of XeO3F2 molecule is", "response_choices": "(A) trigonal bipyramidal, (B) square planar, (C) tetrahedral, (D) see-saw", "answer": "D", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "For a dilute solution containing 2.5 g of a non-volatile non-electrolyte solute in 100 g of water, the elevation in boiling point at 1 atm pressure is 2\u00b0C. Assuming concentration of solute is much lower than the concentration of solvent, the vapour pressure (mm of Hg) of the solution is (take Kb = 0.76 K kg mol^-1)", "response_choices": "(A) 724, (B) 740, (C) 736, (D) 718", "answer": "A", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "The compound that undergoes decarboxylation most readily under mild condition is", "response_choices": "(A) Structure1, (B) Structure2, (C) Structure3, (D) Structure4", "answer": "B", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 27, "question": "Using the data provided, calculate the multiple bond energy (kJ mol^-1) of a C\u2261C bond in C\u2082H\u2082. That energy is (take the bond energy of a C-H bond as 350 kJ mol^-1.)", "response_choices": "A) 1165, B) 837, C) 865, D) 815", "answer": "D", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "The major product H of the given reaction sequence is CH\u2083 \u2013 CH\u2082 \u2013 CO \u2013 CH\u2083 \u2192 G \u2192 H", "response_choices": "A) CH\u2083 \u2013 CH = C \u2013 COOH, B) CH\u2083 \u2013 CH = C \u2013 CN, C) CH\u2083 \u2013 CH\u2082 \u2013 C \u2013 COOH, D) CH\u2083 \u2013 CH = C \u2013 CO \u2013 NH\u2082", "answer": "A", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 29, "question": "Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is", "response_choices": "(A) Cl2O, (B) Cl2O7, (C) ClO2, (D) Cl2O6", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "25 mL of household bleach solution was mixed with 30 mL of 0.50 M KI and 10 mL of 4 N acetic acid. In the titration of the liberated iodine, 48 mL of 0.25 N Na2S2O3 was used to reach the end point. The molarity of the household bleach solution is", "response_choices": "(A) 0.48 M, (B) 0.96 M, (C) 0.24 M, (D) 0.024 M", "answer": "C", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "The solubility product (Ksp: mol3 dm-9) of MX3 at 298 K based on the information available for the given concentration cell is (take 2.303 \u00d7 R \u00d7 298/F = 0.059 V)", "response_choices": "A) 1\u00d710^-15, B) 4\u00d710^-15, C) 1\u00d710^-12, D) 4\u00d710^-12", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "The value of \u0394 G (kJ mol^-1) for the given cell is (take 1F = 96500 C mol^-1)", "response_choices": "A) \u22125.7, B) 5.7, C) 11.4, D) \u221211.4", "answer": "D", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "The compound I is", "response_choices": "(A) O-H (B) -OH (C) O-CH3 (D) H-H-H", "answer": "A", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 34, "question": "The compound K is", "response_choices": "(A) (B) O-O (C) O (D) O", "answer": "C", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 35, "question": "The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement(s) is (are) correct?", "response_choices": "(A) T1 = T2, (B) T3 > T1, (C) wisothermal > wadiabatic, (D) \u0394Uisothermal > \u0394Uadiabatic", "answer": "ACD or AD", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 36, "question": "The given graphs / data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and pressure. Which of the following choice(s) about I, II, III and IV is (are) correct?", "response_choices": "(A) I is physisorption and II is chemisorption (B) I is physisorption and III is chemisorption (C) IV is chemisorption and II is chemisorption (D) IV is chemisorption and III is chemisorption", "answer": "AC", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "For the given aqueous reactions, which of the statement(s) is (are) true ?", "response_choices": "(A) The first reaction is a redox reaction.\n(B) White precipitate is Zn\u2083[Fe(CN)\u2086]\u2082.\n(C) Addition of filtrate to starch solution gives blue colour.\n(D) White precipitate is soluble in NaOH solution.", "answer": "ACD", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 38, "question": "With respect to graphite and diamond, which of the statement(s) given below is (are) correct?", "response_choices": "(A) Graphite is harder than diamond. (B) Graphite has higher electrical conductivity than diamond. (C) Graphite has higher thermal conductivity than diamond. (D) Graphite has higher C-C bond order than diamond.", "answer": "BD", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "With reference to the scheme given, which of the given statment(s) about T, U, V and W is (are) correct ?", "response_choices": "(A) T is soluble in hot aqueous NaOH (B) U is optically active (C) Molecular formula of W is C10H18O4 (D) V gives effervescence on treatment with aqueous NaHCO3", "answer": "ACD", "page_number": 22, "image_available": "yes", "question_subject": "chemistry"} +{"id": 40, "question": "Which of the given statement(s) about M, O, P and Q with respect to M is (are) correct?", "response_choices": "(A) M and N are non-mirror image stereoisomers, (B) M and O are identical, (C) M and P are enantiomers, (D) M and Q are identical", "answer": "ABC", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 41, "question": "The equation of a plane passing through the line of intersection of the planes x + 2y + 3z = 2 and x - y + z = 3 and at a distance 2/\u221a3 from the point (3, 1, - 1) is", "response_choices": "(A) 5x - 11y + z = 17, (B) \u221a(2x + y = 3\u221a2 -1), (C) x + y + z = \u221a3, (D) x - \u221a2y = 1 - \u221a2", "answer": "A", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Let PQR be a triangle of area \u0394 with a = 2, b = 7/2 and c = 5/2, where a, b and c are the lengths of the sides of the triangle opposite to the angles at P, Q and R respectively. Then 2 sin P - sin 2 P / 2 sin P + sin 2 P equals", "response_choices": "(A) 3/4\u039b, (B) 45/4\u039b, (C) (3/4\u039b)^2, (D) (45/4\u039b)^2", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "If a and b are vectors such that |a + b| = \u221a29 and a \u00d7 (2i + 3j + 4k) = (2i + 3j + 4k) \u00d7 b, then a possible value of (a + b)\u00b7(\u20137i + 2j + 3k) is", "response_choices": "(A) 0, (B) 3, (C) 4, (D) 8", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "If P is a 3 x 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 x 3 identity matrix, then there exists a column matrix X = [x y z]T such that", "response_choices": "(A) PX = [0 0 0]T, (B) PX = X, (C) PX = 2X, (D) PX = - X", "answer": "D", "page_number": 25, "image_available": "yes", "question_subject": "mathematics"} +{"id": 45, "question": "Let \u03b1(a) and \u03b2(a) be the roots of the equation \u221a(1+a-1)x^2 + (\u221a(1+a-1)x + (\u221a(1+a-1) = 0 where a > -1. Then lim a\u21920+ \u03b1(a) and lim a\u21920+ \u03b2(a) are", "response_choices": "(A) -5/2 and 1, (B) -1/2 and -1, (C) -7/2 and 2, (D) -9/2 and 3", "answer": "B", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is", "response_choices": "(A) 91/216, (B) 108/216, (C) 125/216, (D) 127/216", "answer": "A", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "The value of the integral \u222b(\u03c0/2)(-\u03c0/2) (x^2 + ln(\u03c0+x/\u03c0-x))cosx dx is", "response_choices": "(A) 0, (B) \u03c0^2/2 - 4, (C) \u03c0^2/2 + 4, (D) \u03c0^2/2", "answer": "B", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Let a1, a2, a3, ... be in harmonic progression with a1 = 5 and a20 = 25. The least positive integer n for which an < 0 is", "response_choices": "(A) 22, (B) 23, (C) 24, (D) 25", "answer": "D", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "The value of b_n is", "response_choices": "(A) 7, (B) 8, (C) 9, (D) 11", "answer": "B", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Which of the following is correct?", "response_choices": "(A) a_n = a_6 + a_5, (B) c_7 \u2260 c_6 + c_5, (C) b_7 \u2260 b_6 + c_6, (D) a_7 = c_7 + b_6", "answer": "A", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Which of the following is true?", "response_choices": "(A) g is increasing on (1, \u221e) \n(B) g is decreasing on (1, \u221e) \n(C) g is increasing on (1, 2) and decreasing on (2, \u221e) \n(D) g is decreasing on (1, 2) and increasing on (2, \u221e)", "answer": "B", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 52, "question": "Consider the statements : \n\nP : There exists some x \u2208 \u211d such that f (x) + 2x = 2(1 + x\u00b2) \n\nQ : There exists some x \u2208 \u211d such that 2f (x) + 1= 2x(1 + x) \n\nThen", "response_choices": "(A) both P and Q are true \n(B) P is true and Q is false \n(C) P is false and Q is true \n(D) both P and Q are false", "answer": "C", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 53, "question": "A possible equation of L is", "response_choices": "A) x - \u221a3 y = 1 , B) x + \u221a3 y = 1 , C) x - \u221a3 y = -1 , D) x + \u221a3 y = 5", "answer": "A", "page_number": 28, "image_available": "yes", "question_subject": "mathematics"} +{"id": 54, "question": "A common tangent of the two circles is", "response_choices": "A) x = 4 , B) y = 2 , C) x + \u221a3 y = 4 , D) x + 2\u221a2 y = 6", "answer": "D", "page_number": 28, "image_available": "yes", "question_subject": "mathematics"} +{"id": 55, "question": "For every integer n, let an and bn be real numbers. Let function f : R \u2192 R be given by f(x) = { an + sin \u03c0 x, for x \u2208 [2n, 2n + 1] for all integers n. bn + cos \u03c0 x, for x \u2208 (2n \u2212 1, 2n) If f is continuous, then which of the following hold(s) for all n?", "response_choices": "(A) an-1 - bn-1 = 0 (B) an - bn = 1 (C) an - bn+1 = 1 (D) an-1 - bn = -1", "answer": "BD", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "If f (x) = \u222b x 0 e2 (t \u2212 2)(t \u2212 3) dt for all x \u2208 (0,\u221e) , then", "response_choices": "(A) f has a local maximum at x = 2 (B) f is decreasing on (2, 3) (C) there exists some c \u2208 (0, \u221e) such that f \u2033(c) = 0 (D) f has a local minimum at x = 3", "answer": "ABCD", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "If the straight lines x-1 = y+1-z/k and x+1 = y+1-z/5 are coplanar, then the plane(s) containing these two lines is(are)", "response_choices": "(A) y + 2z = -1, (B) y + z = -1, (C) y - z = -1, (D) y - 2z = -1", "answer": "BC", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Let X and Y be two events such that P(X | Y) = 1/2, P(Y | X) = 1/3 and P(X \u2229 Y) = 1/6. Which of the following is (are) correct?", "response_choices": "(A) P(X U Y) = 2/3, (B) X and Y are independent, (C) X and Y are not independent, (D) P(X^c \u2229 Y) = 1/3", "answer": "AB", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "If the adjoint of a 3x3 matrix P is [1 4 4, 2 1 7, 1 1 3], then the possible value(s) of the determinant of P is (are)", "response_choices": "(A) \u22122, (B) \u22121, (C) 1, (D) 2", "answer": "AD", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Let f : (-1, 1) \u2192 IR be such that f (cos 4\u03b8) = (2 \u2212 sec\u00b2 \u03b8) for \u03b8 \u2208 (0, \u03c0/4) \u222a (\u03c0/4, \u03c0/2). Then the value(s) of f (1/3) is (are)", "response_choices": "(A) 1 \u2212 \u221a(3/2), (B) 1 + \u221a(3/2), (C) 1 \u2212 \u221a(2/3), (D) 1 + \u221a(2/3)", "answer": "Zero Marks to all", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2013_1.jsonl b/JEE_papers/JSON/JEE_2013_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..e4fb76a8599d16e59843c3a8f7fbe344fcb4ded5 --- /dev/null +++ b/JEE_papers/JSON/JEE_2013_1.jsonl @@ -0,0 +1,60 @@ +{"id": 1, "question": "The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is", "response_choices": "A) 5.112 cm, B) 5.124 cm, C) 5.136 cm, D) 5.148 cm", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "A ray of light travelling in the direction 1/2(i+\u221a3j) is incident on a plane mirror. After reflection, it travels along the direction 1/2(i-\u221a3j). The angle of incidence is", "response_choices": "A) 30\u00b0, B) 45\u00b0, C) 60\u00b0, D) 75\u00b0", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "In the Young's double slit experiment using a monochromatic light of wavelength \u03bb, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is", "response_choices": "(A) (2n+1)\u03bb/2 (B) (2n+1)\u03bb/4 (C) (2n+1)\u03bb/8 (D) (2n+1)\u03bb/16", "answer": "B", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is", "response_choices": "(A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is", "response_choices": "A) 2.0 s, B) 3.0 s, C) 4.5 s, D) 6.0 s", "answer": "A", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 \u00d7 10^8 ms^-1. The final momentum of the object is", "response_choices": "(A) 0.3 \u00d7 10^-17 kg ms^-1, (B) 1.0 \u00d7 10^-17 kg ms^-1, (C) 3.0 \u00d7 10^-17 kg ms^-1, (D) 9.0 \u00d7 10^-17 kg ms^-1", "answer": "B", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A particle of mass m is projected from the ground with an initial speed u0 at an angle \u03b1 with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is", "response_choices": "(A) \u03c0/4, (B) \u03c0/4+\u03b1, (C) \u03c0/2-\u03b1, (D) \u03c0/2", "answer": "A", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "The work done on a particle of mass m by a force, K [ (x^2 + y^2)^(1/2) i + (x^2 + y^2)^(1/2) j] (K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is", "response_choices": "A) 2K\u03c0/a, B) K\u03c0/a, C) K\u03c0/2a, D) 0", "answer": "D", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is", "response_choices": "(A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is", "response_choices": "(A) 1 m (B) 2 m (C) 3 m (D) 6 m", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m^-1) x] cos [(628 s^-1)t]. Assuming \u03c0 = 3.14, the correct statement(s) is (are)", "response_choices": "(A) The number of nodes is 5. (B) The length of the string is 0.25 m. (C) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01 m. (D) The fundamental frequency is 100 Hz.", "answer": "BC", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "A solid sphere of radius R and density \u03c1 is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3\u03c1. The complete arrangement is placed in a liquid of density 2\u03c1 and is allowed to reach equilibrium. The correct statement(s) is (are)", "response_choices": "(A) the net elongation of the spring is 4\u03c0R^3\u03c1g/3k. (B) the net elongation of the spring is 8\u03c0R^3\u03c1g/3k. (C) the light sphere is partially submerged. (D) the light sphere is completely submerged.", "answer": "AD", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "A particle of mass M and positive charge Q, moving with a constant velocity v\u2081 = 4i ms\u207b\u00b9, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity v\u2082 = 2(\u221a3i + j) ms\u207b\u00b9. The correct statement(s) is (are)", "response_choices": "A) The direction of the magnetic field is -z direction. \nB) The direction of the magnetic field is +z direction. \nC) The magnitude of the magnetic field 50\u03c0M/3Q units. \nD) The magnitude of the magnetic field is 100\u03c0M/3Q units.", "answer": "AC", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities \u03c11 and \u03c12 respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio \u03c11/\u03c12 can be", "response_choices": "(A) -4, (B) -32/25, (C) 32/25, (D) 4", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time,", "response_choices": "(A) the charge on the upper plate of C1 is 2CV0; (B) the charge on the upper plate of C1 is CV0; (C) the charge on the upper plate of C2 is 0; (D) the charge on the upper plate of C2 is -CV0", "answer": "BD", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potential versus frequency plot for Silver to that of Sodium is", "response_choices": "", "answer": "1", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first 80 s after preparation of the sample is", "response_choices": "", "answer": "4", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle. If the initial speed (in ms^-1) of the particle is zero, the speed (in ms^-1) after 5 s is", "response_choices": "No response choices provided", "answer": "5", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s^-1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s^-1) of the system is", "response_choices": "No response choices provided", "answer": "8", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 20, "question": "A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is", "response_choices": "", "answer": "5", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 21, "question": "The compound that does NOT liberate CO2, on treatment with aqueous sodium bicarbonate solution, is", "response_choices": "(A) Benzoic acid, (B) Benzenesulphonic acid, (C) Salicylic acid, (D) Carbolic acid (Phenol)", "answer": "D", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of", "response_choices": "(A) NO, (B) NO2, (C) N2O, (D) N2O4", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 \u00b0C. For this process, the correct statement is", "response_choices": "(A) The adsorption requires activation at 25 \u00b0C. (B) The adsorption is accompanied by a decrease in enthalpy. (C) The adsorption increases with increase of temperature. (D) The adsorption is irreversible.", "answer": "B", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "Sulfide ores are common for the metals", "response_choices": "(A) Ag, Cu and Pb (B) Ag, Cu and Sn (C) Ag, Mg and Pb (D) Al, Cu and Pb", "answer": "A", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "The arrangement of X\u00af ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X\u00af is 250 pm, the radius of A+ is", "response_choices": "(A) 104 pm (B) 125 pm (C) 183 pm (D) 57 pm", "answer": "A", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 26, "question": "Upon treatment with ammoniacal H\u2082S, the metal ion that precipitates as a sulfide is", "response_choices": "A) Fe(III), B) Al(III), C) Mg(II), D) Zn(II)", "answer": "D", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "The standard enthalpies of formation of CO\u2082(g), H\u2082O(l) and glucose(s) at 25 \u00b0C are \u2013400 kJ/mol, \u2013300 kJ/mol and \u20131300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25 \u00b0C is", "response_choices": "A) +2900 kJ, B) \u20132900 kJ, C) \u201316.11 kJ, D) +16.11 kJ", "answer": "C", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "Consider the following complex ions, P, Q and R. P = [FeF6]3-, Q = [V(H2O)6]2+ and R = [Fe(H2O)6]2+. The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is", "response_choices": "(A) R < Q < P, (B) Q < R < P, (C) R < P < Q, (D) Q < P < R", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "In the reaction, P + Q \u2192 R + S the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is", "response_choices": "(A) 2, (B) 3, (C) 0, (D) 1", "answer": "D", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 30, "question": "KI in acetone, undergoes SN2 reaction with each of P, Q, R and S. The rates of the reaction vary as", "response_choices": "A) P > Q > R > S, B) S > P > R > Q, C) P > R > Q > S, D) R > P > S > Q", "answer": "B", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 31, "question": "The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)", "response_choices": "(A) [Cr(NH3)5Cl]Cl2 and [Cr(NH3)4Cl2]Cl\n(B) [Co(NH3)4Cl2]+ and [Pt(NH3)2(H2O)Cl]+\n(C) [CoBr2Cl2]2- and [PtBr2Cl2]2-\n(D) [Pt(NH3)3(NO2)]Cl and [Pt(NH3)3Cl]Br", "answer": "BD", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "Among P, Q, R and S, the aromatic compound(s) is/are", "response_choices": "A) P, B) Q, C) R, D) S", "answer": "ABCD", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 33, "question": "The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to", "response_choices": "(A) \u03c3\u2192p (empty) and \u03c3\u2192\u03c0* electron delocalisations. (B) \u03c3\u2192\u03c3* and \u03c3\u2192\u03c0 electron delocalisations. (C) \u03c3\u2192p (filled) and \u03c3\u2192\u03c0 electron delocalisations. (D) p (filled)\u2192\u03c3* and \u03c3\u2192\u03c0* electron delocalisations.", "answer": "A", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is(are)", "response_choices": "(A) \u0394G is positive, (B) \u0394S_system is positive, (C) \u0394S_surroundings = 0, (D) \u0394H = 0", "answer": "BCD", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1M), at 25 \u00b0C. The Ka of HA is", "response_choices": "(A) 1 \u00d7 10^-4, (B) 1 \u00d7 10^-5, (C) 1 \u00d7 10^-6, (D) 1 \u00d7 10^-3", "answer": "A", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 36, "question": "The total number of carboxylic acid groups in the product P is", "response_choices": "No response choices provided", "answer": "2", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "A tetrapeptide has \u2013COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with \u2013NH2 group attached to a chiral center is", "response_choices": "No response choices provided", "answer": "4", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 38, "question": "EDTA4- is ethylenediaminetetraacetate ion. The total number of N-Co-O bond angles in [Co(EDTA)]1- complex ion is", "response_choices": "", "answer": "8", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "The total number of lone-pairs of electrons in melamine is", "response_choices": "", "answer": "6", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of He gas at -73 \u00b0C is \"M\" times that of the de Broglie wavelength of Ne at 727 \u00b0C. M is", "response_choices": "", "answer": "5", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "Let complex numbers \u03b1 and 1/\u03b1 lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2, respectively. If z0 = x0 + iy0 satisfies the equation 2 |z0|2 = r2 + 2, then |\u03b1| =", "response_choices": "A) 1/\u221a2, B) 1/2, C) 1/\u221a7, D) 1/3", "answer": "C", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Four persons independently solve a certain problem correctly with probabilities 1/3, 1/4, 1/8. Then the probability that the problem is solved correctly by at least one of them is", "response_choices": "A) 235/256, B) 21/256, C) 3/256, D) 253/256", "answer": "A", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let f : [1/2, 1] \u2192 \u211d (the set of all real numbers) be a positive, non-constant and differentiable function such that f''(x) < 2 f'(x) and f(1/2) = 1. Then the value of [integral from 1/2 to 1 of f(x) dx] lies in the interval", "response_choices": "(A) (2 e - 1, 2e) (B) (e - 1, 2e - 1) (C) ((e - 1) / 2, e - 1) (D) (0, (e - 1) / 2)", "answer": "D", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "The number of points in (- \u221e, \u221e), for which x^2 - x sin x - cos x = 0, is", "response_choices": "(A) 6 (B) 4 (C) 2 (D) 0", "answer": "C", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "The area enclosed by the curves y = sin x + cos x and y = |cos x - sin x| over the interval [0 , \u03c0/2] is", "response_choices": "(A) 4(\u221a2 - 1) (B) 2\u221a2 (\u221a2 - 1) (C) 2(\u221a2 + 1) (D) 2\u221a2 (\u221a2 + 1)", "answer": "B", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "A curve passes through the point (1 , \u03c0/6) . Let the slope of the curve at each point (x, y) be y/x + sec (y/x), x > 0. Then the equation of the curve is", "response_choices": "(A) sin (y/x) = log x + 1/2 (B) cosec (y/x) = log x + 2 (C) sec (2y/x) = log x + 2 (D) cos (2y/x) = log x + 1/2", "answer": "A", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "The value of cot( \u2211(n=1 to 23) cot^-1 (1 + \u2211(k=1 to n) 2k) ) is", "response_choices": "(A) 23/25, (B) 25/23, (C) 23/24, (D) 24/23", "answer": "B", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2\u221a2. Then", "response_choices": "(A) a + b - c > 0, (B) a - b + c < 0, (C) a - b + c > 0, (D) a + b - c < 0", "answer": "A or C or AC", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Perpendiculars are drawn from points on the line x+2/2 = y+1/-1 = z/3 to the plane x + y + z = 3. The feet of perpendiculars lie on the line", "response_choices": "(A) x/5 = y-1/8 = z-2/-13, (B) x/2 = y-1/3 = z-2/-5, (C) x/4 = y-1/3 = z-2/-7, (D) x/2 = y-1/-7 = z-2/5", "answer": "D", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Let PR = 3i + j - 2k and SQ = i - 3j - 4k determine diagonals of a parallelogram PQRS and PT = i + 2j + 3k be another vector. Then the volume of the parallelepipeddetermined by the vectors PT, PQ and PS is", "response_choices": "(A) 5, (B) 20, (C) 10, (D) 30", "answer": "C", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let S_n = Sum from k=1 to 4n of (-1)^(k(k+1)/2) * k^2. Then S_n can take value(s)", "response_choices": "A) 1056, B) 1088, C) 1120, D) 1332", "answer": "AD", "page_number": 34, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct?", "response_choices": "(A) N^TMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric\n(B) MN - NM is skew symmetric for all symmetric matrices M and N\n(C) MN is symmetric for all symmetric matrices M and N\n(D) (adj M) (adj N) = adj (MN) for all invertible matrices M and N", "answer": "CD", "page_number": 35, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let f(x) = x sin \u03c0x, x > 0. Then for all natural numbers n, f'(x) vanishes at", "response_choices": "A) a unique point in the interval (n, n + 1/2), B) a unique point in the interval (n + 1/2, n + 1), C) a unique point in the interval (n, n + 1), D) two points in the interval (n, n + 1)", "answer": "BC", "page_number": 36, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 3 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are", "response_choices": "(A) 24 (B) 32 (C) 45 (D) 60", "answer": "AC", "page_number": 37, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "A line l passing through the origin is perpendicular to the lines l1 : (3 + 0)i + (-1 + 2t)j + (4 + 2t)k , -\u221e < t < \u221e l2 : (3 + 2s)i + (3 + 2s)j + (2 + s)k , -\u221e < s < \u221e Then, the coordinate(s) of the point(s) on l2 at a distance of \u221a17 from the point of intersection of l and l1 is (are)", "response_choices": "(A) (7/3, 7/3, 3/3) (B) (-1, -1, 0) (C) (1, 1, 1) (D) (7/9, 7/9, 8/9)", "answer": "BD", "page_number": 37, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "The coefficients of three consecutive terms of (1 + x)^n + 5 are in the ratio 5 : 10 : 14. Then n =", "response_choices": "No response choices provided", "answer": "6", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k - 20 =", "response_choices": "No response choices provided", "answer": "5", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Of the three independent events E\u2081, E\u2082 and E\u2083, the probability that only E\u2081 occurs is \u03b1, only E\u2082 occurs is \u03b2 and only E\u2083 occurs is \u03b3. Let the probability p that none of events E\u2081, E\u2082 or E\u2083 occurs satisfy the equations (\u03b1 \u2212 2\u03b2) p = \u03b1\u03b2 and (\u03b2 \u2212 3\u03b3) p = 2\u03b2\u03b3. All the given probabilities are assumed to lie in the interval (0, 1). \n\nThen Probability of occurrence of E\u2081 / Probability of occurrence of E\u2083 =", "response_choices": "", "answer": "6", "page_number": 39, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "A vertical line passing through the point (h, 0) intersects the ellipse x^2/4 + y^2/3 = 1 at the points P and Q. Let the tangents to the ellipse at P and Q meet at the point R. If A(h) = area of the triangle PQR, A1 = max (1/2\u2264h\u22641) A(h) and A2 = min (1/2\u2264h\u22641) A(h), then 8/sqrt(5) A1 - 8A2 =", "response_choices": "No multiple choice options given", "answer": "9", "page_number": 40, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Consider the set of eight vectors V= {ai + bj + ck : a, b, c \u2208 {-1, 1}}. Three non-coplanar vectors can be chosen from V in 2^n ways. Then n is", "response_choices": "No multiple choice options given", "answer": "5", "page_number": 40, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2013_2.jsonl b/JEE_papers/JSON/JEE_2013_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..d8dba9544c1cc52beeff19bad0bdc687d2be3c46 --- /dev/null +++ b/JEE_papers/JSON/JEE_2013_2.jsonl @@ -0,0 +1,64 @@ +{"id": 1, "question": "Using the expression 2d sin \u03b8 = \u03bb, one calculates the values of d by measuring the corresponding angles \u03b8 in the range 0 to 90\u00b0. The wavelength \u03bb is exactly known and the error in \u03b8 is constant for all values of \u03b8. As \u03b8 increases from 0\u00b0,", "response_choices": "(A) the absolute error in d remains constant. (B) the absolute error in d increases. (C) the fractional error in d remains constant. (D) the fractional error in d decreases.", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "Two non-conducting spheres of radii R1 and R2 and carrying uniform volume charge densities +\u03c1 and \u2013\u03c1, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,", "response_choices": "(A) the electrostatic field is zero. (B) the electrostatic potential is constant. (C) the electrostatic field is constant in magnitude. (D) the electrostatic field has same direction.", "answer": "CD", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "The figure below shows the variation of specific heat capacity (C) of a solid as a function of temperature (T). The temperature is increased continuously from 0 to 500 K at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.", "response_choices": "(A) the rate at which heat is absorbed in the range 0-100 K varies linearly with temperature T. (B) heat absorbed in increasing the temperature from 0-100 K is less than the heat required for increasing the temperature from 400-500 K. (C) there is no change in the rate of heat absorption in the range 400-500 K. (D) the rate of heat absorption increases in the range 200-300 K.", "answer": "ABCD or BCD", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a0, where a0 is the Bohr radius. Its orbital angular momentum is 3h/2\u03c0. It is given that h is Planck constant and R is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)", "response_choices": "(A) 9/32R (B) 9/16R (C) 9/5R (D) 4/3R", "answer": "AC", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "Two bodies, each of mass M, are kept fixed with a separation 2L. A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is G. The correct statement(s) is (are)", "response_choices": "(A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4\u221a(GM/L). (B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2\u221a(GM/L). (C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is \u221a(2GM/L). (D) The energy of the mass m remains constant.", "answer": "BD", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "A particle of mass m is attached to one end of a mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t = 0 with an initial velocity u0. When the speed of the particle is 0.5 u0, it collides elastically with a rigid wall. After this collision,", "response_choices": "(A) the speed of the particle when it returns to its equilibrium position is u0. (B) the time at which the particle passes through the equilibrium position for the first time is t = \u03c0\u221a(m/k). (C) the time at which the maximum compression of the spring occurs is t = 4\u03c0/3\u221a(m/k). (D) the time at which the particle passes through the equilibrium position for the second time is t = 5\u03c0/3\u221a(m/k).", "answer": "AD", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point P at a distance r from the common axis. The correct statement(s) is (are)", "response_choices": "(A) In the region 0 < r < R, the magnetic field is non-zero. (B) In the region R < r < 2R, the magnetic field is along the common axis. (C) In the region R < r < 2R, the magnetic field is tangential to the circle of radius r, centered on the axis. (D) In the region r > 2R, the magnetic field is non-zero.", "answer": "AD", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is v. The correct statement(s) is (are)", "response_choices": "(A) If the wind blows from the observer to the source, f2>f1. (B) If the wind blows from the source to the observer, f2>f1. (C) If the wind blows from observer to the source, f2 \u221a2 \u03bc2\n2. \u03bc2 > \u03bc1 and/\u221a\u221a\u221a \u03bc2 > \u03bc3\n3. \u03bc1 = \u03bc2\n4. \u03bc2 < \u03bc1 < \u221a2 \u03bc2 and/\u221a\u221a\u221a \u03bc2 > \u03bc3", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:", "response_choices": "A. 4 2 1 3, B. 1 3 2 4, C. 2 1 4 3, D. 4 3 2 1", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 20, "question": "One mole of a monatomic ideal gas is taken along two cyclic processes E\u2192F\u2192G\u2192E and E\u2192F\u2192H\u2192E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.", "response_choices": "Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.", "answer": "A", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 21, "question": "The correct statement(s) about O3 is(are)", "response_choices": "(A) O-O bond lengths are equal. (B) Thermal decomposition of O3 is endothermic. (C) O3 is diamagnetic in nature. (D) O3 has a bent structure.", "answer": "ACD", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "In the nuclear transmutation \n \u209a\u2079Be + X \u2192 \u2078\u2084Be + Y \n(X, Y) is(are) \n(A) (\u2113, n) (B) (p, D) (C) (n, D) (D) (\u2113, p) \n \u209a\u2079Be + X \u2192 \u2078\u2084Be + Y \nm\u0304 (X, Y) \u0908/\u0939\u0948 \n(A) (\u2113, n) (B) (p, D) (C) (n, D) (D) (\u2113, p)", "response_choices": "(A) (\u2113, n) (B) (p, D) (C) (n, D) (D) (\u2113, p)", "answer": "AB", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "The carbon-based reduction method is NOT used for the extraction of (A) tin from SnO\u2082 (B) iron from Fe\u2082O\u2083 (C) aluminium from Al\u2082O\u2083 (D) magnesium from MgCO\u2083 \u00b7 CaCO\u2083", "response_choices": "(A) SnO\u2082 \u0938\u0947 \u091f\u093f\u0928 (B) Fe\u2082O\u2083 \u0938\u0947 \u0906\u092f\u0930\u0928 (C) Al\u2082O\u2083 \u0938\u0947 \u090f\u0932\u094d\u092f\u0941\u092e\u093f\u0928\u093f\u092f\u092e (D) MgCO\u2083\u00b7CaCO\u2083 \u0938\u0947 \u092e\u0948\u0917\u094d\u0928\u0940\u0936\u093f\u092f\u092e", "answer": "CD", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "The thermal dissociation equilibrium of CaCO\u2083(s) is studied under different conditions. CaCO\u2083(s) \u21cc CaO(s) + CO\u2082(g) For this equilibrium, the correct statement(s) is(are) (A) \u0394H is dependent on T (B) K is independent of the initial amount of CaCO\u2083 (C) K is dependent on the pressure of CO\u2082 at a given T (D) \u0394H is independent of the catalyst, if any", "response_choices": "(A) \u0394H \u0924\u093e\u092a\u092e\u093e\u0928 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948 \u0964 (B) \u0938\u093e\u092e\u092f\u093e\u0935\u0938\u094d\u0925\u093e \u0938\u094d\u0925\u093f\u0930\u093e\u0902\u0915 (K) CaCO\u2083 \u0915\u0947 \u092a\u094d\u0930\u093e\u0930\u0902\u092d\u093f\u0915 \u092a\u0930\u093f\u092e\u093e\u0923 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e \u0939\u0948 \u0964 (C) K \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0924\u093e\u092a\u092e\u093e\u0928 \u092a\u0930 CO\u2082 \u0915\u0947 \u0926\u093e\u092c \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948 \u0964 (D) \u0394H \u0909\u0924\u094d\u092a\u094d\u0930\u0947\u0930\u0915 (\u0905\u0917\u0930 \u0939\u094b) \u0915\u0947 \u092a\u094d\u0930\u092d\u093e\u0935 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e \u0939\u0948 \u0964", "answer": "ABD", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "The Ksp of Ag2CrO4 is 1.1 \u00d7 10\u207b\u00b9\u00b2 at 298 K. The solubility (in mol/L) of Ag2CrO4 in a 0.1 M AgNO3 solution is", "response_choices": "(A) 1.1 \u00d7 10\u207b\u00b9\u00b9 (B) 1.1 \u00d7 10\u207b\u00b9\u2070 (C) 1.1 \u00d7 10\u207b\u00b9\u00b2 (D) 1.1 \u00d7 10\u207b\u2079", "answer": "B", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "In the following reaction, the product(s) formed is(are)", "response_choices": "(A) P (major) (B) Q (minor) (C) R (minor) (D) S (major)", "answer": "BD", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 27, "question": "The major product(s) of the following reaction is(are)", "response_choices": "A) P, B) Q, C) R, D) S", "answer": "Q", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 28, "question": "After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are)", "response_choices": "(A) Reaction I : P and Reaction II : P, (B) Reaction I : U, acetone and Reaction II : Q, acetone, (C) Reaction I : T, U, acetone and Reaction II : P, (D) Reaction I : R, acetone and Reaction II : S, acetone", "answer": "C", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 29, "question": "The succeeding operations that enable this transformation of states are", "response_choices": "(A) Heating, cooling, heating, cooling\n(B) Cooling, heating, cooling, heating\n(C) Heating, cooling, cooling, heating\n(D) Cooling, heating, heating, cooling", "answer": "C", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 30, "question": "The pair of isochoric processes among the transformation of states is", "response_choices": "(A) K to L and L to M\n(B) L to M and N to K\n(C) L to M and M to N\n(D) M to N and N to K", "answer": "B", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 31, "question": "P and Q, respectively, are the sodium salts of", "response_choices": "(A) hypochlorus and chloric acids (B) hypochlorus and perchloric acids (C) chloric and perchloric acids (D) chloric and hypochlorus acids", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "R, S and T, respectively, are", "response_choices": "(A) SO\u2082Cl\u2082, PCl\u2083 and H\u2083PO\u2084 (B) SO\u2082Cl\u2082, PCl\u2083 and H\u2083PO\u2083 (C) SOCl\u2082, PCl\u2083 and H\u2083PO\u2082 (D) SOCl\u2082, PCl\u2083 and H\u2083PO\u2084", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "The precipitate P contains", "response_choices": "(A) Pb2+ (B) Hg22+ (C) Ag+ (D) Hg2+", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "The coloured solution S contains", "response_choices": "(A) Fe2(SO4)3 (B) CuSO4 (C) ZnSO4 (D) Na2CrO4", "answer": "D", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "Compounds formed from P and Q are, respectively", "response_choices": "(A) Optically active S and optically active pair (T, U)\n(B) Optically inactive S and optically inactive pair (T, U)\n(C) Optically active pair (T, U) and optically active S\n(D) Optically inactive pair (T, U) and optically inactive S", "answer": "B", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 36, "question": "In the following reaction sequences V and W are, respectively", "response_choices": "(A), (B), (C), (D)", "answer": "A", "page_number": 25, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "Match the chemical conversions in List I with the appropriate reagents in List II and select the correct answer using the code given below the lists:", "response_choices": "(A) 2 3 1 4, (B) 3 2 1 4, (C) 2 3 4 1, (D) 3 2 4 1", "answer": "A", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} +{"id": 38, "question": "The unbalanced chemical reactions given in List I show missing reagent or condition (?) which are provided in List II. Match List I with List II and select the correct answer using the code given below the lists:", "response_choices": "A) 4 2 3 1 \nB) 3 2 1 4 \nC) 1 4 2 3 \nD) 3 4 2 1", "answer": "D", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "The standard reduction potential data at 25 \u00b0C is given below. \n\nE\u00b0(Fe3+, Fe2+) = + 0.77 V; \nE\u00b0(Fe2+, Fe) = - 0.44 V \nE\u00b0(Cu2+, Cu) = + 0.34 V; \nE\u00b0(Cu+, Cu) = + 0.52 V \nE\u00b0[O2(g) + 4H+ + 4e- \u2192 2H2O] = +1.23 V; \nE\u00b0[O2(g)+2H2O+ 4e- \u2192 4OH-] = + 0.40 V \nE\u00b0(Cr3+, Cr) = - 0.74 V; \nE\u00b0(Cr2+, Cr) = - 0.91 V \n\nMatch E\u00b0 of the redox pair in List I with the values given in List II and select the correct answer using the code given below the lists :", "response_choices": "P. E\u00b0(Fe3+, Fe) \nQ. E\u00b0(4H2O \u2b0c 4H+ + 4OH-) \nR. E\u00b0(Cu2+ + Cu \u2192 2Cu+) \nS. E\u00b0(Cr3+, Cr2+)\n\nCodes : \nP Q R S\n(A) 4 1 2 3\n(B) 2 3 4 1 \n(C) 1 2 3 4\n(D) 3 4 1 2", "answer": "D", "page_number": 28, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List I. The variation in conductivity of these reactions is given in List II. Match List I with List II and select the correct answer using the code given below the lists:", "response_choices": "P. (C2H5)3N + CH3COOH, Q. KI (0.1M) + AgNO3 (0.01M), R. CH3COOH + KOH, S. NaOH + HI", "answer": "A", "page_number": 29, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "Let w = \u221a(3 + i)/2 and P = {w\u207f : n = 1, 2, 3, ...}. Further H\u2081 = {z \u2208 C : Re z > 1/2} and H\u2082 = {z \u2208 C : Re z < -1/2}, where C is the set of all complex numbers. If z\u2081 \u2208 P \u2229 H\u2081, z\u2082 \u2208 P \u2229 H\u2082 and O represents the origin, then \u2220 z\u2081 O z\u2082 =", "response_choices": "A) \u03c0/2, B) \u03c0/6, C) 2\u03c0/3, D) 5\u03c0/6", "answer": "CD", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "If 3\u02e3 = 4\u02e3\u207b\u00b9, then x =", "response_choices": "A) 2 log\u2082 2/(2 log\u2082 2 - 1), B) 2/(2 - log\u2082 3), C) 1/(1 - log\u2084 3), D) 2 log\u2082 3/(2 log\u2082 3 - 1)", "answer": "ABC", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let \u03c9 be a complex cube root of unity with \u03c9 \u2260 1 and P = [pij] be a n \u00d7 n matrix with pij = \u03c9^{ij}. Then P^2 \u2260 0, when n =", "response_choices": "(A) 57 (B) 55 (C) 58 (D) 56", "answer": "BCD", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "The function f(x) = 2 | x | + | x + 2 | - | | x + 2 | - 2 | x || has a local minimum or a local maximum at x =", "response_choices": "(A) -2 (B) -2/3 (C) 2 (D) 2/3", "answer": "AB", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "For a \u2208 \u211d (the set of all real numbers), a \u2260 -1, lim n\u2192\u221e ((1\u00aa + 2^n + ... + n^n) / (n + 1)^n-1 [(na + 1) + (na + 2) + ... + (na + n)]) = 1/60 Then a =", "response_choices": "(A) 5 (B) 7 (C) -15/2 (D) -17/2", "answer": "B", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "Circle(s) touching x -- axis at a distance 3 from the origin and having an intercept of length 2\u221a7 on y -- axis is (are)", "response_choices": "(A) x^2 + y^2 - 6x + 8y + 9 = 0, (B) x^2 + y^2 - 6x + 7y + 9 = 0, (C) x^2 + y^2 - 6x - 8y + 9 = 0, (D) x^2 + y^2 - 6x - 7y + 9 = 0", "answer": "AC", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Two lines L1 : x = 5, y/(3 - \u03b1) = z/-2 and L2 : x = \u03b1, y/(-1 - 2 - \u03b1) = z/2 - \u03b1 are coplanar. Then \u03b1 can take value(s)", "response_choices": "(A) 1, (B) 2, (C) 3, (D) 4", "answer": "AD", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "In a triangle PQR, P is the largest angle and cos P = 1/3. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)", "response_choices": "(A) 16, (B) 18, (C) 24, (D) 22", "answer": "BD", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Area of S = S\u2081 \u2229 S\u2082 \u2229 S\u2083, where S\u2081 = {z \u2208 C : |z| < 4}, S\u2082 = {z \u2208 C : Im[(z - 1 + \u221a3i) / (1 - \u221a3i)] > 0} and S\u2083 = {z \u2208 C : Re z > 0}.", "response_choices": "(A) 10\u03c0/3, (B) 20\u03c0/3, (C) 16\u03c0/3, (D) 32\u03c0/3", "answer": "B", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "min |1 - 3t - z| =", "response_choices": "(A) (2 - \u221a3)/2, (B) (2 + \u221a3)/2, (C) (3 - \u221a3)/2, (D) (3 + \u221a3)/2", "answer": "C", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "If 1 ball is drawn from each of the boxes B1, B2 and B3, the probability that all 3 drawn balls are of the same colour is", "response_choices": "A) 82/648, B) 90/648, C) 558/648, D) 566/648", "answer": "A", "page_number": 34, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box B2 is", "response_choices": "A) 116/181, B) 126/181, C) 65/181, D) 55/181", "answer": "D", "page_number": 34, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Which of the following is true for 0 < x < 1 ?", "response_choices": "(A) 0 < f(x) < \u221e, (B) -1/2 < f(x) < 1/2, (C) -1/4 < f(x) < 1, (D) -\u221e < f(x) < 0", "answer": "D", "page_number": 35, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "If the function e^x f(x) assumes its minimum in the interval [0, 1] at x = 1/4, which of the following is true ?", "response_choices": "(A) f'(x) < f(x), 1/4 < x < 3/4, (B) f'(x) > f(x), 0 < x < 1/4, (C) f'(x) < f(x), 0 < x < 1/4, (D) f'(x) < f(x), 3/4 < x < 1", "answer": "C", "page_number": 35, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "Length of chord PQ is", "response_choices": "A) 7a, B) 5a, C) 2a, D) 3a", "answer": "B", "page_number": 36, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "If chord PQ subtends an angle \u03b8 at the vertex of y^2 = 4ax, then tan \u03b8 =", "response_choices": "A) 2/3 \u221a7, B) -2/3 \u221a7, C) 2/3 \u221a3, D) -2/3 \u221a3", "answer": "D", "page_number": 36, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "A line L : y = mx + 3 meets y - axis at E(0, 3) and the arc of the parabola y\u00b2 = 16x, 0 \u2264 y \u2264 6 at the point F(x0, y0). The tangent to the parabola at F(x0, y0) intersects the y-axis at G(0, y1). The slope m of the line L is chosen such that the area of the triangle EFG has a local maximum. Match List I with List II and select the correct answer using the code given below the lists :", "response_choices": "(A) 4 1 2 3\n(B) 3 4 1 2\n(C) 1 3 2 4\n(D) 1 3 4 2", "answer": "A", "page_number": 37, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Match List I with List II and select the correct answer using the code given below the lists:", "response_choices": "(A) 4 3 2 2, (B) 4 3 2 1, (C) 3 4 2 1, (D) 3 4 1 2", "answer": "B", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "P. (1/(y^2*(cot(sin^-1y)+tan(sin^-1y)))+(y sin(tan^-1y)+y cos(tan^-1y))^2)^(1/2) takes value", "response_choices": "1. (1/2)*sqrt(5/3), 2. sqrt(2), 3. 1/2, 4. 1", "answer": "1", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Q. If cos x + cos y + cos z = 0 = sin x + sin y + sin z then possible value of cos (x-y)/2 is", "response_choices": "1. (1/2)*sqrt(5/3), 2. sqrt(2), 3. 1/2, 4. 1", "answer": "2", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "R. If cos((\u03c0/4)-x) cos 2x + sin x sin 2x sec x = cos x sin 2x sec x +", "response_choices": "1. (1/2)*sqrt(5/3), 2. sqrt(2), 3. 1/2, 4. 1", "answer": "3", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "S. If cot (sin^-1\u221a(1-x^2)) = sin (tan^-1(x\u221a6)) , x \u2260 0, then possible value of x is", "response_choices": "1. (1/2)*sqrt(5/3), 2. sqrt(2), 3. 1/2, 4. 1", "answer": "4", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "Consider the lines L1 : x - 1/2 = y/-1 = z + 3/1 , L2 : x - 4/1 = y + 3/1 = z + 3/2 and the planes P1 : 7x + y + 2z = 3, P2 : 3x + 5y - 6z = 4. Let ax + by + cz = d be the equation of the plane passing through the point of intersection of lines L1 and L2, and perpendicular to planes P1 and P2. Match List - I with List - II and select the correct answer using the code given below the lists.", "response_choices": "P. a =, Q. b =, R. c =, S. d =", "answer": "A", "page_number": 39, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Match List\u2013I with List\u2013II and select the correct answer using the code given below the lists:", "response_choices": "(A) 4 2 3 1\n(B) 2 3 1 4\n(C) 3 4 1 2\n(D) 1 4 3 2", "answer": "C", "page_number": 40, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2014_1.jsonl b/JEE_papers/JSON/JEE_2014_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..d7799b2193a00bf1b96b4bca6381c65a6a8482f6 --- /dev/null +++ b/JEE_papers/JSON/JEE_2014_1.jsonl @@ -0,0 +1,56 @@ +{"id": 1, "question": "At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current i(t) = I0cos(\u03c9t), with I0 = 1A and \u03c9 = 500 rad s-1 starts flowing in it with the initial direction shown in the figure. At t = 7\u03c0/6\u03c9 , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C=20\u03bcF, R= 10 \u03a9 and the battery is ideal with emf of 50V, identify the correct statement (s).", "response_choices": "(A) Magnitude of the maximum charge on the capacitor before t = 7\u03c0/6\u03c9 is 1 \u00d7 10\u22123 C, (B) The current in the left part of the circuit just before t = 7\u03c0/6\u03c9 is clockwise, (C) Immediately after A is connected to D, the current in R is 10A, (D) Q = 2 \u00d7 10\u22123 C.", "answer": "(C) and (D)", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A light source, which emits two wavelengths \u03bb1 = 400 nm and \u03bb2 = 600 nm, is used in a Young's double slit experiment. If recorded fringe widths for \u03bb1 and\u03bb2 are\u03b21 and\u03b22 \u00a9 number of fringes for them within a distance yon one side of the central maximum are m1 and m2, respectively, then", "response_choices": "(A)\u03b22 > \u03b21, (B)m2 > m1, (C) From the central maximum, 3rd maximum of \u03bb2 overlaps with 5th minimum of \u03bb1, (D)The angular separation of fringes for \u03bb1 is greater than \u03bb2", "answer": "(A), (B) and (C)", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "One end of a taut string of length 3m along the x axis is fixed at x=0.The speed of the waves in the string is 100 ms\u22121. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are)", "response_choices": "(A)y(t) = A sin \u03c0x/6 cos 50\u03c0t/3, (B)y(t) = A sin \u03c0x/3 cos 100\u03c0t/3, (C) y(t) = A sin 5\u03c0x/6 cos 250\u03c0t/3, (D) y(t) = A sin 5\u03c0x/2 cos 250\u03c0t", "answer": "(A) , (C) and (D)", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.", "response_choices": "(A) E1/E2 = 1, (B) E1/E2 = 1/K, (C) Q1/Q2 = 3/K, (D) C/C1 = 2+K/K", "answer": "(A) and (D)", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "Let E1(r), E2(r) and E3(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density \u03bb, and an infinite plane with uniform surface charge density \u03c3. If E1(r0) = E2(r0) = E3(r0) at a given distance r0, then", "response_choices": "(A) Q = 4\u03c0r0^2, (B) r0 = \u03bb/2\u03c0\u03c3, (C) E1(r0/2)= 2E2(r0/2), (D) E2(r0/2)=4E3(r0/2)", "answer": "(C)", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "A student is performing an experiment using a resonance column and a tuning fork of frequency 244s^-1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 \u00b1 0.005) m, the gas in the tube is", "response_choices": "(A)Neon(M=20,(10\u204420=7\u204410)),\u200b(B)Nitrogen(M=28,(10\u204428=3\u20445)),\u200b(C)Oxygen(M=32,\u200b(10\u2044\u221a32=9\u204416)),\u200b(D)Argon(M=36,(10\u2044\u221a36=17\u204432))", "answer": "(D)", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d.The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?", "response_choices": "(A)4 if wires are in parallel\u200b(B) 2 if wires are in series\u200b(C) 1 if wires are in series\u200b(D)0.5 if wires are in parallel", "answer": "(B) and (D)", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle \u03b8 with the horizontal floor. The coefficient of friction between the wall and the ladder is \u03bc\u2081 and that between the floor and the ladder is \u03bc\u2082. The normal reaction of the wall on the ladder is N\u2081 and that of the floor is N\u2082. If the ladder is about to slip, then", "response_choices": "(A)\u03bc\u2081 = 0 \u03bc\u2082 \u2260 0andN\u2082 tan\u03b8 = mg/2, (B) \u03bc\u2081 \u2260 0 \u03bc\u2082 = 0andN\u2081 tan\u03b8 = mg/2, (C)\u03bc\u2081 \u2260 0 \u03bc\u2082 \u2260 0andN\u2082 = mg/1+\u03bc\u2081\u03bc\u2082, (D)\u03bc\u2081 = 0 \u03bc\u2082 \u2260 0andN\u2081 tan\u03b8 = mg/2", "answer": "(C) and (D)", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "A transparent thin film of uniform thickness and refractive index n\u2081= 1.4 is coated on the convex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index n\u2082 = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f\u2081 from the film, while rays of light traversing from glass to air get focused at distance f\u2082 from the film. Then", "response_choices": "(A) |f\u2081| =3R, (B)|f\u2081| = 2.8R, (C)|f\u2082|=2R, (D)|f\u2082| = 1.4R", "answer": "(A) and (C)", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if", "response_choices": "(A) V1 = V2 and R1 = R2 = R3, (B) V1 = V2 and R1 = 2R2 = R3, (C) V1 = 2V2 and 2R1 = 2R2 = R3, (D) 2V1 = V2 and 2R1 = R2 = R3", "answer": "(A), (B) and (D)", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30\u00b0 and 60\u00b0 with respect to the horizontal respectively as shown in figure. The speed of A is 100\u221a3 ms\u207b\u00b9. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = t\u2080, A just escapes being hit by B, t\u2080 in seconds is", "response_choices": "No response choices provided.", "answer": "5", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "During Searle's experiment, zero of the Vernier scale lies between 3.20 \u00d7 10\u207b\u00b2 m and 3.25 \u00d7 10\u207b\u00b2 m of the main scale. The 20\u1d57\u02b0 division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 \u00d7 10\u207b\u00b2 m and 3.25 \u00d7 10\u207b\u00b2 m of the main scale but now the 45\u1d57\u02b0 division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 \u00d7 10\u207b\u2077 m\u00b2. The least count of the Vernier scale is 1.0 \u00d7 10\u207b\u2075 m. The maximum percentage error in the Young's modulus of the wire is", "response_choices": "No response choices provided.", "answer": "4", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rad s^-1 is", "response_choices": "No response choices provided", "answer": "2", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R2. If X0/X1 = 3, the value of R1/R2 is", "response_choices": "No response choices provided", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density \u03c1 of the fog, intensity (power/area) S of the light from the signal and its frequency f. The engineer finds that disproportionatos^1/n . The value of n is", "response_choices": "No response choices provided", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 \u03a9 resistance, it can be converted into a voltmeter of range 0 - 30 V. If connected to a 249/2\u03a9 resistance, it becomes an ammeter of range 0 - 1.5 A. The value ofn is", "response_choices": "No response choices provided", "answer": "5", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n \u00d7 10)Joules. The value of n is (take acceleration due to gravity = 10 ms^-2)", "response_choices": "No response choices provided", "answer": "5", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "A rocket is moving in a gravity free space with a constant acceleration of 2 ms^-2 along +x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.3 ms^-1 relative to the rocket. At the same time, another ball is thrown in \u2013x direction with a speed of 0.2 ms^-1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is", "response_choices": "No response choices provided", "answer": "2 OR 8", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 ms^-1 with respect to the ground. The rotational speed of the platform inrads^-1 after the balls leave the platform is", "response_choices": "Answer: 4", "answer": "4", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 20, "question": "A thermodynamic system is taken from an initial state i with internal energy Ui = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are Waf = 200 J, Wib = 50 J and Wbf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qiaf, Qib and Qbf respectively. If the internal energy of the system in the state b is Ub = 200 J and Qiaf = 500 J, the ratio Qbf /Qib is", "response_choices": "Answer : 2", "answer": "2", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 21, "question": "The correct combination of names for isomeric alcohols with molecular formula C4H10O is/are", "response_choices": "(A) tert-butanol and 2-methylpropan-2-ol, (B) tert-butanol and 1, 1-dimethylethan-1-ol, (C) n-butanol and butan-1-ol, (D) isobutyl alcohol and 2-methylpropan-1-ol", "answer": "(A), (C) and (D)", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "he reactivity of compound Z with different halogens under appropriate conditions is given below:, The observed pattern of electrophilic substitution can be explained by", "response_choices": "(A) the steric effect of the halogen, (B) the steric effect of the tert-butyl group, (C) the electronic effect of the phenolic group, (D) the electronic effect of the tert-butyl group", "answer": "(A), (B) and (C)", "page_number": 11, "image_available": "yes", "question_subject": "chemistry"} +{"id": 23, "question": "In the reaction shown below, the major product(s) formed is/are", "response_choices": "A, B, C, D", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 24, "question": "An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1, and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P2, V2 and T2 respectively. For this expansion,", "response_choices": "(A) q = 0 (B) T2 = T1 (C) P2V2 = P1V1 (D) P2V2' = P1V1'", "answer": "(A), (B) and (C)", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 25, "question": "Hydrogen bonding plays a central role in the following phenomena:", "response_choices": "(A) Ice floats in water. (B) Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions. (C) Formic acid is more acidic than acetic acid. (D) Dimerisation of acetic acid in benzene.", "answer": "(A), (B) and (D)", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "In a galvanic cell, the salt bridge", "response_choices": "(A) does not participate chemically in the cell reaction. (B) stops the diffusion of ions from one electrode to another. (C) is necessary for the occurrence of the cell reaction. (D) ensures mixing of the two electrolytic solutions.", "answer": "(A) and (C) or only (A)", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "Upon heating with Cu\u2082S, the reagent(s) that give copper metal is/are", "response_choices": "(A) CuFeS\u2082 (B) CuO (C) Cu\u2082O (D) CuSO\u2084", "answer": "(B), (C) and (D)", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "The correct statement(s) for orthoboric acid is/are", "response_choices": "(A) It behaves as a weak acid in water due to self ionization. (B) Acidity of its aqueous solution increases upon addition of ethylene glycol. (C) It has a three dimensional structure due to hydrogen bonding. (D) It is a weak electrolyte in water.", "answer": "(B) and (D)", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "For the reaction: I\u207b + ClO\u2083\u207b + H\u2082SO\u2084 \u2192 Cl\u207b + HSO\u2084\u207b + I\u2082 The correct statement(s) in the balanced equation is/are:", "response_choices": "(A) Stoichiometric coefficient of HSO\u2084\u207b is 6. (B) Iodide is oxidized. (C) Sulphur is reduced. (D) H\u2082O is one of the products.", "answer": "(A), (B) and (D) OR (A) and (D)*", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "The pair(s) of reagents that yield paramagnetic species is/are", "response_choices": "(A) Na and excess of NH\u2083 (B) K and excess of O\u2082 (C) Cu and dilute HNO\u2083 (D) O\u2082 and 2-ethylanthraquinol", "answer": "(A), (B) and (C)", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "Consider all possible isomeric ketones, including stereoisomers, of MW = 100. All these isomers are independently reacted with NaBH4 (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are", "response_choices": "", "answer": "5", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "A list of species having the formula XZ4 is given below. XeF4, SF4, SiF4, BF4, BrF4, [Cu(NH3)4]2+, [FeCI4]2-, [CoCl4]2- and [PtCl4]2-. Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is", "response_choices": "", "answer": "4", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "Among PbS, CuS, HgS, MnS, Ag2S, NiS, CoS, Bi2S3 and SnS2, the total number of BLACK coloured sulfides is", "response_choices": "", "answer": "6 OR 7", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "The total number(s) of stable conformers with non-zero dipole moment for the following compound is (are)", "response_choices": "", "answer": "3", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 39, "question": "A compound H2X with molar weight of 80 g is dissolved in a solvent having density of 0.4 g ml^-1. Assuming no change in volume upon dissolution, the molality of a 3.2 molar solution is", "response_choices": "", "answer": "4", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "MX2 dissociates into M\u00b2\u207a and X\u207b ions in an aqueous solution, with a degree of dissociation (\u03b1) of 0.5. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is", "response_choices": "", "answer": "2", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "Let M and N be two 3 \u00d7 3 matrices such that MN = NM. Further, if M \u2260 N2 and M2 = N4, then", "response_choices": "(A) determinant of (M2 + MN2) is 0\n\n(B) there is a 3 \u00d7 3 non-zero matrix U such that (M2 + MN2)U is the zero matrix\n\n(C) determinant of (M2 + MN2) \u2265 1\n\n(D) for a 3 \u00d7 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrix", "answer": "(A), (B)", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "For every pair of continuous functions f, g: [0, 1] \u2192 R such that\n\nmax {f(x): x \u2208 [0, 1]} = max {g(x): x \u2208 [0, 1]},\n\nthe correct statement(s) is(are):", "response_choices": "(A) (f(c))2 + 3f(c) = (g(c))2 + 3g(c) for some c \u2208 [0, 1]\n\n(B) (f(c))2 + f(c) = (g(c))2 + 3g(c) for some c \u2208 [0, 1]\n\n(C) (f(c))2 + 3f(c) = (g(c))2 + g(c) for some c \u2208 [0, 1]\n\n(D) (f(c))2 = (g(c))2 for some c \u2208 [0, 1]", "answer": "(A), (D)", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let f : (0, \u221e) \u2192 \u211d be given by f(x) = \u222b(x/2)^x e^(-(t+1)/t) dt/t", "response_choices": "(A) f(x) is monotonically increasing on (1, \u221e)\n(B) f(x) is monotonically decreasing on (0, 1)\n(C) f(x) + f(1/t) = 0, for all x \u2208 (0, \u221e)\n(D) f(2^x) is an odd function of x on \u211d", "answer": "(A), (C), (D)", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "Let a \u2208 \u211d and let f : \u211d \u2192 \u211d be given by f(x) = x^5 - 5x + a.", "response_choices": "(A) f(x) has three real roots if a > 4\n(B) f(x) has only one real root if a > 4\n(C) f(x) has three real roots if a < -4\n(D) f(x) has three real roots if -4 < a < 4", "answer": "(B), (D)", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "Let f: [a, b] \u2192 [1, \u221e) be a continuous function and let g: \u211d \u2192 \u211d be defined as (see image for mathematical expression)", "response_choices": "(A) g(x) is continuous but not differentiable at a, (B) g(x) is differentiable on \u211d, (C) g(x) is continuous but not differentiable at b, (D) g(x) is continuous and differentiable at either a or b but not both", "answer": "(A), (C)", "page_number": 21, "image_available": "yes", "question_subject": "mathematics"} +{"id": 46, "question": "Let f: (\u2212\u03c0/2, \u03c0/2) \u2192 \u211d be given by f(x) = (log(sec x + tan x))\u00b3. Then (see image for options)", "response_choices": "(A) f(x) is an odd function, (B) f(x) is a one-one function, (C) f(x) is an onto function, (D) f(x) is an even function", "answer": "(A), (B) and (C)", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "From a point P(\u03bb, \u03bb, \u03bb), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = \u2212x, z = \u22121. If P is such that \u2220QPR is a right angle, then the possible value(s) of \u03bb is(are)", "response_choices": "(A) \u221a2, (B) 1, (C) \u22121, (D) \u2212\u221a2", "answer": "(C)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Let \ud835\udc65\u20d7, \ud835\udc66\u20d7 and \ud835\udc67\u20d7 be three vectors each of magnitude \u221a2 and the angle between each pair of them is \u03c0/4. If \ud835\udc4e\u20d7 is a nonzero vector perpendicular to \ud835\udc65\u20d7 and \ud835\udc66\u20d7 \u00d7 \ud835\udc67\u20d7 and \ud835\udc4f\u20d7 is a nonzero vector perpendicular to \ud835\udc66\u20d7 and \ud835\udc67\u20d7 \u00d7 \ud835\udc65\u20d7, then", "response_choices": "(A) \ud835\udc4f\u20d7 = (\ud835\udc4f\u20d7 \u00b7 \ud835\udc67\u20d7)(\ud835\udc67\u20d7 \u2212 \ud835\udc65\u20d7), (B) \ud835\udc4e\u20d7 = (\ud835\udc4e\u20d7 \u00b7 \ud835\udc66\u20d7)(\ud835\udc66\u20d7 \u2212 \ud835\udc67\u20d7), (C) \ud835\udc4e\u20d7 \u00b7 \ud835\udc4f\u20d7 = \u2212(\ud835\udc4e\u20d7 \u00b7 \ud835\udc66\u20d7)(\ud835\udc4f\u20d7 \u00b7 \ud835\udc67\u20d7), (D) \ud835\udc4e\u20d7 = (\ud835\udc4e\u20d7 \u00b7 \ud835\udc66\u20d7)(\ud835\udc67\u20d7 \u2212 \ud835\udc66\u20d7)", "answer": "(A), (B) and (C)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "A circle S passes through the point (0,1) and is orthogonal to the circles (x \u2212 1)2 + y2 = 16 and x2 + y2 = 1. Then", "response_choices": "(A) radius of S is 8, (B) radius of S is 7, (C) centre of S is (\u22127,1), (D) centre of S is (\u22128,1)", "answer": "(B), (C)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Let M be a 2 \u00d7 2 symmetric matrix with integer entries. Then M is invertible if", "response_choices": "(A) the first column of M is the transpose of the second row of M\n(B) the second row of M is the transpose of the first column of M\n(C) M is a diagonal matrix with nonzero entries in the main diagonal\n(D) the product of entries in the main diagonal of M is not the square of an integer", "answer": "(C), (D)", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let a, b, c be positive integers such that \u02e2\u221ac is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of\na\u00b2 + a \u2212 14\n----------\na + 1\nIs", "response_choices": "", "answer": "4", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Let n \u2265 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is", "response_choices": "", "answer": "5", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let n\u2081 < n\u2082 < n\u2083 < n\u2084 < n\u2085 be positive integers such that n\u2081 + n\u2082 + n\u2083 + n\u2084 + n\u2085 = 20. Then the number of such distinct arrangements (n\u2081, n\u2082, n\u2083, n\u2084, n\u2085) is", "response_choices": "", "answer": "7", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Let f: R \u2192 R and g: R \u2192 R be respectively given by f(x) = |x| + 1 and g(x) = x^2 + 1. Define h: R \u2192 R by h(x) = { max {f(x), g(x)} if x \u2264 0, min {f(x), g(x)} if x > 0. The number of points at which h(x) is not differentiable is", "response_choices": "", "answer": "3", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "The value of \u222b[1/0] 4x^3 (d^2(1-x^2)^5/dx^2) dx is", "response_choices": "", "answer": "2", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "The slope of the tangent to the curve (y - x^5)^2 = x(1 + x^2)^2 at the point (1, 3) is", "response_choices": "", "answer": "8", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "The largest value of the nonnegative integer a for which lim[x\u21921] {(-ax + sin(x - 1) + a)^(1-x)/(x + sin(x - 1) - 1)} = 1/4 is", "response_choices": "", "answer": "0 (zero)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Let f: [0, 4\u03c0] \u2192 [0, \u03c0] be defined by f(x) = cos\u207b\u00b9(cos x). The number of points x \u2208 [0, 4\u03c0] satisfying the equation f(x) = (10 - x)/10", "response_choices": "", "answer": "3", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "For a point P in the plane, let d\u2081(P) and d\u2082(P) be the distances of the point P from the lines x - y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 \u2264 d\u2081(P) + d\u2082(P) \u2264 4, is", "response_choices": "", "answer": "6", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Let a\u20d7, b\u20d7, and c\u20d7 be three non-coplanar unit vectors such that the angle between every pair of them is \u03c0/3. If a\u20d7 \u00d7 b\u20d7 + b\u20d7 \u00d7 c\u20d7 = pa\u20d7 + qb\u20d7 + rc\u20d7, where p, q and r are scalars, then the value of (p\u00b2+2q\u00b2+r\u00b2)/q\u00b2 is", "response_choices": "", "answer": "4", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2014_2.jsonl b/JEE_papers/JSON/JEE_2014_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..401fbcdc779efdab696fea8eee6082d4105432be --- /dev/null +++ b/JEE_papers/JSON/JEE_2014_2.jsonl @@ -0,0 +1,61 @@ +{"id": 1, "question": "A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with timet most appropriately? The figures are only illustrative and not to the scale.", "response_choices": "A), B), C) and D)", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A wire, whichpasses through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies on the wire is", "response_choices": "(A)always radially outwards. (B)always radially inwards. (C)radially outwards initially and radially inwards later. (D)radially inwards initially and radially outwards later.", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "During an experiment with ametre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90 \u03a9 as shown in the figure. The least count of the scale used in the metre bridge is1 mm. The unknown resistance is", "response_choices": "(A)60 \u00b1 0.15\u03a9 (B)135 \u00b1 0.56\u03a9 (C)60 \u00b1 0.25\u03a9 (D)135 \u00b1 0.23\u03a9", "answer": "C", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R, respectively, as shown in figure. If magnitudes of the electric fields at point P at a distance R from the center of spheres 1, 2 and 3 are E1, E2 and E3 respectively, then", "response_choices": "(A) E1>E2>E3, (B) E3>E1>E2, (C) E2>E1>E3, (D) E3>E2>E1", "answer": "C", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is", "response_choices": "(A) 1.21, (B) 1.30, (C) 1.36, (D) 1.42", "answer": "C", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "Parallel rays of light of intensity I = 912 W/m^-2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant \u03c3 = 5.7 \u00d7 10^-8W/m^-2 K^-4 and assume that the energy exchange with the surroundingsis only through radiation. The final steady state temperature of the black body is close to", "response_choices": "(A) 330 K, (B) 660 K, (C) 990 K, (D) 1550 K", "answer": "(A)", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A metal surface is illuminated by light of two different wavelengths 248nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths areu1 and u2,respectively. If the ratio u1: u2 = 2: 1and hc = 1240 eV nm, the work function of the metal is nearly", "response_choices": "(A) 3.7 eV, (B) 3.2 eV, (C) 2.8 eV, (D) 2.5eV", "answer": "(A)", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "If \u03bbCu is the wavelength of K\u03b1 X-ray line of copper (atomic number 29) and \u03bbMo is the wavelength of the K\u03b1 X-ray line of molybdenum (atomic number 42), then the ratio \u03bbCu/\u03bbMo is close to", "response_choices": "(A) 1.99, (B) 2.14, (C) 0.50, (D) 0.48", "answer": "(B)", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A planet of radius R = 1/10 x (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth=5R on it and lower a wire of the same length and of linear mass density 10^-3 kgm^-1 into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth = 6 x 10^6m and the acceleration due to gravity on Earth is 10 ms^-2)", "response_choices": "A) 96 N, B) 108 N, C) 120 N, D) 150 N", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A glass capillary tube is of the shape of a truncated cone with an apex angle \u03b1 so that its two ends have cross sections of different radii. When dipped in water vertically, water rises in it to a height h, where the radius of its cross section is b. If the surface tension of water is S, its density is \u03c1, and its contact angle with glass is \u03b8, the value of h will be (g is the acceleration due to gravity)", "response_choices": "A) 2S/b\u03c1g cos(\u03b8 \u2212 \u03b1), B) 2S/b\u03c1g cos(\u03b8 + \u03b1), C) 2S/b\u03c1g cos(\u03b8 \u2212 \u03b1/2), D) 2S/b\u03c1g cos(\u03b8 + \u03b1/2)", "answer": "D", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved, the final temperature of the gases will be", "response_choices": "A) 550 K, B) 525 K, C) 513 K, D) 490 K", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then total work done by the gases till the time they achieve equilibrium will be", "response_choices": "A) 250 R, B) 200 R, C)100 R, D) \u2212100R", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "If the piston is pushed at a speed of 5 mms^-1, the air comes out of the nozzle with a speed of", "response_choices": "(A)0.1 ms^-1, (B)1 ms^-1, (C)2 ms^-1, (D)5 ms^-1", "answer": "(C)", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "If the density of air is \u03c1a and that of the liquid \u03c1\u2113 , then for a given piston speed the rate (volume per unit time) at which the liquid is sprayed will be proportional to", "response_choices": "(A) \u03c1a/\u03c1\u2113, (B)\u221a\u03c1a\u03c1\u2113, (C) \u03c1\u2113/\u03c1a, (D)\u03c1\u2113", "answer": "(A)", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "When d\u2248a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case", "response_choices": "(A)current in wire 1 and wire 2 is the direction PQ and RS, respectively and h \u2248 a\n(B) current in wire 1 and wire 2 is the direction PQ and SR, respectively and h \u2248 a\n(C)current in wire 1 and wire 2 is the direction PQ and SR, respectively and h \u2248 1.2a\n(D)current in wire 1 and wire 2 is the direction PQ and RS, respectively and h \u2248 1.2a", "answer": "C", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "Consider d \u226b a, and the loop is rotated about its diameter parallel to the wires by 30\u00b0 from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)", "response_choices": "(A) \u03bc\u2080I\u00b2a\u00b2/a\t(B) \u03bc\u2080I\u00b2a\u00b2/2a\t(C) \u221a3\u03bc\u2080I\u00b2a\u00b2/a\t(D) \u221a3\u03bc\u2080I\u00b2a\u00b2/2a", "answer": "B", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "Four charges Q1, Q2, Q3 and Q4 of same magnitude are fixed along the x axis at x = -2a, -a, +a and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0. Four options of the signs of these charges are given in List I. The direction of the forces on the charge q is given in List II. Match List I with List II and select the correct answer using the code given below the lists.", "response_choices": "A) P-3, Q-1, R-4, S-2\nB) P-4, Q-2, R-3, S-1\nC) P-3, Q-1, R-2, S-4\nD) P-4, Q-2, R-1, S-3", "answer": "A", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "Four combinations of two thin lenses are given in List I. The radius of curvature of all curved surfaces is r and the refractive index of all the lenses is 1.5. Match lens combinations in List I with their focal length in List II and select the correct answer using the code given below the lists.", "response_choices": "(A) P-1, Q-2, R-3, S-4 \n(B) P-2, Q-4, R-3, S-1 \n(C) P-4, Q-1, R-2, S-3 \n(D) P-2, Q-1, R-3, S-4", "answer": "B", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "A block of mass m1 = 1 kg another mass m2 = 2 kg, are placed together (see figure) on an inclined plane with angle of inclination \u03b8. Various values of \u03b8 are given in List I. The coefficient of friction between the block m1 and the plane is always zero. The coefficient of static and dynamic friction between the block m2 and the plane are equal to \u03bc = 0.3. In List II expressions for the friction on block m2 are given. Match the correct expression of the friction in List II with the angles given in List I, and choose the correct option. The acceleration due to gravity is denoted by g.", "response_choices": "A) P-1, Q-1, R-1, S-3 \n B) P-2, Q-2, R-2, S-3 \n C) P-2, Q-2, R-2, S-4 \n D) P-2, Q-2, R-3, S-3", "answer": "D", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 20, "question": "A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance of 1.2 m from the person. In the following, state of the lift's motion is given in List I and the distance where the water jet hits the floor of the lift is given in List II. Match the statements from List I with those in List II and select the correct answer using the code given below the list.", "response_choices": "A) P-2 Q-3 R-2 S-4, B) P-2 Q -3 R-1 S-4, C)P-1 Q-1 R-1 S-4, D)P-2 Q-3 R-1 S-1", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 21, "question": "The acidic hydrolysis of ether (X) shown below is fastest when", "response_choices": "A) one phenyl group is replaced by a methyl group. B) one phenyl group is replaced by a para-methoxyphenyl group. C) two phenyl groups are replaced by two para-methoxyphenyl groups. D) no structural change is made to X.", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 22, "question": "Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure.", "response_choices": "(A) I > II > III, (B) III > II > I, (C) II > III > I, (D) III > I > II", "answer": "B", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 23, "question": "The major product in the following reaction is", "response_choices": "A, B, C, D", "answer": "D", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 24, "question": "Hydrogen peroxide in its reaction with KIO4 and NH4OH respectively, is acting as a", "response_choices": "A) reducing agent, oxidising agent, B) reducing agent, reducing agent, C) oxidising agent, oxidising agent, D) oxidising agent, reducing agent", "answer": "A", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "The product formed in the reaction of SOCl2 with white phosphorous is", "response_choices": "(A) PCl3, (B) SO2Cl2, (C) SCl2, (D) POCl3", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown below is", "response_choices": "(A) 0, (B) 1, (C) 2, (D) 3", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 27, "question": "For the identification of \u03b2-naphthol using dye test, it is necessary to use", "response_choices": "(A) dichloromethane solution of \u03b2-naphthol. (B) acidic solution of \u03b2-naphthol. (C) neutral solution of \u03b2-naphthol. (D) alkaline solution of \u03b2-naphthol.", "answer": "D", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "For the elementary reaction M \u2192 N, the rate of disappearance of M increases by a factor of 8 upon doubling the concentration of M. The order of the reaction with respect to M is", "response_choices": "(A) 4 (B) 3 (C) 2 (D) 1", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "For the process H\u2082O (l) \u2192 H\u2082O (g) at T = 100\u00b0C and 1 atmosphere pressure, the correct choice is", "response_choices": "(A) \u0394Ssystem > 0 and \u0394Ssurroundings > 0 (B) \u0394Ssystem > 0 and \u0394Ssurroundings < 0 (C) \u0394Ssystem < 0 and \u0394Ssurroundings > 0 (D) \u0394Ssystem < 0 and \u0394Ssurroundings < 0", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "Assuming 2s-2p mixing is NOT operative, the paramagnetic species among the following is", "response_choices": "(A) Be2, (B) B2, (C) C2, (D) N2", "answer": "C", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "The product X is", "response_choices": "(A) H3CO CH2 H, (B) H CH3CO, (C) CH3CH2OH, (D) CH3CHO", "answer": "C", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "The product Y is", "response_choices": "(A) BrCH2CH3, (B) Br(CH2)4Br, (C) BrCH2CH2OH, (D) CH3CH(Br)CH3", "answer": "C", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "The correct statement with respect to product Y is", "response_choices": "(A) It gives a positive Tollens test and is a functional isomer of X.\n(B) It gives a positive Tollens test and is a geometrical isomer of X.\n(C) It gives a positive iodoform test and is a functional isomer of X.\n(D) It gives a positive iodoform test and is a geometrical isomer of X.", "answer": "C", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 33, "question": "M1, Q and R, respectively are", "response_choices": "(A) Zn2+, KCN and HCl\n(B) Ni2+, HCl and KCN\n(C) Cd2+, KCN and HCl\n(D) Co2+, HCl, and KCN", "answer": "B", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 34, "question": "Reagent S is", "response_choices": "(A) K4[Fe(CN)6] (B) Na3HPO4 (C) K2CrO4 (D) KOH", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "The value of d in cm (shown in the figure), as estimated from Graham's law, is", "response_choices": "(A) 8\n\n(B) 12\n\n(C) 16\n\n(D) 20", "answer": "C", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 36, "question": "The experimental value of d is found to be smaller than the estimate obtained using Graham's law. This is due to", "response_choices": "(A) larger mean free path for X as compared to that of Y. (B) larger mean free path for Y as compared to that of X. (C) increased collision frequency of Y with the inert gas as compared to that of X with the inert gas. (D) increased collision frequency of X with the inert gas as compared to that of Y with the inert gas.", "answer": "D", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 37, "question": "Different possible thermal decomposition pathways for peroxyesters are shown below. Match each pathway from List I with an appropriate structure from List II and select the correct answer using the code given below the lists.", "response_choices": "Options (A), (B), (C) and (D)", "answer": "(A)", "page_number": 25, "image_available": "yes", "question_subject": "chemistry"} +{"id": 38, "question": "Match the four starting materials (P, Q, R, S) given in List I with the corresponding reaction schemes (I, II, III, IV) provided in List II and select the correct answer using the code given below the lists.", "response_choices": "(A) 1 4 2 3, (B) 3 1 4 2, (C) 3 4 2 1, (D) 4 1 3 2", "answer": "C", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} +{"id": 39, "question": "Match each coordination compound in List-I with an appropriate pair of characteristics from List-II and select the correct answer using the code given below the lists. [en = H2NCH2CH2NH2; atomic numbers: Ti = 22; Cr = 24; Co = 27; Pt = 78]", "response_choices": "List-I: P. [Cr(NH3)4Cl2]Cl, Q. [Ti(H2O)6Cl](NO3)2, R. [Pt(en)(NH3)Cl]NO3, S. [Co(NH3)4(NO3)2]NO3 | List-II: 1. Paramagnetic and exhibits ionisation isomerism, 2. Diamagnetic and exhibits cis-trans isomerism, 3. Paramagnetic and exhibits cis-trans isomerism, 4. Diamagnetic and exhibits ionisation isomerism | Codes: (A) 4 3 2 1, (B) 3 2 1 4, (C) 2 1 4 3, (D) 1 4 3 2", "answer": "(B)", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "Match the orbital overlap figures shown in List-I with the description given in List-II and select the correct answer using the code given below the lists.", "response_choices": "A) P = 2, Q = 1, R = 3, S = 4\nB) P = 4, Q = 3, R = 1, S = 2\nC) P = 2, Q = 3, R = 1, S = 4\nD) P = 4, Q = 1, R = 3, S = 2", "answer": "C", "page_number": 28, "image_available": "yes", "question_subject": "chemistry"} +{"id": 41, "question": "The function y = f (x) is the solution of the differential equation dy/dx = xy/(x^2 - 1) = (x^4 + 2x)/sqrt(1 - x^2) in (-1, 1) satisfying f (0) = 0. Then the integral from -sqrt(3)/2 to sqrt(3)/2 of f (x) dx is", "response_choices": "A) pi - sqrt(3)/2, B) pi - sqrt(3)/4, C) pi - sqrt(3)/4, D) pi - sqrt(3)/2", "answer": "B", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "The following integral from 1 to pi/2 of (2 cosec x)^17 dx is equal to", "response_choices": "A) Integral from 0 to log(1+sqrt(2)) of 2(e^u + e^(-u))^16 du, B) Integral from 0 to log(1+sqrt(2)) of (e^u + e^(-u))^17 du, C) Integral from 0 to log(1+sqrt(2)) of (e^u - e^(-u))^17 du, D) Integral from 0 to log(1+sqrt(2)) of 2(e^u - e^(-u))^16 du", "answer": "A", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Coefficient of x^11 in the expansion of (1 + x^2)^4 (1 + x^5)^7 (1 + x^4)^12 is", "response_choices": "(A) 1051, (B) 1106, (C) 1113, (D) 1120", "answer": "C", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "Let f : [0, 2] -> \u211d be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f'(0) = 1. Let F(x) = \u222b\u2080\u02e3 f(\u221at) dt for x \u2208 [0, 2]. If F'(x) = f'(x) for all x \u2208 (0, 2), then F(2) equals", "response_choices": "(A) e\u00b2 - 1, (B) e\u2074 - 1, (C) e - 1, (D) e\u2075", "answer": "B", "page_number": 30, "image_available": "yes", "question_subject": "mathematics"} +{"id": 45, "question": "The common tangents to the circle x\u00b2 + y\u00b2 = 2 and the parabola y\u00b2 = 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS is", "response_choices": "(A) 3, (B) 6, (C) 9, (D) 15", "answer": "D", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "For x \u2208 (0, \u03c0), the equation sin x + 2 sin 2x \u2212 sin 3x = 3 has", "response_choices": "(A) infinitely many solutions, (B) three solutions, (C) one solution, (D) no solution", "answer": "D", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "In a triangle the sum of two sides is x and the product of the same two sides is y. If x\u00b2 \u2212 c\u00b2 = y, where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is", "response_choices": "(A) 3y/2(x+c), (B) 3y/2(x+c), (C) 3y/4(x+c), (D) 3y/4(x+c)", "answer": "B", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is", "response_choices": "(A) 264, (B) 265, (C) 53, (D) 67", "answer": "C", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is", "response_choices": "(A) 1/2, (B) 1/3, (C) 2/3, (D) 3/4", "answer": "A", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has", "response_choices": "(A) only purely imaginary roots, (B) all real roots, (C) two real and two purely imaginary roots, (D) neither real nor purely imaginary roots", "answer": "D", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "The value of r is", "response_choices": "(A) -1/4, (B) (2+i)/4, (C) 1/4, (D) (2-1)/4", "answer": "D", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is", "response_choices": "(A) (t2+1)^2/2t^3, (B) a(t2+1)^2/2t^3, (C) a(t2+1)^2/t^3, (D) a(t2+2)^2/t^3", "answer": "B", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "The value of g(1/2) is", "response_choices": "(A) \u03c0\n(B) 2\u03c0\n(C) \u03c0/2\n(D) \u03c0/4", "answer": "A", "page_number": 34, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "The value of g'(1/2) is", "response_choices": "(A) \u03c0/2\n(B) \u03c0\n(C) -\u03c0/2\n(D) 0", "answer": "D", "page_number": 34, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "The probability that x1 + x2 + x3 is odd, is", "response_choices": "A) 29/105, B) 53/105, C) 57/105, D) 1/2", "answer": "B", "page_number": 35, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "The probability that x1, x2, x3 are in an arithmetic progression, is", "response_choices": "A) 9/105, B) 10/105, C) 11/105, D) Blank", "answer": "C", "page_number": 35, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Let zk = cos(2k\u03c0/10) + i sin(2k\u03c0/10); k = 1, 2, ..., 9.", "response_choices": "List I: P. For each zk there exists a zj such that zk \u00d7 zj, Q. There exists a k \u2208 {1,2,...,9} such that z1 \u00d7 z \u0338=, zk has no solution z in the set of complex numbers., R. |1-z1|/|1-z2|...|1-z9|/10 equals, S. 1 - \u03a39k=1 cos(2k\u03c0/10) equals", "answer": "(C) 1 2 3 4", "page_number": 36, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "P. The number of polynomials f(x) with non-negative integer coefficients of degree \u2264 2, satisfying f(0) = 0 and \u222b01 f(x)dx = 1, is, Q. The number of points in the interval [\u2212\u221a13, \u221a13] at which sin(x2) + cos(x2) attains its maximum value, is, R. \u222b-12 (1+x2) dx equals (\u222b12 1 (1-x)2 cos 2x log (1+x) dx), S. (\u222b02 cos 2x log (1+x/1-x) dx) equals", "response_choices": "(A) 3 2 4 1, (B) 2 3 4 1, (C) 3 2 1 4, (D) 2 3 1 4", "answer": "(D) 2 3 1 4", "page_number": 36, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "Let y(x) = cos(3 cos^-1 x), x \u2208 [-1,1], x \u2260 \u00b1\u221a(5/2). Then (1/y(x))(x^2 - (d^2y(x)/dx^2 + x (dy(x)/dx)) equals", "response_choices": "A. 4 3 2 1, B. 2 4 3 1, C. 4 3 1 2, D. 2 4 1 3", "answer": "A", "page_number": 37, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "Let f1: \u211d \u2192 \u211d, f2: [0, \u221e) \u2192 \u211d, f3: \u211d \u2192 \u211d and f4: \u211d \u2192 [0, \u221e) be defined by f1(x) = {|x| if x < 0, e^x if x \u2265 0}; f2(x) = x^2; f3(x) = {sin x if x < 0, x if x \u2265 0} and f4(x) = {f2(f1(x)) if x < 0, f2(f1(x)) - 1 if x \u2265 0}. List II P. f4 is Q. f1 is R. f2\u25e6f1 is S. f2 is", "response_choices": "(A) 3 1 4 2, (B) 1 3 4 2, (C) 3 1 2 4, (D) 1 3 2 4", "answer": "D", "page_number": 38, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2015_1.jsonl b/JEE_papers/JSON/JEE_2015_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..18dd463f35a504dcd21b71deb26ca996a3f6203a --- /dev/null +++ b/JEE_papers/JSON/JEE_2015_1.jsonl @@ -0,0 +1,55 @@ +{"id": 7, "question": "A Young's double slit interference arrangement with slits S1 and S2 is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by x^2 = n^2m^2\u03bb^2 - d^2, where \u03bb is the wavelength of light in air (refractive index = 1), 2d is the separation between the slits and m is an integer. The value of n is", "response_choices": "", "answer": "3", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "Consider a concave mirror and a convex lens (refractive index = 1.5) of focal length 10 cm each, separated by a distance of 50 cm in air (refractive index = 1) as shown in the figure. An object is placed at a distance of 15 cm from the mirror. Its erect image formed by this combination has magnification M1. When the set-up is kept in a medium of refractive index 7/6, the magnification becomes M2. The magnitude |M2/M1| is", "response_choices": "", "answer": "7", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "Consider a Vernier callipers in which each 1 cm on the main scale is divided into 8 equal divisions and a screw gauge with 100 divisions on its circular scale. In the Vernier callipers, 5 divisions of the Vernier scale coincide with 4 divisions on the main scale and in the screw gauge, one complete rotation of the circular scale moves it by two divisions on the linear scale. Then:", "response_choices": "(A) If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm. (B) If the pitch of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.005 mm. (C) If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.01 mm. (D) If the least count of the linear scale of the screw gauge is twice the least count of the Vernier callipers, the least count of the screw gauge is 0.005 mm.", "answer": "(B) and (C)", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are)", "response_choices": "(A) M \u221d \u221ac (B) M \u221d \u221aG (C) L \u221d \u221ah (D) L \u221d \u221aG", "answer": "(A), (C) and (D)", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies \u03c9\u2081 and \u03c9\u2082 and have total energies E\u2081 and E\u2082, respectively. The variations of their momenta p with positions x are shown in the figures. If a/b = n^2 and a/R = n, then the correct equation(s) is(are)", "response_choices": "(A) E\u2081\u03c9\u2081 = E\u2082\u03c9\u2082, (B) \u03c9\u2082 = n^2 * \u03c9\u2081, (C) \u03c9\u2081\u03c9\u2082 = n^2, (D) E\u2081/\u03c9\u2081 = E\u2082/\u03c9\u2082", "answer": "(B) and (D)", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "A ring of mass M and radius R is rotating with angular speed \u03c9 about a fixed vertical axis passing through its centre O with two point masses each of mass M/5 at rest at O. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is 8/9 \u03c9 and one of the masses is at a distance of 3/5 R from O. At this instant the distance of the other mass from O is", "response_choices": "A) 2/3 R, B) 1/3 R, C) 3/5 R, D) 4/5 R", "answer": "(C) OR (D) OR (C) and (D)", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density \u03bb are kept parallel to each other. In their resulting electric field, point charges q and -q are kept in equilibrium between them. The point charges are confined to move in the x direction only. If they are given a small displacement about their equilibrium positions, then the correct statement(s) is(are)", "response_choices": "A. Both charges execute simple harmonic motion. B. Both charges will continue moving in the direction of their displacement. C. Charge +q executes simple harmonic motion while charge -q continues moving in the direction of its displacement. D. Charge -q executes simple harmonic motion while charge +q continues moving in the direction of its displacement.", "answer": "C", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod S1 on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside S2. The distance d is", "response_choices": "A. 60 cm B. 70 cm C. 80 cm D. 90 cm", "answer": "B", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field B. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is(are)", "response_choices": "(A) If B is along z, F \u221d (L+R), (B) If B is along x, F=0, (C) If B is along y, F \u221d (L+R), (D) If B is along z, F=0", "answer": "(A), (B) and (C)", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature T: Assuming the gases are ideal, the correct statement(s) is(are)", "response_choices": "(A) The average energy per mole of the gas mixture is 2RT, (B) The ratio of speed of sound in the gas mixture to that in helium gas is \u221a(5/5), (C) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/2, (D) The ratio of the rms speed of helium atoms to that of hydrogen molecules is 1/\u221a2", "answer": "(A), (B) and (D)", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "In an aluminum (Al) bar of square cross section, a square hole is drilled and is filled with iron (Fe) as shown in the figure. The electrical resistivities of Al and Fe are 2.7\u00d710^-8 \u03a9 m and 1.0\u00d710^-7 \u03a9 m, respectively. The electrical resistance between the two faces P and Q of the composite bar is", "response_choices": "(A) 2475 \u03bc\u03a9/64\t(B) 1875 \u03bc\u03a9/64\t(C) 1875 \u03bc\u03a9/49\t(D) 2475 \u03bc\u03a9/132", "answer": "B", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "For photo-electric effect with incident photon wavelength \u03bb, the stopping potential is V0. Identify the correct variation(s) of V0 with \u03bb and 1/\u03bb.", "response_choices": "(A) [Graph A]\t(B) [Graph B]\t(C) [Graph C]\t(D) [Graph D]", "answer": "A and C", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "Match the nuclear processes given in column I with the appropriate option(s) in column II.", "response_choices": "Column I: (A) Nuclear fusion, (B) Fission in a nuclear reactor, (C) \u03b2-decay, (D) \u03b3-ray emission\nColumn II: (P) Absorption of thermal neutrons by 235U92, (Q) 27Co nucleus, (R) Energy production in stars via hydrogen conversion to helium, (S) Heavy water, (T) Neutrino emission", "answer": "(A) Matches to (R) OR (R) and (T), (B) Matches to (P) and (S), (C) Matches to (Q) and (T), (D) Matches to (R)", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 20, "question": "A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column I (a and U0 are constants). Match the potential energies in column I to the corresponding statement(s) in column II.", "response_choices": "Column I: (A) U1(x) = U0 [1 - (x/a)^2]^2/2, (B) U2(x) = U0 (x/a)^2/2, (C) U3(x) = U0 (x/a)^2 exp[-(x/a)^2]/2, (D) U4(x) = U0 [x - 1/(x/a)^3]/2; Column II: (P) The force acting on the particle is zero at x = a, (Q) The force acting on the particle is zero at x = 0, (R) The force acting on the particle is zero at x = -a, (S) The particle experiences an attractive force towards x = 0 in the region |x| < a, (T) The particle with total energy U0/4 can oscillate about the point x = -a", "answer": "(A) Matches to (P), (Q), (R) and (T), (B) Matches to (Q) and (S), (C) Matches to (P), (Q), (R) and (S), (D) Matches to (P), (R) and (T)", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 21, "question": "The total number of stereoisomers that can exist for M is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "2", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 22, "question": "The number of resonance structures for N is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "9", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 23, "question": "The total number of lone pairs of electrons in N2O3 is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "8", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "For the octahedral complexes of Fe3+ in SCN- (thiocyanato-S) and in CN- ligand environments, the difference between the spin-only magnetic moments in Bohr magnetons (when approximated to the nearest integer) is [Atomic number of Fe = 26]", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "4", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "Among the triatomic molecules/ions, BeCl\u2082, N\u2082, N\u2082O, NO\u2082\u207a, O\u2083, SCl\u2082,ICl\u2082\u207b, I\u2083\u207b and XeF\u2082, the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the d-orbital(s) is", "response_choices": "No response choices provided", "answer": "4", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "Not considering the electronic spin, the degeneracy of the second excited state (n = 3) of H atom is 9, while the degeneracy of the second excited state of H\u207b is", "response_choices": "No response choices provided", "answer": "3", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "All the energy released from the reaction X \u2192 Y \u039b G\u2070 = -193 kJ mol\u207b\u00b9 is used for oxidizing M\u207a as M\u207a \u2192 M\u00b3\u207a+ 2e\u207b, E\u2070 = - 0.25 V. Under standard conditions, the number of moles of M\u207a oxidized when one mole of X is converted to Y is [F = 96500 C mol\u207b\u00b9]", "response_choices": "No response choices provided", "answer": "4", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "If the freezing point of a 0.01 molal aqueous solution of a cobalt(III) chloride-ammonia complex (which behaves as a strong electrolyte) is -0.0588\u00b0C, the number of chloride(s) in the coordination sphere of the complex is [K\u1d68 of water = 1.86 K kg mol\u207b\u00b9]", "response_choices": "No response choices provided", "answer": "1", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "Compound(s) that on hydrogenation produce(s) optically inactive compound(s) is(are)", "response_choices": "(A) H3C-CH3, (B) H3C-CH3, (C) H3C-CH3, (D) H3C-CH3", "answer": "(B) and (D)", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 30, "question": "The major product of the following reaction is", "response_choices": "(A) (image), (B) (image), (C) (image), (D) (image)", "answer": "(A)", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 31, "question": "In the following reaction, the major product is", "response_choices": "(A) H2C=CCH3Br, (B) H3C=CBr, (C) H2C=CHBr, (D) H3C=CHBr", "answer": "D", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "The structure of D-(+)-glucose is\n\nCHO\nH OH\nHO H\nH OH\nH OH\nCH2OH\n\nThe structure of L-(-)-glucose is", "response_choices": "(A) CHO HO H H OH HO H H CH2OH, (B) CHO H OH HO H H OH HO H CH2OH, (C) CHO HO H HO H H OH HO H CH2OH, (D) CHO HO H HO H H OH CH2OH", "answer": "A", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 33, "question": "The major product of the reaction is H3C CH2 CO2H + CH3 NH2 + CO2H + NaNO2, aqueous HCl at 0\u00b0C", "response_choices": "(A) H3C CH2 NH2 CH3 OH, (B) H3C CO2H CH3 OH, (C) H3C CO2H CH3 OH, (D) H3C NH2 CH3 OH", "answer": "C", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 34, "question": "The correct statement(s) about Cr2+ and Mn3+ is(are) [Atomic numbers of Cr = 24 and Mn = 25] (A) Cr2+ is a reducing agent, (B) Mn3+ is an oxidizing agent, (C) Both Cr2+ and Mn3+ exhibit d4 electronic configuration, (D) When Cr2+ is used as a reducing agent, the chromium ion attains d5 electronic configuration", "response_choices": "(A) Cr2+ is a reducing agent, (B) Mn3+ is an oxidizing agent, (C) Both Cr2+ and Mn3+ exhibit d4 electronic configuration, (D) When Cr2+ is used as a reducing agent, the chromium ion attains d5 electronic configuration", "answer": "A, B and C", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "Copper is purified by electrolytic refining of blister copper. The correct statement(s) about this process is (are) (A) Impure Cu strip is used as cathode, (B) Acidified aqueous CuSO4 is used as electrolyte, (C) Pure Cu deposits at cathode, (D) Impurities settle as anode-mud", "response_choices": "(A) Impure Cu strip is used as cathode, (B) Acidified aqueous CuSO4 is used as electrolyte, (C) Pure Cu deposits at cathode, (D) Impurities settle as anode-mud", "answer": "B, C and D", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 36, "question": "Fe3+ is reduced to Fe2+ by using (A) H2O2 in presence of NaOH, (B) Na2O2 in water, (C) H2O2 in presence of H2SO4, (D) Na2O2 in presence of H2SO4", "response_choices": "(A) H2O2 in presence of NaOH, (B) Na2O2 in water, (C) H2O2 in presence of H2SO4, (D) Na2O2 in presence of H2SO4", "answer": "A and B", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 37, "question": "The %yield of ammonia as a function of time in the reaction N2(g) + 3H2(g) \u21cc 2NH3(g), \u0394H < 0 at (P, T1) is given below. If this reaction is conducted at (P, T2), with T2 > T1, the %yield of ammonia as a function of time is represented by", "response_choices": "(A) (B) (C) (D)", "answer": "B", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 38, "question": "If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are", "response_choices": "(A) 1/2, 1/8 (B) 1, 1/4 (C) 1/2, 1/2 (D) 1, 1/8", "answer": "A", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 39, "question": "Match the anionic species given in Column I that are present in the ore(s) given in Column II.", "response_choices": "(A) Carbonate, (B) Sulphide, (C) Hydroxide, (D) Oxide", "answer": "(A) Matches to (P), (Q) and (S); (B) Matches to (T); (C) Matches to (Q) and (R); (D) Matches to (R)", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "Match the thermodynamic processes given under Column I with the expressions given under Column II.", "response_choices": "Column I: (A) Freezing of water at 273 K and 1 atm, (B) Expansion of 1 mol of an ideal gas into a vacuum under isolated conditions, (C) Mixing of equal volumes of two ideal gases at constant temperature and pressure in an isolated container, (D) Reversible heating of H2(g) at 1 atm from 300 K to 600 K, followed by reversible cooling to 300 K at 1 atm \n\nColumn II: (P) q = 0, (Q) w = 0, (R) \u0394Ssys < 0, (S) \u0394U = 0, (T) \u0394G = 0", "answer": "(A) Matches to (R) and (T), (B) Matches to (P), (Q) and (S), (C) Matches to (P), (Q) and (S), (D) Matches to (P), (Q), (S) and (T)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "The number of distinct solutions of the equation 5/4 cos^2x + cos^4x + sin^4x + cos^6x + sin^6x = 2 in the interval [0, 2\u03c0] is", "response_choices": "Single digit integer from 0 to 9", "answer": "8", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Let the curve C be the mirror image of the parabola y^2 = 4x with respect to the line x + y + 4 = 0. If A and B are the points of intersection of C with the line y = -5, then the distance between A and B is", "response_choices": "Single digit integer from 0 to 9", "answer": "4", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96, is", "response_choices": "Single digit integer from 0 to 9", "answer": "8", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of m/n is", "response_choices": "Single digit integer from 0 to 9", "answer": "5", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "If the normals of the parabola y^2 = 4x drawn at the end points of its latus rectum are tangents to the circle (x - 3)^2 + (y + 2)^2 = r^2, then the value of r^2 is", "response_choices": "Single digit integer from 0 to 9", "answer": "2", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "Let f : R -> R be a function defined by f(x) = {[x], x \u2264 2, 0, x > 2} where [x] is the greatest integer less than or equal to x. If I = \u222b(2/1) y(x^3) / (2 + f(x + 1)) dx, then the value of (4I - 1) is", "response_choices": "", "answer": "0", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm^3, has a 2 mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness 2 mm and is of radius equal to the outer radius of the container. If the volume of the material used to make the container is minimum when the inner radius of the container is 10 mm, then the value of V/250\u03c0 is", "response_choices": "", "answer": "4", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Let F(x) = \u222b(x/\u03c0)^2 2cos^2 t dt for all x \u2208 R and f : [0, 1/2] \u2192 [0, \u221e) be a continuous function. For \u03b1 \u2208 [0, 1/2], if F'(\u03b1) + 2 is the area of the region bounded by x = 0, y = 0, y = f(x) and x = \u03b1, then f(0) is", "response_choices": "", "answer": "3", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Let X and Y be two arbitrary, 3\u00d73, non-zero, skew-symmetric matrices and Z be an arbitrary 3\u00d73, non-zero, symmetric matrix. Then which of the following matrices is (are) skew symmetric?", "response_choices": "(A) Y^TZ^t - Z^tY^3, (B) X^4 + Y^4, (C) X^tZ^3 - Z^3X^t, (D) X^23 + Y^23", "answer": "(C) and (D)", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Which of the following values of \u03b1 satisfy the equation [(1+\u03b1)^2 (1+2\u03b1)^2 (1+3\u03b1)^2]/[(2+\u03b1)^2 (2+2\u03b1)^2 (2+3\u03b1)^2]/[(3+\u03b1)^2 (3+2\u03b1)^2 (3+3\u03b1)^2] = -648\u03b1^2", "response_choices": "(A) -4, (B) 9, (C) -9, (D) 4", "answer": "(B) and (C)", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "In R^3, consider the planes P\u2081 : y = 0 and P\u2082 : x + z = 1. Let P\u2083 be a plane, different from P\u2081 and P\u2082, which passes through the intersection of P\u2081 and P\u2082. If the distance of the point (0, 1, 0) from P\u2082 is 1 and the distance of a point (\u03b1, \u03b2, \u03b3) from P\u2083 is 2, then which of the following relations is (are) true?", "response_choices": "(A) 2\u03b1 + \u03b2 + 2\u03b3 + 2 = 0, (B) 2\u03b1 - \u03b2 + 2\u03b3 + 4 = 0, (C) 2\u03b1 + \u03b2 - 2\u03b3 - 10 = 0, (D) 2\u03b1 - \u03b2 + 2\u03b3 - 8 = 0", "answer": "(B) and (D)", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "In R\u00b3, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes P\u2081 : x + 2y - z + 1 = 0 and P\u2082 : 2x - y + z - 1 = 0. Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane P\u2081. Which of the following points lie(s) on M?", "response_choices": "(A) (0, -, 5/6, 2/3) (B) (-, 1/6, 1, 1/6) (C) (-5/6, 0, 1/6) (D) (-1/3, 0, 2/3)", "answer": "(A) and (B)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let P and Q be distinct points on the parabola y\u00b2 = 2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle \u0394OPQ is 3\u221a2, then which of the following is (are) the coordinates of P?", "response_choices": "(A) (4, 2\u221a2) (B) (9, 3\u221a2) (C) (1/4, 1/\u221a2) (D) (1, \u221a2)", "answer": "(A) and (D)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Let y(x) be a solution of the differential equation (1 + e^x)y' + ye^x = 1. If y(0) = 2, then which of the following statements is (are) true?", "response_choices": "(A) y(-4) = 0 (B) y(-2) = 0 (C) y(x) has a critical point in the interval (-1, 0) (D) y(x) has no critical point in the interval (-1, 0)", "answer": "(A) and (C)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "Consider the family of all circles whose centers lie on the straight line y = x. If this family of circles is represented by the differential equation Py' + Qy' + 1 = 0, where P, Q are functions of x, y and y' (here y' = dy/dx, y'' = d^2y/dx^2), then which of the following statements is (are) true?", "response_choices": "(A) P = y + x\n(B) P = y - x\n(C) P + Q = 1 - x + y + y' + (y')^2\n(D) P - Q = x + y - y' - (y')^2", "answer": "(B) and (C)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let g : IR -> IR be a differentiable function with g(0) = 0, g'(0) = 0 and g'(1) \u2260 0. Let\n\nf(x) = { x g(x), x \u2260 0\n { 0, x = 0\n\nand h(x) = e^|x| for all x \u2208 IR. Let (f \u2218 h)(x) denote f(h(x)) and (h \u2218 f)(x) denote h(f(x)).\nThen which of the following is (are) true?", "response_choices": "(A) f is differentiable at x = 0\n(B) h is differentiable at x = 0\n(C) f \u2218 h is differentiable at x = 0\n(D) h \u2218 f is differentiable at x = 0", "answer": "(A) and (D)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "Let f(x) = sin(\u03c0/6 - sin(\u03c0/2)sin x) for all x \u2208 \u211d and g(x) = \u03c0/2 sin x for all x \u2208 \u211d. Let (f \u2218 g)(x) denote f(g(x)) and (g \u2218 f)(x) denote g(f(x)). Then which of the following is (are) true?", "response_choices": "(A) Range of f is [-1, 1] (B) Range of f \u2218 g is [-1, 1] (C) lim f(x)/\u03c0 = x\u21920 g(x) 6 (D) There is an x \u2208 \u211d such that (g \u2218 f)(x) = 1", "answer": "(A), (B) and (C)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "Let \u0394PQR be a triangle. Let a\u20d7 = QR\u20d7, b\u20d7 = RP\u20d7 and c\u20d7 = PQ\u20d7. If |a\u20d7| = 12, |b\u20d7| = 4\u221a3 and b\u20d7, c\u20d7 = 24, then which of the following is (are) true?", "response_choices": "(A) |c\u20d7|^2 / 2 - |a\u20d7| = 12 (B) |c\u20d7|^2 / 2 + |a\u20d7| = 30 (C) |a\u20d7 \u00d7 b\u20d7 + c\u20d7 \u00d7 a\u20d7| = 48\u221a3 (D) a\u20d7.b\u20d7 = -72", "answer": "(A), (C) and (D)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "Match the entries in Column I with the entries in Column II. For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in Column I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS. Similarly, for entries (B), (C) and (D).", "response_choices": "Column I: (A), (B), (C), (D) \nColumn II: (P), (Q), (R), (S), (T)", "answer": "Matrix responses by darkening bubbles", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 59, "question": "Column I: (A) In R^3, if the magnitude of the projection vector of the vector \u03b1 i + \u03b2 j on \u221a(3i + j) is \u221a3 and if \u03b1 = 2 + \u221a3\u03b2, then possible value(s) of |\u03b1| is (are) (B) Let a and b be real numbers such that the function f(x) = { -3ax^2 - 2, x < 1 , bx + a^2, x \u2265 1 } is differentiable for all x \u2208 R. Then possible value(s) of a is (are) (C) Let \u03c9 \u2260 1 be a complex cube root of unity. If (3 - 3\u03c9 + 2\u03c9^2)^n+3 + (2 + 3\u03c9 - 3\u03c9^2)^n+3 + (-3 + 2\u03c9 + 3\u03c9^2)^n+3 = 0, then possible value(s) of n is (are) (D) Let the harmonic mean of two positive real numbers a and b be 4. If q is a positive real number such that a, 5, q, b is an arithmetic progression, then the value(s) of |q - a| is (are) Column II: (P) 1 (Q) 2 (R) 3 (S) 4 (T) 5", "response_choices": "(A) Matches to (P) and (Q), (B) Matches to (P) and (Q), (C) Matches to (P), (Q), (S) and (T), (D) Matches to (Q) and (T)", "answer": "(A) Matches to (P) and (Q), (B) Matches to (P) and (Q), (C) Matches to (P), (Q), (S) and (T), (D) Matches to (Q) and (T)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "In a triangle \u0394XYZ, let a, b and c be the lengths of the sides opposite to the angles X, Y and Z, respectively. If 2(a^2 - b^2) = c^2 and \u03bb = sin(X - Y) / sin Z, then possible values of n for which cos(n\u03c0\u03bb) = 0 is (are)\n\nIn a triangle \u0394XYZ, let a, b and c be the lengths of the sides opposite to the angles X, Y and Z, respectively. If 1 + cos 2X - 2 cos 2Y = 2 sin X sin Y, then possible value(s) of c / b is (are)\n\nIn R^2, let \u03b2\u221a3 i + j, i + \u221a3 j and \u03b2 i + (1 - \u03b2) j be the position vectors of X, Y and Z with respect to the origin O, respectively. If the distance of Z from the bisector of the acute angle of OX with OY is 3/\u221a5 , then possible value(s) of | \u03b2 | is (are)\n\nSuppose that F(\u03b1) denotes the area of the region bounded by x = 0, x = 2, y^2 = 4x and y = | \u03b1 x - 1 | + | \u03b1 x - 2 | + \u03b1 x, where \u03b1 \u2208 {0, 1}. Then the value(s) of F(\u03b1) + 8\u221a2/5 when \u03b1 = 0 and \u03b1 = 1, is (are)", "response_choices": "Column I: (A), (B), (C), (D)\nColumn II: (P) 1, (Q) 2, (R) 3, (S) 5, (T) 6", "answer": "(A) Matches to (P), (R) and (S)\n(B) Matches to (P)\n(C) Matches to (P) and (Q)\n(D) Matches to (S) and (T)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2015_2.jsonl b/JEE_papers/JSON/JEE_2015_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..c982a720c7f25ef4e681fc8421b4bf918319dd83 --- /dev/null +++ b/JEE_papers/JSON/JEE_2015_2.jsonl @@ -0,0 +1,65 @@ +{"id": 1, "question": "A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M (see figure). The point masses are connected by a rigid massless rod of length l and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance r = 3l from M, the tension in the rod is zero for m = k (M/238). The value of k is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "7", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "The energy of a system as a function of time t is given as E(t) = A^2 exp(-\u03b1t), where \u03b1 = 0.2 s^-1. The measurement of A has an error of 1.25%. If the error in the measurement of time is 1.50%, the percentage error in the value of E(t) at t = 5 s is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "4", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "The densities of two solid spheres A and B of the same radii R vary with radial distance r as \u03c1A(r) = k (R/r) and \u03c1B(r) = k (R/r)^5, respectively, where k is a constant. The moments of inertia of the individual spheres about axes passing through their centres are IA and IB, respectively. If IB = n/10 IA, the value of n is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "6", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, \u03c0/3, 2\u03c0/3 and \u03c0. When they are superposed, the intensity of the resulting wave is nI0. The value of n is", "response_choices": "", "answer": "3", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "For a radioactive material, its activity A and rate of change of its activity R are defined as A = dN/dt and R = dA/dt, where N(t) is the number of nuclei at time t. Two radioactive sources P (mean life \u03c4) and Q (mean life 2\u03c4) have the same activity at t = 0. Their rates of change of activities at t = 2\u03c4 are Rp and Rq, respectively. If Rp = n, then the value of n is Rq", "response_choices": "", "answer": "2", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "A monochromatic beam of light is incident at 60\u00b0 on one face of an equilateral prism of refractive index n and emerges from the opposite face making an angle \u03b8(n) with the normal (see the figure). For n = \u221a3 the value of \u03b8 is 60\u00b0 and d\u03b8/dn = m. The value of m is", "response_choices": "", "answer": "2", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "In the following circuit, the current through the resistor R (= 2\u03a9) is I Amperes. The value of I is", "response_choices": "No response choices provided", "answer": "1", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "An electron in an excited state of Li\u00b2+ ion has angular momentum 3\u210f/2\u03c0 . The de Broglie wavelength of the electron in this state is p \u03c0a\u2080 (where a\u2080 is the Bohr radius). The value of p is", "response_choices": "No response choices provided", "answer": "2", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "Two spheres P and Q of equal radii have densities \u03c1\u2081 and \u03c1\u2082, respectively. The spheres are connected by a massless string and placed in liquids L\u2081 and L\u2082 of densities \u03c3\u2081 and \u03c3\u2082 and viscosities \u03b7\u2081 and \u03b7\u2082, respectively. They float in equilibrium with the sphere P in L\u2081 and sphere Q in L\u2082 and the string being taut (see figure). If sphere P alone in L\u2082 has terminal velocity V\u0305p and Q alone in L\u2081 has terminal velocity V\u0305q, then", "response_choices": "(A) |V\u0305p| = \u03b7\u2081 / |V\u0305q| \u03b7\u2082, (B) |V\u0305p| = \u03b7\u2082 / |V\u0305q| \u03b7\u2081, (C) V\u0305p\u22c5V\u0305q > 0, (D) V\u0305p\u22c5V\u0305q < 0", "answer": "(A) and (D)", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "In terms of potential difference V, electric current I, permittivity \u03b5\u2080, permeability \u03bc\u2080 and speed of light c, the dimensionally correct equation(s) is(are)", "response_choices": "(A) \u03bc\u2080I\u00b2 = \u03b5\u2080V\u2074, (B) \u03b5\u2080I = \u03bc\u2080V, (C) I = \u03b5\u2080cV, (D) \u03bc\u2080cI = \u03b5\u2080V", "answer": "(A) and (C)", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "Consider a uniform spherical charge distribution of radius R2 centred at the origin O. In this distribution, a spherical cavity of radius R1, centred at P with distance OP=a=R2-R1 (see figure) is made. If the electric field inside the cavity at position r\u0304 is \u0112(r\u0304), then the correct statement(s) is(are)", "response_choices": "(A) \u0112 is uniform, its magnitude is independent of R2 but its direction depends on r\u0304\n(B) \u0112 is uniform, its magnitude depends on R2 and its direction depends on r\u0304\n(C) \u0112 is uniform, its magnitude is independent of a but its direction depends on \u0101\n(D) \u0112 is uniform and both its magnitude and direction depend on \u0101", "answer": "(D)", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is(are)", "response_choices": "(A) P has more tensile strength than Q\n(B) P is more ductile than Q\n(C) P is more brittle than Q\n(D) The Young's modulus of P is more than that of Q", "answer": "(A) and (B)", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r) is the pressure at r(r < R), then the correct option(s) is(are)", "response_choices": "(A) P(r = 0) = 0, (B) P(r = 3R/4) / P(r = 2R/3) = 63 / 80, (C) P(r = 3R/5) / P(r = 2R/5) = 16 / 21, (D) P(r = R/2) / P(r = R/3) = 20 / 27", "answer": "(B) and (C)", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectrics of different relative permittivities (\u03b51 = 2 and \u03b52 = 4) are introduced between the two plates as shown in the figure, the capacitance becomes C2. The ratio C2/C1 is", "response_choices": "(A) 6/5, (B) 5/3, (C) 7/5, (D) 7/3", "answer": "(D)", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initially the gas is at temperature T1, pressure P1 and volume V1 and the spring is in its relaxed state. The gas is then heated very slowly to temperature T2, pressure P2 and volume V2. During this process the piston moves out by a distance x. Ignoring the friction between the piston and the cylinder, the correct statement(s) is(are)", "response_choices": "(A) If V2 = 2V1 and T2 = 3T1, then the energy stored in the spring is 1/4 P1V1\n(B) If V2 = 2V1 and T2 = 3T1, then the change in internal energy is 3P1V1\n(C) If V2 = 3V1 and T2 = 4T1, then the work done by the gas is 7/3 P1V1\n(D) If V2 = 3V1 and T2 = 4T1, then the heat supplied to the gas is 17/6 P1V1", "answer": "(A), (B) and (C)", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A fission reaction is given by 236U \u2192 140Xe + 94Sr + x + y, where x and y are two particles. Considering 236U to be at rest, the kinetic energies of the products are denoted by Kxe, Ksr, Kx (2 MeV) and Ky (2 MeV), respectively. Let the binding energies per nucleon of 236U, 140Xe and 94Sr be 7.5 MeV, 8.5 MeV and 8.5 MeV, respectively. Considering different conservation laws, the correct option(s) is(are)", "response_choices": "(A) x = n, y = n, Ksr = 129 MeV, Kxe = 86 MeV\n(B) x = p, y = e-, Ksr = 129 MeV, Kxe = 86 MeV\n(C) x = p, y = n, Ksr = 129 MeV, Kxe = 86 MeV\n(D) x = n, y = n, Ksr = 86 MeV, Kxe = 129 MeV", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "This section contains TWO paragraphs", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "Based on each paragraph, there will be TWO questions", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "Marking scheme : +4 If only the bubble(s) corresponding to all the correct option(s) is(are) darkened, 0 If none of the bubbles is darkened, -2 In all other cases", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w1 and w2 and thicknesses are d1 and d2, respectively. Two points K and M are symmetrically located on the opposite faces parallel to the x-y plane (see figure). V1 and V2 are the potential differences between K and M in strips 1 and 2, respectively. Then, for a given current I flowing through them in a given magnetic field strength B, the correct statement(s) is(are)", "response_choices": "(A) If w1 = w2 and d1 = 2d2, then V2 = 2V1\n(B) If w1 = w2 and d1 = 2d2, then V2 = V1\n(C) If w1 = 2w2 and d1 = d2, then V2 = 2V1\n(D) If w1 = 2w2 and d1 = d2, then V2 = V1", "answer": "(A) and (D)", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n1 and n2, respectively. Strip 1 is placed in magnetic field B1 and strip 2 is placed in magnetic field B2, both along positive y-directions. Then V1 and V2 are the potential differences developed between K and M in strips 1 and 2, respectively. Assuming that the current I is the same for both the strips, the correct option(s) is(are)", "response_choices": "(A) If B1 = B2 and n1 = 2n2, then V2 = 2V1\n(B) If B1 = B2 and n1 = 2n2, then V2 = V1\n(C) If B1 = 2B2 and n1 = n2, then V2 = 0.5V1\n(D) If B1 = 2B2 and n1 = n2, then V2 = V1", "answer": "(A) and (C)", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "For two structures namely S1 with n1 = \u221a45/4 and n2 = 3/2, and S2 with n1 = 8/5 and n2 = 7/5 and taking the refractive index of water to be 4/3 and that of air to be 1, the correct option(s) is(are)", "response_choices": "(A) NA of S1 immersed in water is the same as that of S2 immersed in a liquid of refractive index 16/3\u221a15, (B) NA of S1 immersed in liquid of refractive index 6/\u221a15 is the same as that of S2 immersed in water, (C) NA of S1 placed in air is the same as that of S2 immersed in liquid of refractive index 4/\u221a15, (D) NA of S1 placed in air is the same as that of S2 placed in water", "answer": "(A) and (C)", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 20, "question": "If two structures of same cross-sectional area, but different numerical apertures NA1 and NA2 (NA2 < NA1) are joined longitudinally, the numerical aperture of the combined structure is", "response_choices": "(A) NA1 NA2 / (NA1 + NA2), (B) NA1 + NA2, (C) NA1, (D) NA2", "answer": "(D)", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 21, "question": "The number of hydroxyl group(s) in Q is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "4", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 22, "question": "Among the following, the number of reaction(s) that produce(s) benzaldehyde is", "response_choices": "I. CO, HCl; II. CHCl2, H2O; III. COCl, H2; IV. CO2Me, DIBAL-H", "answer": "4", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 23, "question": "In the complex acetylbromidodicarbonylbis(triethylphosphine)iron(II), the number of Fe-C bond(s) is", "response_choices": "Single digit integer ranging from 0 to 9", "answer": "3", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "Among the complex ions, [Co(NH\u2083)\u2082CH\u2083-CH\u2082-NH\u2082)\u2082Cl\u2082]+, [CrCl\u2084(C\u2082O\u2084)\u2082]\u00b3\u207b, [Fe(H\u2082O)\u2084(OH)\u2082]+, [Fe(NH\u2083)\u2086(CN)\u2086]\u00b3+ and [Co(NH\u2083)\u2084(H\u2082O)Cl]\u00b2\u207a, the number of complex ion(s) that show(s) cis-trans isomerism is", "response_choices": "", "answer": "6", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "Three moles of B\u2082H\u2086 are completely reacted with methanol. The number of moles of boron containing product formed is", "response_choices": "", "answer": "6", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a solution of a weak acid HY (0.10 M). If \u03bb\u00b0m \u2248 \u03bb\u00b0c , the difference in their pK\u200ba values, pK\u200ba(HX) - pK\u200ba(HY), is (consider degree of ionization of both acids to be \u226a 1)", "response_choices": "", "answer": "3", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "A closed vessel with rigid walls contains 1 mol of \u00b2\u00b3\u2078U and 1 mol of air at 298 K. Considering complete decay of \u00b2\u00b3\u2078U to \u00b2\u2070\u2076Pb, the ratio of the final pressure to the initial pressure of the system at 298 K is", "response_choices": "", "answer": "9", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "In dilute aqueous H\u2082SO\u2084, the complex diaquodioxalatoferrate(II) is oxidized by MnO\u2084\u207b. For this reaction, the ratio of the rate of change of [H\u207a] to the rate of change of [MnO\u2084\u207b] is", "response_choices": "", "answer": "8", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "In the following reactions, the product S is", "response_choices": "(A) [chemical structure] (B) [chemical structure] (C) [chemical structure] (D) [chemical structure]", "answer": "A", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 30, "question": "The major product U in the following reactions is", "response_choices": "(A) [chemical structure] (B) [chemical structure] (C) [chemical structure] (D) [chemical structure]", "answer": "B", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 31, "question": "In the following reactions, the major product W is", "response_choices": "(A) (B) (C) (D)", "answer": "(A)", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "The correct statement(s) regarding, (i) HClO, (ii) HClO2, (iii) HClO3 and (iv) HClO4, is(are)", "response_choices": "(A) The number of Cl=O bonds in (ii) and (iii) together is two (B) The number of lone pairs of electrons on Cl in (ii) and (iii) together is three (C) The hybridization of Cl in (iv) is sp3 (D) Amongst (i) to (iv), the strongest acid is (i)", "answer": "(B) and (C)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "The pair(s) of ions where BOTH the ions are precipitated upon passing H2S gas in presence of dilute HCl, is(are)", "response_choices": "(A) Ba2+, Zn2+ (B) Bi3+, Fe3+ (C) Cu2+, Pb2+ (D) Hg2+, Bi3+", "answer": "(C) and (D)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectively, are", "response_choices": "(A) CH3SiCl3 and Si(CH3)4 (B) (CH3)2SiCl2 and (CH3)3SiCl (C) (CH3)2SiCl2 and CH3SiCl3 (D) SiCl4 and (CH3)3SiCl", "answer": "(B)", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "When O2 is adsorbed on a metallic surface, electron transfer occurs from the metal to O2. The TRUE statement(s) regarding this adsorption is(are)", "response_choices": "(A) O2 is physi\u00adsorbed (B) heat is released (C) occupancy of \u03c02p of O2 is increased (D) bond length of O2 is increased", "answer": "(B), (C) and (D)", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 36, "question": "One mole of a monoatomic real gas satisfies the equation pV\u2212b=RT where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by", "response_choices": "(A) (B) (C) (D)", "answer": "(C)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "Compound X is", "response_choices": "(A) [Toluene structure], (B) [Cresol structure], (C) [Benzyl alcohol structure], (D) [Benzaldehyde structure]", "answer": "(C)", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 38, "question": "The major compound Y is", "response_choices": "(A) [Ethylbenzene structure], (B) [Isopropylbenzene structure], (C) [Cumene structure], (D) [Diethylbenzene structure]", "answer": "(D)", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 39, "question": "Enthalpy of dissociation (in kJ mol^-1) of acetic acid obtained from the Expt. 2 is", "response_choices": "(A) 1.0 (B) 10.0 (C) 24.5 (D) 51.4", "answer": "(A)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 40, "question": "The pH of the solution after Expt. 2 is", "response_choices": "(A) 2.8 (B) 4.7 (C) 5.0 (D) 7.0", "answer": "(B)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 41, "question": "For any integer k, let \u03b1k = cos(k\u03c0/7) + i sin(k\u03c0/7), where i = \u221a-1. The value of the expression (\u03a3|\u03b1k+1 - \u03b1k|)/(\u03a3|\u03b1k+1 - \u03b1k-2|) is", "response_choices": "Options not provided (Integer answer expected)", "answer": "4", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6 : 11 and the seventh term lies in between 130 and 140, then the common difference of this A.P. is", "response_choices": "Options not provided (Integer answer expected)", "answer": "9", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "The coefficient of x^9 in the expansion of (1 + x)(1 + x^2)(1 + x^3) ... (1 + x^100) is", "response_choices": "Options not provided (Integer answer expected)", "answer": "8", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "Suppose that the foci of the ellipse (x^2/9) + (y^2/5) = 1 are (f1, 0) and (f2, 0) where f1 > 0 and f2 < 0. Let P1 and P2 be two parabolas with a common vertex at (0, 0) and with foci at (f1, 0) and (2f2, 0), respectively. Let T1 be a tangent to P2 which passes through (2f2, 0) and T2 be a tangent to P2 which passes through (f1, 0). If m1 is the slope of T1 and m2 is the slope of T2, then the value of (1/m1^2 + m2^2) is", "response_choices": "No multiple choice options given", "answer": "4", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "Let m and n be two positive integers greater than 1. If lim(a->0)((e^(a(e^r) - e^r))/(a^m)) = (e^r/2), then the value of m/n is", "response_choices": "No multiple choice options given", "answer": "2", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "If \u03b1 = \u222b(e^(8x+3tan^-1x)*(12+9x^2))/(1+x^2) dx where tan^-1 x takes only principal values, then the value of [log(e)(1+\u03b1)-(3\u03c0/4)] is", "response_choices": "No multiple choice options given", "answer": "9", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let f : R \u2192 R be a continuous odd function, which vanishes exactly at one point and f(t) = 1/2. Suppose that F(x)= \u222bf(t) dt for all x \u2208 [-1, 2] and G(x)= \u222b|f(f(t))| dt for all x \u2208 [-1, 2]. If lim F(x)/G(x) = 1/14, then the value of f(1/2) is", "response_choices": "No multiple choice options provided", "answer": "7", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Suppose that p\u0302, q\u0302 and r\u0302 are three non-coplanar vectors in R\u00b3. Let the components of a vector \u015d along p\u0302, q\u0302 and r\u0302 be 4, 3 and 5, respectively. If the components of this vector \u015d along (-p\u0302+q\u0302+r\u0302), (p\u0302-q\u0302+r\u0302) and (-p\u0302-q\u0302+r\u0302) are x, y and z, respectively, then the value of 2x+y+z is", "response_choices": "No multiple choice options provided", "answer": "9", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Let S be the set of all non-zero real numbers \u03b1 such that the quadratic equation \u03b1x^2 - x + \u03b1 = 0 has two distinct real roots x1 and x2 satisfying the inequality |x1 - x2| < 1. Which of the following intervals is(are) a subset(s) of S?", "response_choices": "(A) (-1/2, -1/\u221a5), (B) (-1/\u221a5, 0), (C) (0, 1/\u221a5), (D) (1/\u221a5, 1/2)", "answer": "(A) and (D)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "If \u03b1 = 3sin^-1(6/11) and \u03b2 = 3cos^-1(4/9), where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)", "response_choices": "(A) cos \u03b2 > 0, (B) sin \u03b2 < 0, (C) cos(\u03b1 + \u03b2) > 0, (D) cos \u03b1 < 0", "answer": "(B), (C) and (D)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let E\u2081 and E\u2082 be two ellipses whose centers are at the origin. The major axes of E\u2081 and E\u2082 lie along the x-axis and the y-axis, respectively. Let S be the circle x\u00b2 + (y - 1)\u00b2 = 2. The straight line x + y = 3 touches the curves S, E\u2081 and E\u2082 at P, Q and R, respectively. Suppose that PQ = PR = 2\u221a2/3 . If e\u2081 and e\u2082 are the eccentricities of E\u2081 and E\u2082, respectively, then the correct expression(s) is(are)", "response_choices": "(A) e\u2081\u00b2 + e\u2082\u00b2 = 43/40 (B) e\u2081e\u2082 = \u221a7/2\u221a10 (C) |e\u2081\u00b2 - e\u2082\u00b2| = 5/8 (D) e\u2081e\u2082 = \u221a3/4", "answer": "(A) and (B)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Consider the hyperbola H : x\u00b2 - y\u00b2 = 1 and a circle S with center N(x\u2082, 0). Suppose that H and S touch each other at a point P(x\u2081, y\u2081) with x\u2081 > 1 and y\u2081 > 0. The common tangent to H and S at P intersects the x-axis at point M. If (l, m) is the centroid of the triangle \u0394PMN, then the correct expression(s) is(are)", "response_choices": "(A) dl/dx\u2081 = 1 - 1/3x\u2081 for x\u2081 > 1 (B) dm/dx\u2081 = x\u2081/\u221a(x\u2081\u00b2 - 1) for x\u2081 > 1 (C) dl/dx\u2081 = 1 + 1/3x\u2081 for x\u2081 > 1 (D) dm/dy\u2081 = 1/3 for y\u2081 > 0", "answer": "(A), (B) and (D)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "The option(s) with the values of a and L that satisfy the following equation is(are) [equation 1] = L? [equation 2]", "response_choices": "(A) a = 2, L = e^(4\u03c0 - 1)/(e^\u03c0 - 1) (B) a = 2, L = e^(4\u03c0 + 1)/(e^\u03c0 + 1) (C) a = 4, L = e^(4\u03c0 - 1)/(e^\u03c0 - 1) (D) a = 4, L = e^(4\u03c0 + 1)/(e^\u03c0 + 1)", "answer": "(A) and (C)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Let f,g:[-1,2] \u2192 R be continuous functions which are twice differentiable on the interval (-1,2). Let the values of f and g at the points -1, 0 and 2 be as given in the following table: [table with values]. In each of the intervals (-1,0) and (0,2) the function (f-3g)^' never vanishes. Then the correct statement(s) is(are)", "response_choices": "(A) f'(x)-3g'(x)=0 has exactly three solutions in (-1,0) U (0,2) (B) f'(x)-3g'(x)=0 has exactly one solution in (-1,0) (C) f'(x)-3g'(x)=0 has exactly one solution in (0,2) (D) f'(x)-3g'(x)=0 has exactly two solutions in (-1,0) and exactly two solutions in (0,2)", "answer": "(B) and (C)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 55, "question": "Let f(x) = 7 tan^8 x + 7 tan^6 x - 3 tan^4 x - 3 tan^2 x for all x \u2208 (- \u03c0/2, \u03c0/2). Then the correct expression(s) is(are)", "response_choices": "(A) \u222b^(\u03c0/4)_0 x f(x) dx = 1/12, (B) \u222b^(\u03c0/4)_0 f(x) dx = 0, (C) \u222b^(\u03c0/4)_0 x f(x) dx = 1/6, (D) \u222b^(\u03c0/4)_0 f(x) dx = 1", "answer": "(A) and (B)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 56, "question": "Let f'(x) = 192 x^3 / (2 + sin^4 x) for all x \u2208 \u211d with f(1/2) = 0. If m \u2264 \u222b^1/2_0 f(x) dx \u2264 M , then the possible values of m and M are", "response_choices": "(A) m = 13 , M = 24, (B) m = 1/4, M = 1/2, (C) m = -11, M = 0, (D) m = 1, M = 12", "answer": "(D)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 57, "question": "One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is 1/3, then the correct option(s) with the possible values of n1, n2, n3 and n4 is(are)", "response_choices": "(A) n1 = 3 , n2 = 3 , n3 = 5 , n4 = 15, (B) n1 = 3 , n2 = 6 , n3 = 10 , n4 = 50, (C) n1 = 8 , n2 = 6 , n3 = 5 , n4 = 20, (D) n1 = 6 , n2 = 12 , n3 = 5 , n4 = 20", "answer": "(A) and (B)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 58, "question": "A ball is drawn at random from box I and transferred to box II. If the probability of drawing a red ball from box I, after this transfer, is 1/3, then the correct option(s) with the possible values of n1 and n2 is(are)", "response_choices": "(A) n1 = 4 and n2 = 6, (B) n1 = 2 and n2 = 3, (C) n1 = 10 and n2 = 20, (D) n1 = 3 and n2 = 6", "answer": "(C) and (D)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 59, "question": "The correct statement(s) is(are)", "response_choices": "(A) f'(1) < 0, (B) f(2) < 0, (C) f'(x) \u2260 0 for any x \u2208 (1, 3), (D) f'(x) = 0 for some x \u2208 (1, 3)", "answer": "(A), (B) and (C)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 60, "question": "If \u222b\u2081\u00b3 xf''(x) dx = -12 and \u222b\u2081\u00b3 x\u00b3 f'''(x) dx = 40, then the correct expression(s) is(are)", "response_choices": "(A) 9f'(3) + f'(1) - 32 = 0, (B) \u222b\u2081\u00b3 f(x) dx = 12, (C) 9f'(3) - f'(1) + 32 = 0, (D) \u222b\u2081\u00b3 f(x) dx = -12", "answer": "(C) and (D)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2016_1.jsonl b/JEE_papers/JSON/JEE_2016_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..509f1387f942e53db72e93104dfebf5b5ba98f55 --- /dev/null +++ b/JEE_papers/JSON/JEE_2016_1.jsonl @@ -0,0 +1,54 @@ +{"id": 1, "question": "In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength (\u03bb) of incident light and the corresponding stopping potential (V0) are given below: \n\n\u03bb (\u03bcm) V0 (Volt)\n0.3 2.0\n0.4 1.0\n0.5 0.4\n\nGiven that c = 3 x 10^8 m s^-1 and e =1.6 x 10^-19 C , Planck's constant (in units of J s) found from such an experiment is", "response_choices": "(A) 6.0 x 10^-34 (B) 6.4 x 10^-34 (C) 6.6 x 10^-34 (D) 6.8 x 10^-34", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wall of height h (< l), such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of 30\u00b0 with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio h/l and the frictional force f at the bottom of the stick are", "response_choices": "(A) h \u221a3/l 16, f= 16\u221a3/3 N; (B) h 3/l 16, f= 16\u221a3/3 N; (C) h 3\u221a3/l 16, f= 8\u221a3/3 N; (D) h 3\u221a3/l 16, f= 16\u221a3/3 N", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A water cooler of storage capacity 120 litres can cool water at a constant rate of P watts. In a closed circulation system (as shown schematically in the figure), the water from the cooler is used to cool an external device that generates constantly 3 kW of heat (thermal load). The temperature of water fed into the device cannot exceed 30 \u00b0C and the entire stored 120 litres of water is initially cooled to 10 \u00b0C. The entire system is thermally insulated. The minimum value of P (in watts) for which the device can be operated for 3 hours is", "response_choices": "(A) 1600; (B) 2067; (C) 2533; (D) 3933", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A parallel beam of light is incident from air at an angle \u03b1 on the side PQ of a right angled triangular prism of refractive index n = \u221a2. Light undergoes total internal reflection in the prism at the face PR when \u03b1 has a minimum value of 45\u00b0. The angle \u03b8 of the prism is", "response_choices": "A) 15\u00b0, B) 22.5\u00b0, C) 30\u00b0, D) 45\u00b0", "answer": "A", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "An infinite line charge of uniform electric charge density \u03bb lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity \u03b5 and electrical conductivity \u03c3. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?", "response_choices": "A, B, C, D", "answer": "C", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "Highly excited states for hydrogen-like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n , where n>>1. Which of the following statement(s) is(are) true?", "response_choices": "(A) Relative change in the radii of two consecutive orbitals does not depend on Z\n(B) Relative change in the radii of two consecutive orbitals varies as 1/n\n(C) Relative change in the energy of two consecutive orbitals varies as 1/n^3\n(D) Relative change in the angular momenta of two consecutive orbitals varies as 1/n", "answer": "(A), (B), and (D)", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz and 121 Hz, respectively. A car is initially at a point P, 1800 m away from the midpoint Q of the line MN and moves towards Q constantly at 60 km/hr along the perpendicular bisector of MN. It crosses Q and eventually reaches a point R, 1800 m away from Q. Let v(t) represent the beat frequency measured by a person sitting in the car at time t. Let vp, vq and vr be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is 330 m s^-1. Which of the following statement(s) is(are) true regarding the sound heard by the person?", "response_choices": "(A) vp = vr - 2 vq (B) The rate of change in beat frequency is maximum when the car passes through Q (C) The plot below represents schematically the variation of beat frequency with time [Plot image 1] (D) The plot below represents schematically the variation of beat frequency with time [Plot image 2]", "answer": "(A), (B), and (C)", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?", "response_choices": "(A) The temperature distribution over the filament is uniform (B) The resistance over small sections of the filament decreases with time (C) The filament emits more light at higher band of frequencies before it breaks up (D) The filament consumes less electrical power towards the end of the life of the bulb", "answer": "(C) and (D)", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A plano-convex lens is made of a material of refractive index n. When a small object is placed 30 cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement(s) is(are) true?", "response_choices": "(A) The refractive index of the lens is 2.5 (B) The radius of curvature of the convex surface is 45 cm (C) The faint image is erect and real (D) The focal length of the lens is 20 cm", "answer": "(A) and (D)", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A length-scale (l) depends on the permittivity (\u03b5) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for l is(are) dimensionally correct?", "response_choices": "(A) l = \u221a(nq\u00b2/\u03b5kBT), (B) l = \u221a(\u03b5kBT/nq\u00b2), (C) l = \u221a(q\u00b2/\u03b5n\u00b2/\u00b3kBT), (D) l = \u221a(q\u00b2/\u03b5n\u00b9/\u00b3kBT)", "answer": "(B) and (D)", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the 90\u00b0 vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 A s^-1. Which of the following statement(s) is(are) true?", "response_choices": "(A) The magnitude of induced emf in the wire is (\u03bc0/\u03c0) volt, (B) If the loop is rotated at a constant angular speed about the wire, an additional emf of (\u03bc0/\u03c0) volt is induced in the wire, (C) The induced current in the wire is in opposite direction to the current along the hypotenuse, (D) There is a repulsive force between the wire and the loop", "answer": "(A) and (D)", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "The position vector r of a particle of mass m is given by the following equation: r(t)=\u03b1t^3 i + \u03b2t^2 j, where \u03b1=10/3 m s^-3, \u03b2=5 m s^-2 and m=0.1 kg. At t=1 s, which of the following statement(s) is(are) true about the particle?", "response_choices": "(A) The velocity v is given by v=(10i + 10j) m s^-1\n(B) The angular momentum L with respect to the origin is given by L=-(5/3)k N m s\n(C) The force F is given by F=(i + 2j) N\n(D) The torque \u03c4 with respect to the origin is given by \u03c4=-(20/3)k N m", "answer": "(A), (B) and (D)", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices n1 and n2 (>n1), as shown in the figure. A ray of light is incident with angle \u03b8i from medium 1 and emerges in medium 2 with refraction angle \u03b8f with a lateral displacement l. Which of the following statement(s) is(are) true?", "response_choices": "(A) n1 sin \u03b8i = n2 sin \u03b8f (B) n1 sin \u03b8i = (n2 - n1) sin \u03b8f (C) l is independent of n2 (D) l is dependent on n(z)", "answer": "(A), (C) and (D)", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays log\u2082(P/P\u2080), where P\u2080 is a constant. When the metal surface is at a temperature of 487 \u00b0C, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767 \u00b0C?", "response_choices": "", "answer": "9", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "The isotope \u00b9\u00b3B having a mass 12.014 u undergoes \u03b2-decay to \u00b9\u00b2C. \u00b9\u00b2C has an excited state of the nucleus (\u00b9\u00b2C*) at 4.041 MeV above its ground state. If \u00b9\u00b3B decays to \u00b9\u00b2C*, the maximum kinetic energy of the \u03b2-particle in units of MeV is (1 u = 931.5 MeV/c\u00b2, where c is the speed of light in vacuum).", "response_choices": "", "answer": "8 OR 9", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "A hydrogen atom in its ground state is irradiated by light of wavelength 970 \u00c5. Taking hc/e = 1.237 \u00d7 10^-5 eV m and the ground state energy of hydrogen atom as -13.6 eV, the number of lines present in the emission spectrum is", "response_choices": "No response choices provided.", "answer": "(5)", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Consider two solid spheres P and Q each of density 8 gm cm^-3 and diameters 1 cm and 0.5 cm, respectively. Sphere P is dropped into a liquid of density 0.8 gm cm^-3 and viscosity \u03b7=3 poiseulles. Sphere Q is dropped into a liquid of density 1.6 gm cm^-3 and viscosity \u03b7=2 poiseulles. The ratio of the terminal velocities of P and Q is", "response_choices": "No response choices provided.", "answer": "(3)", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "Two inductors L1 (inductance 1 mH, internal resistance 3 \u03a9) and L2 (inductance 2 mH, internal resistance 4 \u03a9), and a resistor R (resistance 12 \u03a9) are all connected in parallel across a 5 V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (Imax / Imin) drawn from the battery is", "response_choices": "No response choices provided.", "answer": "(8)", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is 4 \u03c0r^2 dr. The qualitative sketch of the dependence of P on r is", "response_choices": "(A), (B), (C), (D)", "answer": "(D)", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 20, "question": "One mole of an ideal gas at 300 K in thermal contact with surroundings expands isothermally from 1.0 L to 2.0 L against a constant pressure of 3.0 atm. In this process, the change in entropy of surroundings (\u0394Ssur) in J K^-1 is", "response_choices": "(A) 5.763 (B) 1.013 (C) -1.013 (D) -5.763", "answer": "C", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 21, "question": "The increasing order of atomic radii of the following Group 13 elements is", "response_choices": "(A) Al < Ga < In < Tl (B) Ga < Al < In < Tl (C) Al < In < Ga < Tl (D) Al < Ga < Tl < In", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "Among [Ni(CO)4], [NiCl4]^2-, [Co(NH3)6Cl3]Cl, Na3[CoF6], Na2O2 and CsO2, the total number of paramagnetic compounds is", "response_choices": "(A) 2 (B) 3 (C) 4 (D) 5", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "On complete hydrogenation, natural rubber produces", "response_choices": "(A) ethylene-propylene copolymer (B) vulcanised rubber (C) polypropylene (D) polybutylene", "answer": "A", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "According to the Arrhenius equation, (A) a high activation energy usually implies a fast reaction. (B) rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy. (C) higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant. (D) the pre-exponential factor is a measure of the rate at which collisions occur, irrespective of their energy.", "response_choices": "(A), (B), (C) and (D)", "answer": "(B), (C) and (D)", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 25, "question": "A plot of the number of neutrons (N) against the number of protons (P) of stable nuclei exhibits upward deviation from linearity for atomic number, Z > 20. For an unstable nucleus having N/P ratio less than 1, the possible mode(s) of decay is(are) (A) \u03b2\u207b-decay (\u03b2 emission) (B) orbital or K-electron capture (C) neutron emission (D) \u03b2\u207a-decay (positron emission)", "response_choices": "(A), (B), (C) and (D)", "answer": "(B) and (D)", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 26, "question": "The crystalline form of borax has", "response_choices": "(A) tetranuclear [B\u2084O\u2085(OH)\u2084]\u00b2\u207b unit\n(B) all boron atoms in the same plane\n(C) equal number of sp\u00b2 and sp\u00b3 hybridized boron atoms\n(D) one terminal hydroxide per boron atom", "answer": "(A), (C) and (D)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "The compound(s) with TWO lone pairs of electrons on the central atom is(are)", "response_choices": "(A) BrF\u2083\t(B) ClF\u2083\t(C) XeF\u2084\t(D) SF\u2084", "answer": "(B) and (C)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "The reagent(s) that can selectively precipitate S\u00b2\u207b from a mixture of S\u00b2\u207b and SO\u2084\u00b2\u207b in aqueous solution is(are)", "response_choices": "(A) CuCl\u2082\t(B) BaCl\u2082\t(C) Pb(OOCCH\u2083)\u2082\t(D) Na\u2082[Fe(CN)\u2085NO]", "answer": "(A) OR (A) and (C)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "Positive Tollen's test is observed for", "response_choices": "(A) [Structure 1]\n\n(B) [Structure 2]\n\n(C) [Structure 3]\n\n(D) [Structure 4]", "answer": "(A), (B) and (C)", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 30, "question": "The product(s) of the following reaction sequence is(are)", "response_choices": "A) (A), B) (B), C) (C), D) (D)", "answer": "B", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 31, "question": "The correct statement(s) about the following reaction sequence is(are)", "response_choices": "(A) R is steam volatile, (B) Q gives dark violet coloration with 1% aqueous FeCl3 solution, (C) S gives yellow precipitate with 2, 4-dinitrophenylhydrazine, (D) S gives dark violet coloration with 1% aqueous FeCl3 solution", "answer": "(B) and (C)", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as its molality. Density of this solution at 298 K is 2.0 g cm^-3. The ratio of the molecular weights of the solute and solvent, (MW_solute / MW_solvent), is", "response_choices": "A SINGLE DIGIT INTEGER ranging from 0 to 9", "answer": "9", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 33, "question": "The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is", "response_choices": "A SINGLE DIGIT INTEGER ranging from 0 to 9", "answer": "4", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 34, "question": "In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is", "response_choices": "", "answer": "6", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "The number of geometric isomers possible for the complex [CoL\u2082Cl\u2082]\u207b (L = H\u2083NCH\u2082CH\u2082O\u207b)", "response_choices": "", "answer": "5", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 36, "question": "In the following monobromination reaction, the number of possible chiral products is", "response_choices": "", "answer": "5", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "Let \u03c0/6 < \u03b8 < \u03c0/12. Suppose \u03b11 and \u03b21 are the roots of the equation x^2 - 2xsec\u03b8 +1 = 0 and \u03b12 and \u03b22 are the roots of the equation x^2 + 2xtan\u03b8 - 1 = 0. If \u03b11 > \u03b21 and \u03b12 > \u03b22, then \u03b11 + \u03b22 equals", "response_choices": "(A) 2(sec\u03b8 - tan\u03b8), (B) 2sec\u03b8, (C) -2tan\u03b8, (D) 0", "answer": "(C)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is", "response_choices": "(A) 380, (B) 320, (C) 260, (D) 95", "answer": "(A)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "Let S ={(x \u03f5 (-\u03c0, \u03c0)): x \u2260 0, \u00b1\u03c0/2}. The sum of all distinct solutions of the equation \u221a3 secx + cosecx + 2(tanx - cotx) = 0 in the set S is equal to", "response_choices": "(A) 7\u03c0/9, (B) 2\u03c0/9, (C) 0, (D) 5\u03c0/9", "answer": "(C)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 40, "question": "A computer producing factory has only two plants T1 and T2. Plant T1 produces 20% and plant T2 produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective given that it is produced in plant T1) = 10P(computer turns out to be defective given that it is produced in plant T2), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2 is", "response_choices": "A) 36/73, B) 47/79, C) 78/93, D) 75/83", "answer": "C", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 41, "question": "The least value of a \u2208 R for which 4\u03b1x^2 + 1/x \u2265 1, for all x > 0, is", "response_choices": "A) 1/64, B) 1/32, C) 1/27, D) 1/25", "answer": "C", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Consider a pyramid OPQRS located in the first octant (x \u2265 0, y \u2265 0, z \u2265 0) with O as origin, and OP and OR along the x-axis and the y-axis, respectively. The base OPQR of the pyramid is a square with OP = 3. The point S is directly above the mid-point T of diagonal OQ such that TS = 3. Then", "response_choices": "(A) the acute angle between OQ and OS is 2/3 \n(B) the equation of the plane containing the triangle OQS is x - y = 0 \n(C) the length of the perpendicular from P to the plane containing the triangle OQS is 3/\u221a2 \n(D) the perpendicular distance from O to the straight line containing RS is \u221a15/2", "answer": "(B), (C) and (D)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let f : (0, \u221e) \u2192 R be a differentiable function such that f'(x) = 2 - f(x)/x for all x \u2208 (0, \u221e) and f(1) = 1. Then", "response_choices": "(A) lim x\u21920+ f'(1/x) = 1, (B) lim x\u21920+ xf'(1/x) = 2, (C) lim x\u21920+ x^2 f''(x) = 0, (D) |f(x)| \u2264 2 for all x \u2208 (0, 2)", "answer": "(A)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "Let P = [3 -1 -2; 2 0 \u03b1; 3 -5 0], where \u03b1 \u2208 R . Suppose Q = [qij] is a matrix such that PQ = kI, where k \u2208 R , k \u2260 0 and I is the identity matrix of order 3. If \u03b123 = -k/8 and det(Q) = k^2/2, then", "response_choices": "(A) \u03b1 = 0, k = 8, (B) 4\u03b1 - k + 8 = 0, (C) det(P adj(Q)) = 2^9, (D) det(Q adj(P)) = 2^13", "answer": "(B) and (C)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "In a triangle XYZ, let x, y, z be the lengths of sides opposite to the angles X,Y,Z, respectively, and 2s = x + y + z. If x/4 = y/3 = z/2 and area of incircle of the triangle XYZ is 8\u03c0/3, then", "response_choices": "(A) area of the triangle XYZ is 6\u221a6\n(B) the radius of circumcircle of the triangle XYZ is 35/6 \u221a6\n(C) sinX/sinY sinZ/sinY = 4/35\n(D) sin\u00b2(X+Y)/2 = 3/5", "answer": "(A), (C) and (D)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "A solution curve of the differential equation (x\u00b2 +xy + 4x + 2y + 4)dy/dx - y\u00b2 = 0 , x > 0, passes through the point (1,3). Then the solution curve", "response_choices": "(A) intersects y = x + 2 exactly at one point\n(B) intersects y = x + 2 exactly at two points\n(C) intersects y = (x + 2)\u00b2\n(D) does NOT intersect y = (x + 3)\u00b2", "answer": "(A) and (D)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let f : R\u2192R, g : R\u2192R and h : R\u2192R be differentiable functions such that f(x) = x^3 + 3x + 2, g(f(x)) = x and h(g(g(x))) = x for all x \u2208 R. Then", "response_choices": "(A) g'(2) = 1/15, (B) h'(1) = 666, (C) h(0) = 16, (D) h(g(3)) = 36", "answer": "(B) and (C)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "The circle C1 : x^2 + y^2 = 3, with centre at O, intersects the parabola x^2 = 2y at the point P in the first quadrant. Let the tangent to the circle C1 at P touches other two circles C2 and C3 at R2 and R3, respectively. Suppose C2 and C3 have equal radii 2\u221a3 and centres Q2 and Q3, respectively. If Q2 and Q3 lie on the y-axis, then", "response_choices": "(A) Q2Q3 = 12, (B) R2R3 = 4\u221a6, (C) area of the triangle OR2R3 is 6\u221a2, (D) area of the triangle PQ2Q3 is 4\u221a2", "answer": "(A), (B) and (C)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Let RS be the diameter of the circle x^2 + y^2 = 1, where S is the point (1, 0). Let P be a variable point (other than R and S) on the circle and tangents to the circle at S and P meet at the point Q. The normal to the circle at P intersects a line drawn through Q parallel to RS at point E. Then the locus of E passes through the point(s)", "response_choices": "(A) (1/3, 1/\u221a3), (B) (1/4, 1/2), (C) (1, -1/\u221a3), (D) (1/4, -1/2)", "answer": "(A) and (C)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "The total number of distinct x \u2208 R for which [2x 4x^2 1+8x^3] = 10 is [3x 9x^2 1+27x^3]", "response_choices": "No multiple choice options provided", "answer": "2", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "Let m be the smallest positive integer such that the coefficient of x^3 in the expansion of (1+x)^2 + (1+x)^3 + ... + (1+x)^(3+mx)^m is (3n+1) ^(n/3) for some positive integer n. Then the value of n is", "response_choices": "No multiple choice options provided", "answer": "5", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "The total number of distinct x \u2208 [0,1] for which \\int_{0}^{1} \\frac{t^2}{1+t^4} dt = 2x - 1 is", "response_choices": "", "answer": "(1)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let \u03b1, \u03b2 \u2208 \u211d be such that lim \\frac{x^2sin(\u03b2x)}{x\u21920 \u03b1x - sinx} = 1. Then 6(\u03b1 + \u03b2) equals", "response_choices": "", "answer": "(7)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "Let z = (-1 + \u221a3i)/2, where i = \u221a-1, and r, s \u2208 {1, 2, 3}. Let P = [(-z)^r z^s; z^s z^r] and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P^2 = -I is", "response_choices": "", "answer": "(1)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2016_2.jsonl b/JEE_papers/JSON/JEE_2016_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..f05d2859b56d69e15cbca19ebb9ab77314b2d65f --- /dev/null +++ b/JEE_papers/JSON/JEE_2016_2.jsonl @@ -0,0 +1,55 @@ +{"id": 1, "question": "The electrostatic energy of Z protons uniformly distributed throughout a spherical nucleus of radius R is given by E=3Z(Z-1)e^2/5(4\u03c0\u03f5\u2080R). The measured masses of the neutron, \u00b9H, \u00b9\u2075N and \u00b9\u2077O are 1.008665 u, 1.007825 u, 15.000109 u and 15.003065 u, respectively. Given that the radii of both the \u00b9\u2075N and \u00b9\u2077O nuclei are same, 1 u = 931.5 MeV/c^2 (c is the speed of light) and e\u00b2/(4\u03c0\u03f5\u2080)=1.44 MeV fm. Assuming that the difference between the binding energies of \u00b9\u2075N and \u00b9\u2077O is purely due to the electrostatic energy, the radius of either of the nuclei is (1 fm = 10^-15 m)", "response_choices": "(A) 2.85 fm (B) 3.03 fm (C) 3.42 fm (D) 3.80 fm", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?", "response_choices": "(A) 64 (B) 90 (C) 108 (D) 120", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure Pi=10^6 Pa and volume Vi=10^(-3) m^3 changes to a final state at Pf=(1/32)\u00d710^6 Pa and Vf=8\u00d710^(-3) m^3 in an adiabatic quasi-static process, such that PV^(gamma)= constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at Pi followed by an isochoric (isovolumetric) process at volume Vf. The amount of heat supplied to the system in the two-step process is approximately", "response_choices": "(A) 112 J (B) 294 J (C) 588 J (D) 813 J", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of 1 m at 10 \u00b0C. Now the end P is maintained at 10 \u00b0C, while the end S is heated and maintained at 400 \u00b0C. The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is 1.2 \u00d7 10^(-5) K^(-1), the change in length of the wire PQ is", "response_choices": "(A) 0.78 mm (B) 0.90 mm (C) 1.56 mm (D) 2.34 mm", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle \u03b8 = 30\u00b0 to the axis of the lens, as shown in the figure. If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x, y) at which the image is formed are", "response_choices": "(A) (0, 0) (B) (50 - 25\u221a3, 25) (C) (25, 25\u221a3) (D) (125/3, 25/\u221a3)", "answer": "(C)", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "There are two Vernier calipers both of which have 1 cm divided into 10 equal divisions on the main scale. The Vernier scale of one of the calipers (C1) has 10 equal divisions that correspond to 9 main scale divisions. The Vernier scale of the other caliper (C2) has 10 equal divisions that correspond to 11 main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in cm) by calipers C1 and C2, respectively, are", "response_choices": "(A) 2.85 and 2.82 (B) 2.87 and 2.83 (C) 2.87 and 2.86 (D) 2.87 and 2.87", "answer": "B", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "Two thin circular discs of mass m and 4m, having radii of a and 2a, respectively, are rigidly fixed by a massless, rigid rod of length l = \u221a24a through their centers. This assembly is laid on a firm and flat surface, and set rolling without slipping on the surface so that the angular speed about the axis of the rod is \u03c9. The angular momentum of the entire assembly about the point 'O' is L (see the figure). Which of the following statement(s) is(are) true?", "response_choices": "(A) The center of mass of the assembly rotates about the z-axis with an angular speed of \u03c9/5, (B) The magnitude of angular momentum of center of mass of the assembly about the point O is 81ma\u00b2\u03c9, (C) The magnitude of angular momentum of the assembly about its center of mass is 17ma\u00b2\u03c9/2, (D) The magnitude of the z-component of L is 55ma\u00b2\u03c9", "answer": "(A) OR (A) and (C)", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "Light of wavelength \u03bbph falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is \u03d5 and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is \u03bbc, which of the following statement(s) is(are) true?", "response_choices": "(A) \u03bbc decreases with increase in \u03d5 and \u03bbph\n(B) \u03bbc is approximately halved, if d is doubled\n(C) For large potential difference (V \\gg \u03d5e), \u03bbc is approximately halved if V is made four times\n(D) \u03bbc increases at the same rate as \u03bbph for \u03bbph < hc/\u03d5", "answer": "C", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T' = 2\u03c0\u221a((7(R - r) / 5g). The values of R and r are measured to be (60 \u00b1 1) mm and (10 \u00b1 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?", "response_choices": "(A) The error in the measurement of r is 10% (B) The error in the measurement of T' is 3.57% (C) The error in the measurement of T' is 2% (D) The error in the determined value of g is 11%", "answer": "(A), (B) and (D)", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc < R/2, which of the following statement(s) about any one of the galvanometers is(are) true?", "response_choices": "(A) The maximum voltage range is obtained when all the components are connected in series (B) The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer (C) The maximum current range is obtained when all the components are connected in parallel (D) The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors", "answer": "(B) and (C)", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "In the circuit shown below, the key is pressed at time t = 0. Which of the following statement(s) is(are) true?", "response_choices": "(A) The voltmeter displays - 5 V as soon as the key is pressed, and displays + 5 V after a long time\n(B) The voltmeter will display 0 V at time t = ln 2 seconds\n(C) The current in the ammeter becomes 1/e of the initial value after 1 second\n(D) The current in the ammeter becomes zero after a long time", "answer": "(A), (B), (C) and (D)", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x0. Consider two cases: (i) when the block is at x0; and (ii) when the block is at x = x0 + A. In both the cases, a particle with mass m(< M) is softly placed on the block after which they stick to each other. Which of the following statement(s) is(are) true about the motion after the mass m is placed on the mass M?", "response_choices": "(A) The amplitude of oscillation in the first case changes by a factor of \u221a(M/(m+M)), whereas in the second case it remains unchanged\n(B) The final time period of oscillation in both the cases is same\n(C) The total energy decreases in both the cases\n(D) The instantaneous speed at x0 of the combined masses decreases in both the cases", "answer": "(A), (B) and (D)", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the x-y plane containing two small holes that act as two coherent point sources (S1, S2) emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the x-z plane (for z > 0) at a distance D = 3 m from the mid-point of S1S2, as shown schematically in the figure. The distance between the sources d = 0.6003 mm. The origin O is at the intersection of the screen and the line joining S1S2. Which of the following is(are) true of the intensity pattern on the screen?", "response_choices": "(A) Straight bright and dark bands parallel to the x-axis\n(B) The region very close to the point O will be dark\n(C) Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction\n(D) Semi circular bright and dark bands centered at point O", "answer": "(B) and (D)", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "A rigid wire loop of square shape having side of length L and resistance R is moving along the x-axis with a constant velocity v0 in the plane of the paper. At t = 0, the right edge of the loop enters a region of length 3L where there is a uniform magnetic field B0 into the plane of the paper, as shown in the figure. For sufficiently large v0, the loop eventually crosses the region. Let x be the location of the right edge of the loop. Let v(x), I(x) and F(x) represent the velocity of the loop, current in the loop, and force on the loop, respectively, as a function of x. Counter-clockwise current is taken as positive. Which of the following schematic plot(s) is(are) correct? (Ignore gravity)", "response_choices": "A, B, C, D", "answer": "A and B", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "This section contains instructions about the format and scoring of the following questions. No specific question text is provided.", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "The distance r of the block at time t is", "response_choices": "(A) R/4 (e\u03c9t + e-\u03c9t) (B) R/2 cos \u03c9t (C) R/4 (e2\u03c9t + e-2\u03c9t) (D) R/2 cos 2\u03c9t", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "The net reaction of the disc on the block is", "response_choices": "(A) 1/2 m\u03c92R(e2\u03c9t - e-2\u03c9t) j + mgk (B) 1/2 m\u03c92R(e\u03c9t - e-\u03c9t) j + mgk (C) - m\u03c92R cos \u03c9t j - mgk (D) m\u03c92R sin \u03c9t j - mgk", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "Which one of the following statements is correct?", "response_choices": "(A) The balls will stick to the top plate and remain there\n(B) The balls will bounce back to the bottom plate carrying the same charge they went up with\n(C) The balls will bounce back to the bottom plate carrying the opposite charge they went up with\n(D) The balls will execute simple harmonic motion between the two plates", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "The average current in the steady state registered by the ammeter in the circuit will be", "response_choices": "(A) zero\n(B) proportional to the potential V\u2080\n(C) proportional to V\u2080\u00b9\u2044\u00b2\n(D) proportional to V\u2080\u00b2", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "For the following electrochemical cell at 298 K, Pt(s)|H2(g,1 bar)| H\u207a(aq,1 M)| M\u207a\u207a(aq),M\u207a\u207a(aq)| Pt(s) E_cell = 0.092 V when [M^(+2)]/[M^(+4)] = 10^4. Given : E^0_(M^(+4)/M^(+2)) = 0.151 V;2.303RT/F = 0.059 V The value of x is", "response_choices": "(A) -2 (B) -1 (C) 1 (D) 2", "answer": "D", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "The qualitative sketches I, II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of KCl, CH3OH and CH3(CH2)11OSO3-Na+ at room temperature. The correct assignment of the sketches is", "response_choices": "(A) I : KCl \n\nII : CH3OH \n\nIII : CH3(CH2)11OSO3-Na+\n\n(B) I : CH3(CH2)11OSO3-Na+ II : CH3OH \n\nIII : KCl\n\n(C) I : KCl \n\nII : CH3(CH2)11OSO3-Na+ III : CH3OH\n\n(D) I : CH3OH \n\nII : KCl \n\nIII : CH3(CH2)11OSO3-Na+", "answer": "D", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 21, "question": "In the following reaction sequence in aqueous solution, the species X, Y and Z, respectively, are", "response_choices": "(A) [Ag(S2O3)]3-, Ag2S2O3, Ag2S\n\n(B) [Ag(S2O3)3]5-, Ag2SO3, Ag2S\n\n(C) [Ag(SO4)2]3-, Ag2S2O3, Ag\n\n(D) [Ag(SO4)3]3-, Ag2SO4, Ag", "answer": "A", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "The geometries of the ammonia complexes of Ni2+, Pt2+ and Zn2+, respectively, are", "response_choices": "(A) octahedral, square planar and tetrahedral\n(B) square planar, octahedral and tetrahedral\n(C) tetrahedral, square planar and octahedral\n(D) octahedral, tetrahedral and square planar", "answer": "(A)", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "The correct order of acidity for the following compounds is", "response_choices": "(A) I > II > III > IV\n(C) III > IV > II > I\n(B) III > I > II > IV\n(D) I > III > IV > II", "answer": "(A)", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 24, "question": "The major product of the following reaction sequence is", "response_choices": "(A) \n(B) \n(C) \n(D) ", "answer": "(A)", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 25, "question": "According to Molecular Orbital Theory,", "response_choices": "(A) C2+ is expected to be diamagnetic\n(B) O2+ is expected to have a longer bond length than O2\n(C) N2+ and N2- have the same bond order\n(D) He2+ has the same energy as two isolated He atoms", "answer": "(A) and (C)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 26, "question": "Mixture(s) showing positive deviation from Raoult's law at 35 \u00b0C is(are)", "response_choices": "(A) carbon tetrachloride + methanol\n(B) carbon disulphide + acetone\n(C) benzene + toluene\n(D) phenol + aniline", "answer": "(A) and (B)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "The CORRECT statement(s) for cubic close packed (ccp) three dimensional structure is(are)", "response_choices": "(A) The number of the nearest neighbours of an atom present in the topmost layer is 12\n(B) The efficiency of atom packing is 74%\n(C) The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively\n(D) The unit cell edge length is 2\u221a2 times the radius of the atom", "answer": "(B), (C) and (D)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "Extraction of copper from copper pyrite (CuFeS\u2082) involves", "response_choices": "(A) crushing followed by concentration of the ore by froth-flotation\n(B) removal of iron as slag\n(C) self-reduction step to produce 'blister copper' following evolution of SO\u2082\n(D) refining of 'blister copper' by carbon reduction", "answer": "(A), (B) and (C)", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "The nitrogen containing compound produced in the reaction of HNO\u2083 with P\u2084O\u2081\u2080", "response_choices": "(A) can also be prepared by reaction of P\u2084 and HNO\u2083\n(B) is diamagnetic\n(C) contains one N-N bond\n(D) reacts with Na metal producing a brown gas", "answer": "(B) and (D)", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "For 'invert sugar', the correct statement(s) is(are)\n(Given: specific rotations of (+)-sucrose, (+)-maltose, L-(-)-glucose and L-(+)-fructose in aqueous solution are +66\u00b0, +140\u00b0, -52\u00b0 and +92\u00b0, respectively)", "response_choices": "(A) 'invert sugar' is prepared by acid catalyzed hydrolysis of maltose\n(B) 'invert sugar' is an equimolar mixture of D-(+)-glucose and D-(-)-fructose\n(C) specific rotation of 'invert sugar' is -20\u00b0\n(D) on reaction with Br\u2082 water, 'invert sugar' forms saccharic acid as one of the products", "answer": "(B) and (C)", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "Reagent(s) which can be used to bring about the following transformation is(are)", "response_choices": "(A) LiAlH4 in (C2H5)2O, (B) BH4 in THF, (C) NaBH4 in C2H5OH, (D) Raney Ni/H2 in THF", "answer": "(C) and (D)", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 32, "question": "Among the following, reaction(s) which gives(give) tert-butyl benzene as the major product is(are)", "response_choices": "(A), (B), (C), (D)", "answer": "(B), (C) and (D)", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 33, "question": "The equilibrium constant Kp for this reaction at 298 K, in terms of \u03b2equilibrium, is", "response_choices": "(A) 8\u03b2\u00b2equilibrium/(2 - \u03b2equilibrium) (B) 8\u03b2\u00b2equilibrium/(4 - \u03b2\u00b2equilibrium) (C) 4\u03b2\u00b2equilibrium/(2 - \u03b2equilibrium) (D) 4\u03b2\u00b2equilibrium/(4 - \u03b2\u00b2equilibrium)", "answer": "B", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "The INCORRECT statement among the following, for this reaction, is", "response_choices": "(A) Decrease in the total pressure will result in formation of more moles of gaseous X (B) At the start of the reaction, dissociation of gaseous X\u2082 takes place spontaneously (C) \u03b2equilibrium = 0.7 (D) Kc < 1", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "The compound R is", "response_choices": "(A) NH2, (B) Br, (C) NHBr, (D) NBr", "answer": "(A)", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 36, "question": "The compound T is", "response_choices": "(A) glycine, (B) alanine, (C) valine, (D) serine", "answer": "(B)", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 37, "question": "Let P = [1 0 0; 4 1 0; 16 4 1] and I be the identity matrix of order 3. If Q = [qij] is a matrix such that P^50 - Q = I, then q31 + q32 / q21 equals", "response_choices": "(A) 52 (B) 103 (C) 201 (D) 205", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "Let bi > 1 for i = 1, 2, ..., 101. Suppose log2 b1, log2 b2, ..., log2 b101 are in Arithmetic Progression (A.P.) with the common difference log2 2. Suppose a1, a2, ..., a101 are in A.P. such that a1 = b1 and a51 = b51. If t = b1 + b2 + ... + b51 and s = a1 + a2 + ... + a51, then", "response_choices": "(A) s > t and a101 > b101 (B) s > t and a101 < b101 (C) s < t and a101 > b101 (D) s < t and a101 < b101", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "The value of \u03a3 (1 / sin(\u03c0/4 + (k - 1)\u03c0/6) * sin(\u03c0/4 + k\u03c0/6)) from k=1 to 3 is equal to", "response_choices": "(A) 3 - \u221a3 (B) 2(3 - \u221a3) (C) 2(\u221a3 - 1) (D) 2(2 + \u221a3)", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 40, "question": "The value of \u222b(x^2 cos x / 1 + e^(x/2)) dx is equal to", "response_choices": "(A) \u03c0^2/4 - 2, (B) \u03c0^2/4 + 2, (C) x^2 - e^x, (D) x^2 + e^(x/2)", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 41, "question": "Area of the region {(x, y) \u2208 R^2 : y \u2265 \u221a(x + 3), 5y \u2264 x + 9 \u2264 15} is equal to", "response_choices": "(A) 1/6, (B) 4/3, (C) 3/2, (D) 5/3", "answer": "C", "page_number": 23, "image_available": "yes", "question_subject": "mathematics"} +{"id": 42, "question": "Let P be the image of the point (3, 1, 7) with respect to the plane x - y + z = 3. Then the equation of the plane passing through P and containing the straight line x/2 = y/2 = z/1 is", "response_choices": "(A) x + y - 3z = 0, (B) 3x + z = 0, (C) x - 4y + 7z = 0, (D) 2x - y = 0", "answer": "C", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let f(x) = lim [n^(x+n)/(x+n/2)*...(x+n)/n!] / [n!*(x^2+n^2)*(x^2+n^2/4)*...(x^2+n^4/n^2)], for all x > 0. Then", "response_choices": "(A) f(1/2) \u2265 f(1) (B) f(1/3) \u2264 f(2/3) (C) f'(2) \u2264 0 (D) f'(3)/f(3) \u2265 f'(2)/f(2)", "answer": "(B) and (C)", "page_number": 24, "image_available": "yes", "question_subject": "mathematics"} +{"id": 44, "question": "Let a, b \u2208 \u211d and f : \u211d\u2192\u211d be defined by f(x) = a cos(|x^3 - x|) + b|x|sin(|x^3 + x|). Then f is", "response_choices": "(A) differentiable at x = 0 if a = 0 and b = 1 (B) differentiable at x = 1 if a = 1 and b = 0 (C) NOT differentiable at x = 0 if a = 1 and b = 0 (D) NOT differentiable at x = 1 if a = 1 and b = 1", "answer": "(A) and (B)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "Let f : R \u2192(0, \u221e) and g : R \u2192 R be twice differentiable functions such that f'' and g'' are continuous functions on R. Suppose f''(2)=g(2)=0, f''(2)\u22600 and g'(2)\u22600. If lim(x\u21922) f(x)/g(x) = -1, then", "response_choices": "(A) f has a local minimum at x = 2\n(B) f has a local maximum at x = 2\n(C) f''(2) > f(2)\n(D) f(x) - f''(x) = 0 for at least one x \u2208 R", "answer": "(A) and (D)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "Let f : [1/2, 2] \u2192 R and g : [-1/2, 2] \u2192 R be functions defined by f(x) = [x^2 - 3] and g(x) = [x] f(x) + [4x - 7] f(x), where [y] denotes the greatest integer less than or equal to y for y \u2208 R. Then", "response_choices": "(A) f is discontinuous exactly at three points in [-1/2, 2]\n(B) f is discontinuous exactly at four points in [-1/2, 2]\n(C) g is NOT differentiable exactly at four points in (-1/2, 2)\n(D) g is NOT differentiable exactly at five points in (-1/2, 2)", "answer": "(B) and (C)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let a, b \u2208 \u211d and a^2 + b^2 \u2260 0. Suppose S = {z \u2208 \u2102 : z = (1 +/- i sqrt(-1)t) / (a +/- ibt), t \u2208 \u211d, t \u2260 0}. If z = x + iy and z \u2208 S, then (x, y) lies on", "response_choices": "(A) the circle with radius 1/2a and centre (1/2a, 0) for a > 0, b \u2260 0\n(B) the circle with radius -1/2a and centre (-1/2a, 0) for a < 0, b \u2260 0\n(C) the x-axis for a \u2260 0, b = 0\n(D) the y-axis for a = 0, b \u2260 0", "answer": "(A), (C) and (D)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "Let P be the point on the parabola y^2 = 4x which is at the shortest distance from the center S of the circle x^2 + y^2 - 4x - 16y + 64 = 0. Let Q be the point on the circle dividing the line segment SP internally. Then", "response_choices": "(A) SP = 2\u221a5\n(B) SQ : QP = (\u221a5 + 1) : 2\n(C) the x-intercept of the normal to the parabola at P is 6\n(D) the slope of the tangent to the circle at Q is 1/2", "answer": "(A), (C) and (D)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "Let \u03b1, \u03bb, \u03bc \u2208 \u211d. Consider the system of linear equations \u03b1x + 2y = \u03bb 3x - 2y = \u03bc Which of the following statement(s) is(are) correct?", "response_choices": "(A) If \u03b1 = -3, then the system has infinitely many solutions for all values of \u03bb and \u03bc (B) If \u03b1 \u2260 -3, then the system has a unique solution for all values of \u03bb and \u03bc (C) If \u03bb + \u03bc = 0, then the system has infinitely many solutions for \u03b1 = -3 (D) If \u03bb + \u03bc \u2260 0, then the system has no solution for \u03b1 = -3", "answer": "(B), (C) and (D)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "Let \u016b = u\u2081i + u\u2082j + u\u2083k be a unit vector in \u211d\u00b3 and \u0175 = (1/\u221a6)(i + j + 2k). Given that there exists a vector v\u0304 in \u211d\u00b3 such that |\u016b \u00d7 v\u0304| = 1 and \u0175 \u00b7 (\u016b \u00d7 v\u0304) = 1. Which of the following statement(s) is(are) correct?", "response_choices": "(A) There is exactly one choice for such v\u0304 (B) There are infinitely many choices for such v\u0304 (C) If \u016b lies in the xy-plane then |u\u2081| = |u\u2082| (D) If \u016b lies in the xz-plane then 2|u\u2081| = |u\u2083|", "answer": "(B) and (C)", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "P(X > Y) is", "response_choices": "A) 1/4, B) 5/12, C) 1/2, D) 7/12", "answer": "B", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "P(X = Y) is", "response_choices": "A) 11/36, B) 1/3, C) 13/36, D) 1/2", "answer": "C", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "The orthocentre of the triangle FiMN is", "response_choices": "(A) (-9/10, 0) (B) (2/3, 0) (C) (-9/10, 0) (D) (2/\u221a3, 0)", "answer": "(A)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MFiNF2 is", "response_choices": "(A) 3 : 4 (B) 4 : 5 (C) 5 : 8 (D) 2 : 3", "answer": "(C)", "page_number": 29, "image_available": "yes", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2017_1.jsonl b/JEE_papers/JSON/JEE_2017_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..86ec63b4fa79e35c086419fb831ec6f391fddaeb --- /dev/null +++ b/JEE_papers/JSON/JEE_2017_1.jsonl @@ -0,0 +1,57 @@ +{"id": 1, "question": "A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true?", "response_choices": "[A] The pressure difference between the leading and trailing faces of the plate is proportional to uv, [B] The resistive force experienced by the plate is proportional to v, [C] The plate will continue to move with constant non-zero acceleration, at all times, [D] At a later time the external force F balances the resistive force", "answer": "(A), (B), and (D)", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at x = 0, in a co-ordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following options is/are correct?", "response_choices": "[A] The position of the point mass m is: x = -\u221a(2*(mR)/(M+m))\n[B] The velocity of the point mass m is: v = \u221a((2gR)/(1+(M/m)))\n[C] The x component of displacement of the center of mass of the block M is: -(mR)/(M+m)\n[D] The velocity of the block M is: V = (m/M)*\u221a(2gR)", "answer": "B and C", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength \u03bbo is produced at point O on the rope. The pulse takes time ToA to reach point A. If the wave pulse of wavelength \u03bbo is produced at point A (Pulse 2) without disturbing the position of M it takes time TAO to reach point O. Which of the following options is/are correct?", "response_choices": "[A] The time TAO = TOA \n\n[B] The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope \n\n[C] The wavelength of Pulse 1 becomes longer when it reaches point A \n\n[D] The velocity of any pulse along the rope is independent of its frequency and wavelength", "answer": "(A) and (D)", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A human body has a surface area of approximately 1 m\u00b2. The normal body temperature is 10 K above the surrounding room temperature T\u2080. Take the room temperature to be T\u2080 = 300 K. For T\u2080 = 300 K, the value of \u03c3T\u2080\u2074 = 460 Wm\u207b\u00b2 (where \u03c3 is the Stefan-Boltzmann constant). Which of the following options is/are correct?", "response_choices": "A] The amount of energy radiated by the body in 1 second is close to 60 Joules\n\nB] If the surrounding temperature reduces by a small amount \u0394T\u2080 << T\u2080, then to maintain the same body temperature the same (living) human being needs to radiate \u0394W = 4\u03c3T\u2080\u00b3\u0394T\u2080 more energy per unit time\n\nC] Reducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation\n\nD] If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths", "answer": "C", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A circular insulated copper wire loop is twisted to form two loops of area A and 2A as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field B points into the plane of the paper. At t = 0, the loop starts rotating about the common diameter as axis with a constant angular velocity \u03c9 in the magnetic field. Which of the following options is/are correct?", "response_choices": "[A] The emf induced in the loop is proportional to the sum of the areas of the two loops\n\n[B] The amplitude of the maximum net emf induced due to both the loops is equal to the amplitude of maximum emf induced in the smaller loop alone\n\n[C] The net emf induced due to both the loops is proportional to cos \u03c9t\n\n[D] The rate of change of the flux is maximum when the plane of the loops is perpendicular to plane of the paper", "answer": "B) and D)", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "In the circuit shown, L = 1 \u03bcH, C = 1 \u03bcF and R = 1 k\u03a9. They are connected in series with an a.c. source V = V0 sin \u03c9t as shown. Which of the following options is/are correct?", "response_choices": "[A] The current will be in phase with the voltage if \u03c9 = 10\u2074 rad.s\u207b\u00b9\n[B] The frequency at which the current will be in phase with the voltage is independent of R\n[C] At \u03c9\u223c0 the current flowing through the circuit becomes nearly zero\n[D] At \u03c9 \u226b 10\u2076 rad.s\u207b\u00b9, the circuit behaves like a capacitor", "answer": "B) and C)", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "For an isosceles prism of angle A and refractive index \u03bc, it is found that the angle of minimum deviation \u03b4m = A. Which of the following options is/are correct?", "response_choices": "[A] For the angle of incidence i1 = A, the ray inside the prism is parallel to the base of the prism\n[B] For this prism, the refractive index \u03bc and the angle of prism A are related as A = 2cos\u207b\u00b9(\u03bc/2)\n[C] At minimum deviation, the incident angle i1 and the refracting angle r1 at the first refracting surface are related by r1 = (i1/2)\n[D] For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is i1 = sin\u207b\u00b9[sinA\u221a(A cos\u00b2(A/2) - 1 - cos A)]", "answer": "A), C) and D)", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A drop of liquid of radius R = 10^-2 m having surface tension S = 0.1 Nm^-1 divides itself into K identical drops. In this process the total change in the surface energy \u0394U = 10^-3 J. If K = 10^6 then the value of \u03ba is", "response_choices": "Multiple choice options not provided", "answer": "6", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "An electron in a hydrogen atom undergoes a transition from an orbit with quantum number ni to another with quantum number nf. Vi and Vf are respectively the initial and final potential energies of the electron. If Vf = 6.25, then the smallest possible ni is", "response_choices": "Multiple choice options not provided", "answer": "5", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A monochromatic light is travelling in a medium of refractive index n = 1.6. It enters a stack of glass layers from the bottom side at an angle \u03b8 = 30\u00b0. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as nm = n - m\u0394n, where nm is the refractive index of the mth slab and \u0394n = 0.1 (see the figure). The ray is refracted out parallel to the interface between the (m - 1)th and mth slabs from the right side of the stack. What is the value of m?", "response_choices": "No response choices provided", "answer": "(8)", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "A stationary source emits sound of frequency f0 = 492 Hz. The sound is reflected by a large car approaching the source with a speed of 2 ms^-1. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is 330 ms^-1 and the car reflects the sound at the frequency it has received).", "response_choices": "", "answer": "(6)", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "131I is an isotope of Iodine that \u03b2 decays to an isotope of Xenon with a half-life of 8 days. A small amount of a serum labelled with 131I is injected into the blood of a person. The activity of the amount of 131I injected was 2.4 \u00d7105 Becquerel (Bq). It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After 11.5 hours, 2.5 ml of blood is drawn from the person's body, and gives an activity of 115 Bq. The total volume of blood in the person's body, in liters is approximately (you may use e^ = 1 + x for |x| \u226a 1 and ln 2 \u2248 0.7).", "response_choices": "", "answer": "(5)", "page_number": 9, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "In which case will the particle move in a straight line with constant velocity?", "response_choices": "[A] (III) (ii) (R)\t\t[B] (IV) (i) (S)\t\t[C] (III) (iii) (P)\t\t[D] (II) (iii) (S)", "answer": "D", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "In which case will the particle describe a helical path with axis along the positive z direction?", "response_choices": "[A] (IV) (i) (S)\t\t[B] (II) (ii) (R)\t\t[C] (III) (iii) (P)\t\t[D] (IV) (ii) (R)", "answer": "A", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "In which case would the particle move in a straight line along the negative direction of y-axis (i.e., move along - y)?", "response_choices": "[A] (II) (iii) (Q)\t\t[B] (III) (ii) (R)\t\t[C] (IV) (ii) (S)\t\t[D] (III) (ii) (P)", "answer": "B", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "Answer Q.16, Q.17 and Q.18 by appropriately matching the information given in the three columns of the following table.", "response_choices": "", "answer": "", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "An ideal gas is undergoing a cyclic thermodynamic process in different ways as shown in the corresponding P \u2013 V diagrams in column 3 of the table. Consider only the path from state 1 to state 2. W denotes the corresponding work done on the system. The equations and plots in the table have standard notations as used in thermodynamic processes. Here \u03b3 is the ratio of heat capacities at constant pressure and constant volume. The number of moles in the gas is n.", "response_choices": "(I) Isothermal, (II) Isochoric, (III) Isobaric, (IV) Adiabatic", "answer": "(I) Path 2->1, (II) Path 2->1, (III) Path 1->2, (IV) Path 1->2", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "Match the equations in Column 1 and processes in Column 2 with the corresponding P-V plots in Column 3.", "response_choices": "", "answer": "", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "Which of the following options is the only correct representation of a process in which \u0394U = \u0394Q - P\u0394V?", "response_choices": "[A] (II) (iv) (R)\t[B] (III) (iii) (P)\t[C] (II) (iii) (S)\t[D] (II) (iii) (P)", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Which one of the following options is the correct combination?", "response_choices": "[A] (IV) (ii) (S)\t[B] (III) (ii) (S)\t[C] (II) (iv) (P)\t[D] (II) (iv) (R)", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "Which one of the following options correctly represents a thermodynamic process that is used as a correction in the determination of the speed of sound in an ideal gas?", "response_choices": "[A] (I) (ii) (Q)\t[B] (IV) (ii) (R)\t[C] (III) (iv) (R)\t[D] (I) (iv) (Q)", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "An ideal gas is expanded from (p1, V1, T1) to (p2, V2, T2) under different conditions. The correct statement(s) among the following is(are)", "response_choices": "[A] The work done on the gas is maximum when it is compressed irreversibly from (p2, V2) to (p1, V1) against constant pressure p1\n\n[B] If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic\n\n[C] The work done by the gas is less when it is expanded reversibly from V1 to V2 under adiabatic conditions as compared to that when expanded reversibly from V1 to V2 under isothermal conditions\n\n[D] The change in internal energy of the gas is (i) zero, if it is expanded reversibly with T1 = T2, and (ii) positive, if it is expanded reversibly under adiabatic conditions with T1 \u2260 T2", "answer": "(A), (B), and (C)", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 20, "question": "For a solution formed by mixing liquids L and M, the vapour pressure of L plotted against the mole fraction of M in solution is shown in the following figure. Here xL and xM represent mole fractions of L and M, respectively, in the solution. The correct statement(s) applicable to this system is(are)", "response_choices": "A) The point Z represents vapour pressure of pure liquid M and Raoult's law is obeyed from xL = 0 to xL = 1; B) The point Z represents vapour pressure of pure liquid L and Raoult's law is obeyed when xL > 1; C) The point Z represents vapour pressure of pure liquid M and Raoult's law is obeyed when xL > 0; D) Attractive intermolecular interactions between L-L in pure liquid L and M-M in pure liquid M are stronger than those between L-M when mixed in solution", "answer": "B) and D)", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 21, "question": "The correct statement(s) about the oxoacids, HClO4 and HClO3 is(are)", "response_choices": "[A] The central atom in both HClO4 and HClO3 is sp3 hybridized\n[B] HClO4 is more acidic than HClO3 because of the resonance stabilization of its anion\n[C] HClO4 is formed in the reaction between Cl2 and H2O\n[D] The conjugate base of HClO4 is weaker base than H2O", "answer": "(A), (B), and (D)", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "The colour of the X2 molecules of group 17 elements changes gradually from yellow to violet down the group. This is due to", "response_choices": "[A] the physical state of X2 at room temperature changes from gas to solid down the group\n[B] decrease in ionization energy down the group\n[C] decrease in \u03c0*-\u03c3* gap down the group\n[D] decrease in HOMO-LUMO gap down the group", "answer": "(C) and (D)", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "Addition of excess aqueous ammonia to a pink coloured aqueous solution of MCl2\u00b76H2O (X) and NH4Cl gives an octahedral complex Y in the presence of air. In aqueous solution, complex Y behaves as 1:3 electrolyte. The reaction of X with excess HCl at room temperature results in the formation of a blue coloured complex Z. The calculated spin only magnetic moment of X and Z is 3.87 B.M., whereas it is zero for complex Y. Among the following options, which statement(s) is(are) correct?", "response_choices": "[A] Addition of silver nitrate to Y gives only two equivalents of silver chloride\n[B] The hybridization of the central metal ion in Y is d sp3\n[C] Z is a tetrahedral complex\n[D] When X and Z are in equilibrium at 0\u00b0C, the colour of the solution is pink", "answer": "(B), (C), and (D)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "The IUPAC name(s) of the following compound is(are)", "response_choices": "[A] 1-chloro-4-methylbenzene\n[B] 4-chlorotoluene\n[C] 4-methylchlorobenzene\n[D] 1-methyl-4-chlorobenzene", "answer": "(A) and (B)", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 25, "question": "The correct statement(s) for the following addition reactions is(are)", "response_choices": "[A] Q and P are identical molecules\n\n[B] (M and O) and (N and P) are two pairs of diastereomers\n\n[C] (M and O) and (N and P) are two pairs of enantiomers\n\n[D] Bromination proceeds through trans-addition in both the reactions", "answer": "(B) and (D)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 26, "question": "A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is 8 g cm^-3, then the number of atoms present in 256 g of the crystal is N \u00d7 10^24. The value of N is", "response_choices": "There are no multiple choice options provided for this question.", "answer": "2", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "The conductance of a 0.0015 M aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized Pt electrodes. The distance between the electrodes is 120 cm with an area of cross section of 1 cm^2. The conductance of this solution was found to be 5 \u00d7 10^-7 S. The pH of the solution is 4. The value of limiting molar conductivity (\u03bb_m) of this weak monobasic acid in aqueous solution is Z \u00d7 10^-5 S cm^-1 mol^-1. The value of Z is", "response_choices": "There are no multiple choice options provided for this question.", "answer": "6", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "The sum of the number of lone pairs of electrons on each central atom in the following species is [TeBr6]2-, [BrF5]2-, SNF3, and [XeF5]+ (Atomic numbers: N = 7, F = 9, S = 16, Br = 35, Te = 52, Xe = 54)", "response_choices": "", "answer": "6", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "Among H2, He2+, Li2, Be2, B2-, C2, N2, O2-, and F2, the number of diamagnetic species is (Atomic numbers: H = 1, He = 2, Li = 3, Be = 4, B = 5, C = 6, N = 7, O = 8, F = 9)", "response_choices": "", "answer": "", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 30, "question": "Among the following, the number of aromatic compound(s) is", "response_choices": "", "answer": "5", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 31, "question": "For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is", "response_choices": "[A] (I) (ii) (S) [B] (IV) (iv) (R) [C] (II) (ii) (P) [D] (III) (iii) (P)", "answer": "C", "page_number": 22, "image_available": "yes", "question_subject": "physics"} +{"id": 32, "question": "For hydrogen atom, the only CORRECT combination is", "response_choices": "[A] (I) (i) (S) [B] (II) (i) (Q) [C] (I) (i) (P) [D] (I) (iv) (R)", "answer": "A", "page_number": 22, "image_available": "yes", "question_subject": "physics"} +{"id": 33, "question": "For He+ ion, the only INCORRECT combination is", "response_choices": "[A] (I) (i) (R) [B] (II) (ii) (Q) [C] (I) (iii) (R) [D] (I) (i) (S)", "answer": "C", "page_number": 22, "image_available": "yes", "question_subject": "physics"} +{"id": 34, "question": "For the synthesis of benzoic acid, the only CORRECT combination is", "response_choices": "A] (II) (i) (S) B] (IV) (ii) (P) C] (I) (iv) (Q) D] (III) (iv) (R)", "answer": "A", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 35, "question": "The only CORRECT combination that gives two different carboxylic acids is", "response_choices": "A] (II) (iv) (R) B] (IV) (iii) (Q) C] (III) (iii) (P) D] (I) (i) (S)", "answer": "C", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 36, "question": "The only CORRECT combination in which the reaction proceeds through radical mechanism is", "response_choices": "A] (III) (ii) (P) B] (IV) (i) (Q) C] (II) (iii) (R) D] (I) (ii) (R)", "answer": "D", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "If 2x \u2212 y + 1 = 0 is a tangent to the hyperbola x^2/a^2 - y^2/16 = 1, then which of the following CANNOT be sides of a right angled triangle?", "response_choices": "[A] a, 4, 1 [B] a, 4, 2 [C] 2a, 8, 1 [D] 2a, 4, 1", "answer": "(A), (B), and (C)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "If a chord, which is not a tangent, of the parabola y^2 = 16x has the equation 2x + y = p, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h and k?", "response_choices": "[A] p = \u22122, h = 2, k = \u22124 [B] p = \u22121, h = 1, k = \u22123 [C] p = 2, h = 3, k = \u22124 [D] p = 5, h = 4, k = \u22123", "answer": "(C)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function f(x) = x cos(\u03c0(x + [x])) is discontinuous?", "response_choices": "[A] x = -1, [B] x = 0, [C] x = 1, [D] x = 2", "answer": "Due to printing inconsistency in Q.39 in Code1 of Paper1 (and the corresponding question in all other codes), +4 marks will be awarded to all candidates for this question.", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 40, "question": "Let f: \u211d \u2192 (0,1) be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval (0,1)?", "response_choices": "[A] x^9 - f(x), [B] x - \u222b(0 to x) f(t) cos t dt, [C] ex - \u222b(0 to x) f(t) sin t dt, [D] f(x) + \u222b(0 to x) f(t) sin t dt", "answer": "Ans for Q.40: (A) and (B)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 41, "question": "Which of the following is(are) NOT the square of a 3\u00d73 matrix with real entries?", "response_choices": "[A] [[1, 0, 0], [0, 1, 0], [0, 0, 1]], [B] [[1, 0, 0], [0, 1, 0], [0, 0, -1]], [C] [[1, 0, 0], [0, -1, 0], [0, 0, -1]], [D] [[-1, 0, 0], [0, -1, 0], [0, 0, -1]]", "answer": "Ans for Q.41: (B) and (D)", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Let a, b, x and y be real numbers such that a \u2013 b = 1 and y \u2260 0. If the complex number z = x + iy satisfies Im((a+b)/(x+y)) = y, then which of the following is(are) possible value(s) of x?", "response_choices": "[A] -1 + \u221a(1 - y^2), [B] -1 - \u221a(1 - y^2), [C] 1 + \u221a(1 + y^2), [D] 1 - \u221a(1 + y^2)", "answer": "(A) and (B)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Let X and Y be two events such that P(X) = 1/3, P(X|Y) = 1/2 and P(Y|X) = 2/5. Then", "response_choices": "[A] P(Y) = 4/15, [B] P(X'|Y) = 1/2, [C] P(X \u2229 Y) = 1/5, [D] P(X \u222a Y) = 2/5", "answer": "(A) and (B)", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "For how many values of p, the circle x^2 + y^2 + 2x + 4y - p = 0 and the coordinate axes have exactly three common points?", "response_choices": "A, B, C, D, E, F, G, H, I, J (0 to 9 digits)", "answer": "2", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "Let f: R \u2192 R be a differentiable function such that f(0) = 0, f(\u03c0/2) = 3 and f'(0) = 1. If g(x) = \u222b[x to \u03c0/2] [f'(t) coset - cot t coset f(t)] dt for x \u2208 (0, \u03c0/2], then lim(x\u21920) g(x) =", "response_choices": "A, B, C, D, E, F, G, H, I, J (0 to 9 digits)", "answer": "2", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "For a real number \u03b1, if the system [1 \u03b1 \u03b1^2] [X] = [1] [\u03b1 1 \u03b1] [Y] = [-1] [\u03b1^2 \u03b1 1] [Z] [-1] of linear equations, has infinitely many solutions, then 1 + \u03b1 + \u03b1^2 =", "response_choices": "No multiple choice options provided.", "answer": "(1)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Words of length 10 are formed using the letters A,B,C,D,E,F,G,H,I,J. Let x be the number of such words where no letter is repeated; and let y be the number of such words where exactly one letter is repeated twice and no other letter is repeated. Then, y/x =", "response_choices": "No multiple choice options provided.", "answer": "(5)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?", "response_choices": "No multiple choice options provided.", "answer": "(6)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "For a = \u221a2, if a tangent is drawn to a suitable conic (Column 1) at the point of contact (-1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?", "response_choices": "[A] (I) (i) (P) \t [B] (I) (ii) (Q) \t [C] (II) (ii) (Q) \t [D] (III) (i) (P)", "answer": "B", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "If a tangent to a suitable conic (Column 1) is found to be y = x + 8 and its point of contact is (8, 16), then which of the following options is the only CORRECT combination?", "response_choices": "[A] (I) (ii) (Q) \t [B] (II) (iv) (R) \t [C] (III) (i) (P) \t [D] (III) (ii) (Q)", "answer": "C", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "The tangent to a suitable conic (Column 1) at (\u221a3, 1/\u221a3) is found to be \u221a3x + 2y = 4, then which of the following options is the only CORRECT combination?", "response_choices": "[A] (IV) (iii) (S) \t [B] (IV) (iv) (S) \t [C] (II) (iii) (R) \t [D] (II) (iv) (R)", "answer": "D", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "Which of the following options is the only CORRECT combination?", "response_choices": "A] (I) (i) (P) , B] (II) (ii) (Q) , C] (III) (iii) (R) , D] (IV) (iv) (S)", "answer": "B", "page_number": 31, "image_available": "yes", "question_subject": "mathematics"} +{"id": 53, "question": "Which of the following options is the only CORRECT combination?", "response_choices": "A] (I) (ii) (R) , B] (II) (iii) (S) , C] (III) (iv) (P) , D] (IV) (i) (S)", "answer": "B", "page_number": 31, "image_available": "yes", "question_subject": "mathematics"} +{"id": 54, "question": "Which of the following options is the only INCORRECT combination?", "response_choices": "A] (I) (iii) (P) , B] (II) (iv) (Q) , C] (III) (i) (R) , D] (II) (iii) (P)", "answer": "C", "page_number": 31, "image_available": "yes", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2017_2.jsonl b/JEE_papers/JSON/JEE_2017_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..adc604399b49fd3f6d40c0a3274d40ea7f0a1543 --- /dev/null +++ b/JEE_papers/JSON/JEE_2017_2.jsonl @@ -0,0 +1,54 @@ +{"id": 1, "question": "Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density \u03c1 remains uniform throughout the volume. The rate of fractional change in density (1/\u03c1 d\u03c1/dt) is constant. The velocity v of any point on the surface of the expanding sphere is proportional to", "response_choices": "[A] R [B] R\u00b3 [C] 1/R [D] R^2/3", "answer": "A", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "Consider regular polygons with number of sides n = 3, 4, 5, ..... as shown in the figure. The center of mass of all the polygons is at height h from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is \u0394. Then \u0394 depends on n and h as", "response_choices": "[A] \u0394= h sin^2 (\u03c0/n), [B] \u0394= h ((1/cos(\u03c0/n)) - 1), [C] \u0394= h sin (2\u03c0/n), [D] \u0394= h tan^2 (\u03c0/2n)", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "mathematics"} +{"id": 3, "question": "A photoelectric material having work-function \u03d50 is illuminated with light of wavelength \u03bb (\u03bb < hc/\u03d50). The fastest photoelectron has a de Broglie wavelength \u03bbd. A change in wavelength of the incident light by \u0394\u03bb results in a change \u0394\u03bbd in \u03bbd. Then the ratio \u0394\u03bbd/\u0394\u03bb is proportional to", "response_choices": "[A] \u03bbd/\u03bb [B] \u03bbd2/\u03bb2 [C] \u03bbd3/\u03bb [D] \u03bbd3/\u03bb2", "answer": "D", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "A symmetric star shaped conducting wire loop is carrying a steady state current I as shown in the figure. The distance between the diametrically opposite vertices of the star is 4a. The magnitude of the magnetic field at the center of the loop is", "response_choices": "[A] \u03bc0I/4\u03c0a 6[\u221a3 \u2212 1] [B] \u03bc0I/4\u03c0a 6[\u221a3 + 1] [C] \u03bc0I/4\u03c0a 3[\u221a3 \u2212 1] [D] \u03bc0I/4\u03c0a 3[2 \u2212 \u221a3]", "answer": "A", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "Three vectors P, Q and R are shown in the figure. Let S be any point on the vector R. The distance between the points P and S is b|R|. The general relation among vectors P, Q and S is", "response_choices": "[A] S = (1 - b)P + bQ, [B] S = (b - 1)P + bQ, [C] S = (1 - b\u00b2)P + bQ, [D] S = (1 - b)P + b\u00b2Q", "answer": "A", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is 3\u00d710^5 times heavier than the Earth and is at a distance 2.5\u00d710^8 times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is ve = 11.2 km s^-1. The minimum initial velocity (vs) required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)", "response_choices": "A) vs = 22 km s^-1\nB) vs = 42 km s^-1\nC) vs = 62 km s^-1\nD) vs = 72 km s^-1", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is \u03b4T = 0.01 seconds and he measures the depth of the well to be L = 20 meters. Take the acceleration due to gravity g = 10 ms^-2 and the velocity of sound is 300 ms^-1. Then the fractional error in the measurement, \u03b4L/L, is closest to", "response_choices": "A) 0.2%\nB) 1%\nC) 3%\nD) 5%", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A uniform magnetic field B exists in the region between x = 0 and x = 3R (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge +Q and momentum p directed along x-axis enters region 2 from region 1 at point P1 (y = -R). Which of the following option(s) is/are correct?", "response_choices": "[A] For B > 2 p/(3 QR), the particle will re-enter region 1 \n\n[B] For B = 8 p/(13 QR), the particle will enter region 3 through the point P2 on x-axis \n\n[C] When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linear momentum between point P1 and the farthest point from y-axis is p/\u221a2 \n\n[D] For a fixed B, particles of same charge Q and same velocity v, the distance between the point P1 and the point of re-entry into region 1 is inversely proportional to the mass of the particle", "answer": "(A) and (B)", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "The instantaneous voltages at three terminals marked X, Y and Z are given by Vx = V0 sin \u03c9t, Vy = V0 sin (\u03c9t + 2\u03c0/3) and Vz = V0 sin (\u03c9t + 4\u03c0/3). An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z. The reading(s) of the voltmeter will be", "response_choices": "[A] VXYrms = V0\u221a(3/2), [B] VYZrms = V0\u221a(1/2), [C] VXYrms = V0, [D] independent of the choice of the two terminals", "answer": "A and D", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A point charge +Q is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?", "response_choices": "[A] The electric flux passing through the curved surface of the hemisphere is (Q/(2\u03b50)) * (1 - 1/2), [B] Total flux through the curved and the flat surfaces is Q/\u03b50, [C] The component of the electric field normal to the flat surface is constant over the surface, [D] The circumference of the flat surface is an equipotential", "answer": "A and D", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "Two coherent monochromatic point sources S1 and S2 of wavelength \u03bb = 600 nm are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance d = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is \u0394\u03b8. Which of the following options is/are correct?", "response_choices": "[A] A dark spot will be formed at the point P2 \n\n[B] At P2 the order of the fringe will be maximum \n\n[C] The total number of fringes produced between P1 and P2 in the first quadrant is close to 3000 \n\n[D] The angular separation between two consecutive bright spots decreases as we move from P1 to P2 along the first quadrant", "answer": "B) and (C)", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "A source of constant voltage V is connected to a resistance R and two ideal inductors L1 and L2 through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At t = 0, the switch is closed and current begins to flow. Which of the following options is/are correct?", "response_choices": "[A] After a long time, the current through L1 will be V * L2 / (R L1 + L2) \n\n[B] After a long time, the current through L2 will be V * L1 / (R L1 + L2) \n\n[C] The ratio of the currents through L1 and L2 is fixed at all times (t > 0) \n\n[D] At t = 0, the current through the resistance R is V/R", "answer": "(A), (B), and (C)", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vertical is \u03b8. Which of the following statements about its motion is/are correct?", "response_choices": "[A] The midpoint of the bar will fall vertically downward\n\n[B] The trajectory of the point A is a parabola\n\n[C] Instantaneous torque about the point in contact with the floor is proportional to sin \u03b8\n\n[D] When the bar makes an angle \u03b8 with the vertical, the displacement of its midpoint from the initial position is proportional to (1 \u2212 cos \u03b8)", "answer": "(A), (C), and (D)", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque \u03c4 about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?", "response_choices": "[A] If the force is applied at point P tangentially then \u03c4 decreases continuously as the wheel climbs\n\n[B] If the force is applied normal to the circumference at point X then \u03c4 is constant\n\n[C] If the force is applied normal to the circumference at point P then \u03c4 is zero\n\n[D] If the force is applied tangentially at point S then \u03c4 \u2260 0 but the wheel never climbs the step", "answer": "{{C}} or {{C} and {D}}", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "In Process 1, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by:", "response_choices": "[A] EC = ED, [B] EC = ED ln 2, [C] EC = 1/2 ED, [D] EC = 2ED", "answer": "A", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "In Process 2, total energy dissipated across the resistance ED is:", "response_choices": "[A] ED = 1/2 CV0^2, [B] ED = 3 (1/2 CV0^2), [C] ED = 1/3 (1/2 CV0^2), [D] ED = 3 CV0^2", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "The total kinetic energy of the ring is", "response_choices": "[A] M\u03c9\u2080\u00b2R\u00b2\n[B] \u00bd M\u03c9\u2080\u00b2(R \u2212 r)\u00b2\n[C] M\u03c9\u2080\u00b2(R \u2212 r)\u00b2\n[D] \u00b2\u2044\u2083 M\u03c9\u2080\u00b2(R \u2212 r)\u00b2", "answer": "Due to internal review, all candidates are awarded +3 marks.", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "The minimum value of \u03c9\u2080 below which the ring will drop down is", "response_choices": "[A] \u221a(g/\u03bc(R\u2212r))\n[B] \u221a(2g/\u03bc(R\u2212r))\n[C] \u221a(3g/2\u03bc(R\u2212r))\n[D] \u221a(g/2\u03bc(R\u2212r))", "answer": "A", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K kg mol^-1. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is 46 g mol^-1] Among the following, the option representing change in the freezing point is", "response_choices": "[A] [B] [C] [D]", "answer": "C", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 20, "question": "For the following cell, Zn(s) | ZnSO4(aq) || CuSO4(aq) | Cu(s) when the concentration of Zn^2+ is 10 times the concentration of Cu^2+, the expression for \u0394G (in J mol^-1) is [F is Faraday constant; R is gas constant; T is temperature; E^0(cell) = 1.1 V]", "response_choices": "[A] 1.1F\n[B] 2.303RT \u2013 2.2F\n[C] 2.303RT + 1.1F\n[D] \u20132.2F", "answer": "B", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 21, "question": "The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at T = 298 K are \n \u0394f G\u00b0[C(graphite)] = 0 kJ mol^-1\n \u0394f G\u00b0[C(diamond)] = 2.9 kJ mol^-1.\nThe standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by 2\u00d710^-6 m\u00b3 mol^-1. If C(graphite) is converted to C(diamond) isothermally at T = 298 K, the pressure at which C(graphite) is in equilibrium with C(diamond), is\n[Useful information: 1 J = 1 kg m\u00b2 s^-2; 1 Pa = 1 kg m^-1 s^-2; 1 bar = 10\u2075 Pa]", "response_choices": "[A] 14501 bar\n[B] 58001 bar\n[C] 1450 bar\n[D] 29001 bar", "answer": "A", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 22, "question": "Which of the following combination will produce H2 gas?", "response_choices": "[A] Fe metal and conc. HNO3\n[B] Cu metal and conc. HNO3\n[C] Zn metal and NaOH(aq)\n[D] Au metal and NaCN(aq) in the presence of air", "answer": "C", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 23, "question": "The order of the oxidation state of the phosphorus atom in H3PO2, H3PO3, H3PO4, and H4P2O6 is", "response_choices": "[A] H3PO3 > H3PO2 > H3PO4 > H4P2O6, [B] H3PO4 > H3PO2 > H3PO3 > H4P2O6, [C] H3PO4 > H4P2O6 > H3PO3 > H3PO2, [D] H3PO2 > H3PO3 > H4P2O6 > H3PO4", "answer": "C", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 24, "question": "The major product of the following reaction is", "response_choices": "[A], [B], [C], [D]", "answer": "C", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 25, "question": "The order of basicity among the following compounds is", "response_choices": "[A] II > I > IV > III, [B] IV > II > III > I, [C] IV > I > II > III, [D] I > IV > III > II", "answer": "C", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 26, "question": "The correct statement(s) about surface properties is(are)", "response_choices": "[A] Adsorption is accompanied by decrease in enthalpy and decrease in entropy of the system, [B] The critical temperatures of ethane and nitrogen are 563 K and 126 K, respectively. The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature, [C] Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium, [D] Brownian motion of colloidal particles does not depend on the size of the particles but depends on viscosity of the solution", "answer": "A, B", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 27, "question": "For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant K in terms of change in entropy is described by", "response_choices": "[A] With increase in temperature, the value of K for exothermic reaction decreases because the entropy change of the system is positive\n\n[B] With increase in temperature, the value of K for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases\n\n[C] With increase in temperature, the value of K for endothermic reaction increases because the entropy change of the system is negative\n\n[D] With increase in temperature, the value of K for exothermic reaction decreases because favourable change in entropy of the surroundings decreases", "answer": "B and D", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 28, "question": "In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are)", "response_choices": "[A] The activation energy of the reaction is unaffected by the value of the steric factor\n\n[B] Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation\n\n[C] Since P = 4.5, the reaction will not proceed unless an effective catalyst is used\n\n[D] The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally", "answer": "A and B", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 29, "question": "For the following compounds, the correct statement(s) with respect to nucleophilic substitution reactions is(are)", "response_choices": "[A] I and III follow SN1 mechanism\n\n[B] I and II follow SN2 mechanism\n\n[C] Compound IV undergoes inversion of configuration\n\n[D] The order of reactivity for I, III and IV is: IV > I > III", "answer": "{{(A), (B), and (C)}} or {{(A), (B), (C), and (D)}}", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 30, "question": "Among the following, the correct statement(s) is(are)", "response_choices": "[A] Al(CH3)3 has the three-centre two-electron bonds in its dimeric structure\n\n[B] BH3 has the three-centre two-electron bonds in its dimeric structure\n\n[C] AlCl3 has the three-centre two-electron bonds in its dimeric structure\n\n[D] The Lewis acidity of BCl3 is greater than that of AlCl3", "answer": "(A), (B), and (D)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 31, "question": "The option(s) with only amphoteric oxides is(are)", "response_choices": "[A] Cr2O3, BeO, SnO, SnO2\n\n[B] Cr2O3, CrO, SnO, PbO\n\n[C] NO, B2O3, PbO, SnO2\n\n[D] ZnO, Al2O3, PbO, PbO2", "answer": "(A) and (D)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 32, "question": "Compounds P and R upon ozonolysis produce Q and S, respectively. The molecular formula of Q and S is C8H8O. Q undergoes Cannizzaro reaction but not haloform reaction, whereas S undergoes haloform reaction but not Cannizzaro reaction.", "response_choices": "[A], [B], [C], [D]", "answer": "(A) and (B)", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 33, "question": "W and X are, respectively", "response_choices": "[A] O3 and P4O6\n[B] O2 and P4O6\n[C] O2 and P4O10\n[D] O3 and P4O10", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 34, "question": "Y and Z are, respectively", "response_choices": "[A] N2O3 and H3PO4\n[B] N2O5 and HPO3\n[C] N2O4 and HPO3\n[D] N2O4 and H3PO4", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 35, "question": "The product S is", "response_choices": "[A] (Structure A) [B] (Structure B) [C] (Structure C) [D] (Structure D)", "answer": "A", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 36, "question": "The reactions, Q to R and R to S, are", "response_choices": "[A] Dehydration and Friedel-Crafts acylation [B] Aromatic sulfonation and Friedel-Crafts acylation [C] Friedel-Crafts alkylation, dehydration and Friedel-Crafts acylation [D] Friedel-Crafts alkylation and Friedel-Crafts acylation", "answer": "D", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 37, "question": "The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y - 2z = 5 and 3x - 6y - 2z = 7, is", "response_choices": "A) 14x + 2y - 15z = 1\nB) 14x - 2y + 15z = 27\nC) 14x + 2y + 15z = 31\nD) -14x + 2y + 15z = 3", "answer": "C", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 38, "question": "Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP \u00b7 OQ + OR \u00b7 OS = OR \u00b7 OP + OQ \u00b7 OS = OQ \u00b7 OR + OP \u00b7 OS\nThen the triangle PQR has S as its", "response_choices": "A) centroid\nB) circumcentre\nC) incentre\nD) orthocenter", "answer": "D", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 39, "question": "If y = y(x) satisfies the differential equation (8/sqrt(9 + sqrt(x)) dy = ((4 + sqrt(9 + sqrt(x)))^-1) dx, x > 0) and y(0) = sqrt(7), then y(256) =", "response_choices": "[A] 3 [B] 9 [C] 16 [D] 80", "answer": "A", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 40, "question": "If f: R \u2192 R is a twice differentiable function such that f''(x) > 0 for all x \u2208 R, and f(1/2) = 1/2 f'(1) = 1, then", "response_choices": "[A] f'(1) \u2264 0 [B] 0 < f'(1) \u2264 1/2 [C] 1/2 < f'(1) \u2264 1 [D] f'(1) > 1", "answer": "D", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 41, "question": "How many 3\u00d73 matrices M with entries from {0,1,2} are there, for which the sum of the diagonal entries of M^TM is 5?", "response_choices": "[A] 126, [B] 198, [C] 162, [D] 135", "answer": "B", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 42, "question": "Let S = {1,2,3,...,9}. For k = 1,2,...,5, let Nk be the number of subsets of S, each containing five elements out of which exactly k are odd. Then N1 + N2 + N3 + N4 + N5 =", "response_choices": "[A] 210, [B] 252, [C] 125, [D] 126", "answer": "D", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 43, "question": "Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is", "response_choices": "[A] 36/55, [B] 6/11, [C] 1/2, [D] 5/11", "answer": "B", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 44, "question": "If g(x) = (\u222bsin(2x)/sinx)*1(t) dt, then", "response_choices": "[A] g'(\u03c0/2) = -2\u03c0, [B] g'(-\u03c0/2) = 2\u03c0, [C] g'(\u03c0/2) = 2\u03c0, [D] g'(-\u03c0/2) = -2\u03c0", "answer": "[A], [C] and [D]", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 45, "question": "Let \u03b1 and \u03b2 be nonzero real numbers such that 2(cos \u03b2 - cos \u03b1) + cos \u03b1 cos \u03b2 = 1. Then which of the following is/are true?", "response_choices": "[A] tan(\u03b1/2) + \u221a3 tan(\u03b2/2) = 0, [B] \u221a3 tan(\u03b1/2) + tan(\u03b2/2) = 0, [C] tan(\u03b1/2) - \u221a3 tan(\u03b2/2) = 0, [D] \u221a3 tan(\u03b1/2) - tan(\u03b2/2) = 0", "answer": "All candidates are awarded +4 marks.", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 46, "question": "If f: R \u2192 R is a differentiable function such that f'(x) > 2f(x) for all x \u2208 R, and f(0) = 1, then", "response_choices": "[A] f(x) is increasing in (0, \u221e)\n[B] f(x) is decreasing in (0, \u221e)\n[C] f(x) > e^2x in (0, \u221e)\n[D] f'(x) < e^2x in (0, \u221e)", "answer": "(A) and (C)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 47, "question": "Let f(x) = (1-x^(1+|1-x|)) / |1-x| * cos(1 / 1-x) for x \u2260 1. Then", "response_choices": "[A] lim(x\u21921-) f(x) = 0\n[B] lim(x\u21921+) f(x) does not exist\n[C] lim(x\u21921-) f(x) = 0\n[D] lim(x\u21921+) f(x) does not exist", "answer": "(A) and (D)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 48, "question": "If f(x) = [cos(2x) cos(2x) sin(2x)] [- cos x cos x - sin x], then\n [ sin x sin x cos x ]", "response_choices": "[A] f'(x) = 0 at exactly three points in (-\u03c0, \u03c0)\n[B] f'(x) = 0 at more than three points in (-\u03c0, \u03c0)\n[C] f(x) attains its maximum at x = 0\n[D] f(x) attains its minimum at x = 0", "answer": "(B) and (C)", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 49, "question": "If the line x = \u03b1 divides the area of region R = {(x, y) \u2208 R^2 : x^3 \u2264 y \u2264 x, 0 \u2264 x \u2264 1} into two equal parts, then", "response_choices": "[A] 0 < \u03b1 \u2264 1/2, [B] 1/2 < \u03b1 < 1, [C] 2\u03b1^4 \u2212 4\u03b1^2 + 1 = 0, [D] \u03b1^4 + 4\u03b1^2 \u2212 1 = 0", "answer": "B and C", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 50, "question": "If I = \u2211(98 k=1) \u222b(k k+1) (k+1 x(x+1)) dx, then", "response_choices": "[A] I > log\u2091 99, [B] I < log\u2091 99, [C] I < 49/50, [D] I > 49/50", "answer": "B and D", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 51, "question": "| OX \u00d7 OY |=", "response_choices": "[A] sin(P + Q) [B] sin 2R [C] sin(P + R) [D] sin(Q + R)", "answer": "A", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 52, "question": "If the triangle PQR varies, then the minimum value of cos(P + Q) + cos(Q + R) + cos(R + P) is", "response_choices": "[A] -5/3 [B] -3/2 [C] 3/2 [D] 5/3", "answer": "B", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 53, "question": "Let p, q be integers and let \u03b1, \u03b2 be the roots of the equation, x^2 - x - 1 = 0, where \u03b1 \u2260 \u03b2. For n = 0, 1, 2, ... let an = p\u03b1^n + q\u03b2^n. FACT: If a and b are rational numbers and a + b\u221a5 = 0, then a = 0 = b. Q.53 a12 =", "response_choices": "[A] a11 - a10, [B] a11 + a10, [C] 2a11 + a10, [D] a11 + 2a10", "answer": "B", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 54, "question": "If a4 = 28, then p + 2q =", "response_choices": "[A] 21, [B] 14, [C] 7, [D] 12", "answer": "D", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2018_1.jsonl b/JEE_papers/JSON/JEE_2018_1.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..1652120a1dea485d6eb513213d4c6d75de3b4431 --- /dev/null +++ b/JEE_papers/JSON/JEE_2018_1.jsonl @@ -0,0 +1,59 @@ +{"id": 1, "question": "The potential energy of a particle of mass m at a distance r from a fixed point O is given by V(r) = kr^2/2, where k is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius R about the point O. If v is the speed of the particle and L is the magnitude of its angular momentum about O, which of the following statements is (are) true?", "response_choices": "(A) v = \u221a(k/2m) R, (B) v = \u221a(k/m) R, (C) L = \u221a(mkR^2), (D) L = \u221a(mk/2) R^2", "answer": "C,D", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "Consider a body of mass 1.0 kg at rest at the origin at time t = 0. A force F = (\u03b1t i + \u03b2 j) is applied on the body, where \u03b1 = 1.0 N/s^-1 and \u03b2 = 1.0 N. The torque acting on the body about the origin at time t = 1.0 s is \u03c4. Which of the following statements is (are) true?", "response_choices": "(A) |\u03c4| = 1/3 N m\n(B) The torque \u03c4 is in the direction of the unit vector + k\n(C) The velocity of the body at t = 1 s is v = 1/2 (i + 2j) m s^-1\n(D) The magnitude of displacement of the body at t = 1 s is 1/6 m", "answer": "B", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water is \u03c3. The angle of contact between water and the wall of the capillary tube is \u03b8. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?", "response_choices": "(A) For a given material of the capillary tube, h decreases with increase in r\n(B) For a given material of the capillary tube, h is independent of \u03c3\n(C) If this experiment is performed in a lift going up with a constant acceleration, then h decreases\n(D) h is proportional to contact angle \u03b8", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "In the figure below, the switches S1 and S2 are closed simultaneously at t = 0 and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wire reaches its maximum magnitude Imax at time t = \u03c4. Which of the following statements is (are) true?", "response_choices": "(A) Imax = V/2R, (B) Imax = V/4R, (C) \u03c4 = L/R ln 2, (D) \u03c4 = 2L/R ln 2", "answer": "C", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "Two infinitely long straight wires lie in the xy-plane along the lines x = \u00b1R. The wire located at x = +R carries a constant current I1 and the wire located at x = \u2212R carries a constant current I2. A circular loop of radius R is suspended with its centre at (0, 0, \u221a3R) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the +j direction. Which of the following statements regarding the magnetic field B is (are) true?", "response_choices": "(A) If I1 = I2, then B cannot be equal to zero at the origin (0, 0, 0), (B) If I1 > 0 and I2 < 0, then B can be equal to zero at the origin (0, 0, 0), (C) If I1 < 0 and I2 > 0, then B can be equal to zero at the origin (0, 0, 0), (D) If I1 = I2, then the z-component of the magnetic field at the centre of the loop is (\u2212 \u03bc0I/2R)", "answer": "D", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (where V is the volume and T is the temperature). Which of the statements below is (are) true?", "response_choices": "A) Process I is an isochoric process, B) In process II, gas absorbs heat, C) In process IV, gas releases heat, D) Processes I and III are not isobaric", "answer": "B", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "Two vectors A and B are defined as A = a i and B = a (cos \u03c9t i + sin \u03c9t j), where a is a constant and \u03c9 = \u03c0/6 rad s^(-1). If |A + B| = \u221a3|A - B| at time t = \u03c4 for the first time, the value of \u03c4, in seconds, is _________.", "response_choices": "N/A", "answer": "Numerical response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 m s^(-1) and the man behind walks at a speed 2.0 m s^(-1). A third man is standing at a height 12 m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430 Hz. The speed of sound in air is 330 m s^(-1). At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is _________.", "response_choices": "N/A", "answer": "Numerical response required", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an angle 60\u00b0 with the horizontal. They start to roll without slipping at the same instant of time along the shortest path. If the time difference between their reaching the ground is (2 - \u221a3) /\u221a10 s, then the height of the top of the inclined plane, in metres, is _________. Take g = 10 m s^(-2).", "response_choices": "N/A", "answer": "Numerical response required", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is 2.0 N m^-1 and the mass of the block is 2.0 kg. Ignore the mass of the spring. Initially the spring is in an unstretched condition. Another block of mass 1.0 kg moving with a speed of 2.0 m s^-1 collides elastically with the first block. The collision is such that the 2.0 kg block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is _________.", "response_choices": "No multiple choice options given", "answer": "Numerical answer required", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "Three identical capacitors C1, C2 and C3 have a capacitance of 1.0 \u03bcF each and they are uncharged initially. They are connected in a circuit as shown in the figure and C3 is filled completely with a dielectric material of relative permittivity \u03b5r. The cell electromotive force (emf) V0 = 8 V. First the switch S1 is closed while the switch S2 is kept open. When the capacitor C3 is fully charged, S1 is opened and S2 is closed simultaneously. When all the capacitors reach equilibrium, the charge on C3 is found to be 5 \u03bcC. The value of \u03b5r = ___________.", "response_choices": "No multiple choice options given", "answer": "Numerical answer required", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "In the xy-plane, the region y > 0 has a uniform magnetic field B1k and the region y < 0 has another uniform magnetic field B2k. A positively charged particle is projected from the origin along the positive y-axis with speed v0 = \u03c0 m s^-1 at t = 0, as shown in the figure. Neglect gravity in this problem. Let t = T be the time when the particle crosses the x-axis from below for the first time. If B2 = 4B1, the average speed of the particle, in m s^-1, along the x-axis in the time interval T is _________.", "response_choices": "", "answer": "", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "Sunlight of intensity 1.3 kW m^-2 is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in kW m^-2, at a distance 22 cm from the lens on the other side is _________.", "response_choices": "", "answer": "", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T1 = 300 K and T2 = 100 K, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K1 and K2 respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K1/K2 = _________.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "The relation between [E] and [B] is", "response_choices": "(A) [E] = [B] [L] [T], (B) [E] = [B] [L]^-1 [T], (C) [E] = [B] [L] [T]^-1, (D) [E] = [B] [L]^-1 [T]^-1", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "The relation between [\u03f50] and [\u03bc0] is", "response_choices": "A) [\u03bc0] = [\u03f50] [L]2 [T]\u22122, B) [\u03bc0] = [\u03f50] [L]\u22122 [T]2, C) [\u03bc0] = [\u03f50]\u22121 [L]2 [T]\u22122, D) [\u03bc0] = [\u03f50]\u22121 [L]\u22122 [T]2", "answer": "", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Consider the ratio r = (1-a)/(1+a) to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is \u0394a (\u0394a/a << 1), then what is the error \u0394r in determining r?", "response_choices": "A) \u0394a/(1+a)^2, B) 2\u0394a/(1+a)^2, C) 2\u0394a/(1-a^2), D) 2a\u0394a/(1-a^2)", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "In an experiment the initial number of radioactive nuclei is 3000. It is found that 1000 \u00b1 40 nuclei decayed in the first 1.0 s. For |x| \u226a 1, ln(1 + x) = x up to first power in x. The error \u2206\u03bb, in the determination of the decay constant \u03bb, in s\u207b\u00b9, is", "response_choices": "(A) 0.04 (B) 0.03 (C) 0.02 (D) 0.01", "answer": "(C) 0.02", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "The compound(s) which generate(s) N2 gas upon thermal decomposition below 300\u00b0C is (are)", "response_choices": "(A) NH4NO3, (B) (NH4)2Cr2O7, (C) Ba(N3)2, (D) Mg3N2", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The correct statement(s) regarding the binary transition metal carbonyl compounds is (are) (Atomic numbers: Fe = 26, Ni = 28)", "response_choices": "(A) Total number of valence shell electrons at metal centre in Fe(CO)5 or Ni(CO)4 is 16, (B) These are predominantly low spin in nature, (C) Metal\u2013carbon bond strengthens when the oxidation state of the metal is lowered, (D) The carbonyl C\u2013O bond weakens when the oxidation state of the metal is increased", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Based on the compounds of group 15 elements, the correct statement(s) is (are)", "response_choices": "(A) Bi2O5 is more basic than N2O5, (B) NF3 is more covalent than BIF3, (C) PH3 boils at lower temperature than NH3, (D) The N-N single bond is stronger than the P-P single bond", "answer": "", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "In the following reaction sequence, the correct structure(s) of X is (are)", "response_choices": "(A), (B), (C), (D)", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "The reaction(s) leading to the formation of 1,3,5-trimethylbenzene is (are)", "response_choices": "(A), (B), (C), (D)", "answer": "(C)", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "A reversible cyclic process for an ideal gas is shown below. Here, P, V, and T are pressure, volume and temperature, respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.", "response_choices": "(A) qAC = \u0394UBC and wAB = P2(V2 \u2013 V1) \n(B) wBC = P2(V2 \u2013 V1) and qBC = \u0394HAC \n(C) \u0394HCA < \u0394UCA and qAC = \u0394UBC \n(D) qBC = \u0394HAC and \u0394HCA > \u0394UCA", "answer": "", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "Among the species given below, the total number of diamagnetic species is ____.", "response_choices": "", "answer": "", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "The ammonia prepared by treating ammonium sulphate with calcium hydroxide is completely used by NiCl2.6H2O to form a stable coordination compound. Assume that both the reactions are 100% complete. If 1584 g of ammonium sulphate and 952 g of NiCl2.6H2O are used in the preparation, the combined weight (in grams) of gypsum and the nickel-ammonia coordination compound thus produced is ____.", "response_choices": "", "answer": "", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is constructed from the unit cell of MX following the sequential instructions given below. Neglect the charge balance. (i) Remove all the anions (X) except the central one (ii) Replace all the face centered cations (M) by anions (X) (iii) Remove all the corner cations (M) (iv) Replace the central anion (X) with cation (M) The value of (number of anions/number of cations) in Z is _____.", "response_choices": "", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "For the electrochemical cell, Mg(s) | Mg2+ (aq, 1 M) || Cu2+ (aq, 1 M) | Cu(s) the standard emf of the cell is 2.70 V at 300 K. When the concentration of Mg2+ is changed to x M, the cell potential changes to 2.67 V at 300 K. The value of x is _____. (given, F = 11500 K V^-1, where F is the Faraday constant and R is the gas constant, ln(10) = 2.30)", "response_choices": "", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "A closed tank has two compartments A and B, both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure 1). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure 2), the volume (in m3) of the compartment A after the system attains equilibrium is _____.", "response_choices": "Multiple choice options not provided", "answer": "No answer provided", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids A and B has vapour pressure 45 Torr. At the same temperature, a new solution of A and B having mole fractions xA and xB, respectively, has vapour pressure of 22.5 Torr. The value of xA/xB in the new solution is _____. (given that the vapour pressure of pure liquid A is 20 Torr at temperature T)", "response_choices": "Multiple choice options not provided", "answer": "No answer provided", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "The solubility of a salt of weak acid (AB) at pH 3 is Y\u00d710^-3 mol L^-1. The value of Y is _____.", "response_choices": "No response choices provided", "answer": "(Given that the value of solubility product of AB (Ksp) = 2\u00d710^-10 and the value of ionization constant of HB (Ka) = 1\u00d710^-8)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "The plot given below shows P \u2013 T curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles of a non-volatile solute S in equal amount (in kg) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y. Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y, the degree of dimerization in solvent X is _____.", "response_choices": "No response choices provided", "answer": "The image shows curves numbered 1, 2, 3, and 4 representing: 1. solvent X, 2. solution of NaCl in solvent X, 3. solvent Y, 4. solution of NaCl in solvent Y", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 15, "question": "The compound Y is", "response_choices": "A) COBr, B) OH with Br and HO attached to a ring, C) Ring with triple bond, D) Br attached to a ring with COBr attached", "answer": "B", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 16, "question": "The compound Z is", "response_choices": "(A) [molecular structure 1] (B) [molecular structure 2] (C) [molecular structure 3] (D) [molecular structure 4]", "answer": "B", "page_number": 22, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "The compound R is", "response_choices": "(A) / (B) / (C) / (D)", "answer": "(B)", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 18, "question": "The compound S is", "response_choices": "(A) (B) (C) (D)", "answer": "D", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 1, "question": "This section contains SIX (06) questions.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Each question has FOUR options for correct answer(s). ONE OR MORE THAN ONE of these four option(s) is (are) correct option(s).", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "For each question, choose the correct option(s) to answer the question.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If only (all) the correct option(s) is (are) chosen. Partial Marks : +3 If all the four options are correct but ONLY three options are chosen. Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct options. Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option. Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered). Negative Marks : -2 In all other cases.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "For Example: If first, third and fourth are the ONLY three correct options for a question with second option being an incorrect option; selecting only all the three correct options will result in +4 marks. Selecting only two of the three correct options (e.g. the first and fourth options), without selecting any incorrect option (second option in this case), will result in +2 marks. Selecting only one of the three correct options (either first or third or fourth option) , without selecting any incorrect option (second option in this case), will result in +1 marks. Selecting any incorrect option(s) (second option in this case), with or without selection of any correct option(s) will result in -2 marks.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "For a non-zero complex number z, let arg(z) denote the principal argument with - \u03c0 < arg(z) \u2264 \u03c0. Then, which of the following statement(s) is (are) FALSE?", "response_choices": "(A) arg(\u22121 \u2212 i) = \u03c0/4, where i = \u221a\u22121\n\n(B) The function f : \u211d \u2192 (\u2212\u03c0, \u03c0], defined by f(t) = arg(\u22121 + it) for all t \u2208 \u211d, is continuous at all points of \u211d, where i = \u221a\u22121\n\n(C) For any two non-zero complex numbers z1 and z2, arg(z1/z2) \u2212 arg(z1) + arg(z2) is an integer multiple of 2\u03c0\n\n(D) For any three given distinct complex numbers z1, z2 and z3, the locus of the point z satisfying the condition arg((z\u2212z1)(z2\u2212z3)/((z\u2212z3)(z2\u2212z1))) = \u03c0, lies on a straight line", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "In a triangle PQR, let \u2220PQR = 30\u00b0 and the sides PQ and QR have lengths 10\u221a3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) \u2220QPR = 45\u00b0\n\n(B) The area of the triangle PQR is 25\u221a3 and \u2220QRP = 120\u00b0\n\n(C) The radius of the incircle of the triangle PQR is 10\u221a3 \u2212 15\n\n(D) The area of the circumcircle of the triangle PQR is 100 \u03c0", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let P1: 2x + y - z = 3 and P2: x + 2y + z = 2 be two planes. Then, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) The line of intersection of P1 and P2 has direction ratios 1, 2, -1\n(B) The line\n3x - 4 = 1 - 3y = z\n9 9 3\nis perpendicular to the line of intersection of P1 and P2\n(C) The acute angle between P1 and P2 is 60\u00b0\n(D) If P3 is the plane passing through the point (4, 2, -2) and perpendicular to the line of intersection of P1 and P2, then the distance of the point (2, 1, 1) from the plane P3 is 2/\u221a3", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "For every twice differentiable function f: R \u2192 [-2, 2] with (f'(0))^2 + (f''(0))^2 = 85, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) There exist r, s \u2208 R, where r < s, such that f is one-one on the open interval (r, s)\n(B) There exists x0 \u2208 (-4, 0) such that |f''(x0)| \u2264 1\n(C) lim f(x) = 1\nx\u2192\u221e\n(D) There exists \u03b1 \u2208 (-4, 4) such that f(\u03b1) + f''(\u03b1) = 0 and f'(\u03b1) \u2260 0", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let f: R \u2192 R and g: R \u2192 R be two non-constant differentiable functions. If\nf'(x) = (e^(f(x)-g(x))) g'(x) for all x \u2208 R,\nand f(1) = g(2) = 1, then which of the following statement(s) is (are) TRUE?", "response_choices": "(A) f(2) < 1 - loge 2\t(B) f(2) > 1 - loge 2\n(C) g(1) > 1 - loge 2\t(D) g(1) < 1 - loge 2", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let f: [0, \u221e) \u2192 \u211d be a continuous function such that f(x) = 1 - 2x + \u222b(0 to x) e^(x-t) f(t) dt for all x \u2208 [0, \u221e). Then, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) The curve y = f(x) passes through the point (1, 2) (B) The curve y = f(x) passes through the point (2, -1) (C) The area of the region {(x, y) \u2208 [0, 1] \u00d7 \u211d : f(x) \u2264 y \u2264 \u221a(1 - x^2) } is \u03c0-2/4 (D) The area of the region {(x, y) \u2208 [0,1] \u00d7 \u211d : f(x) \u2264 y \u2264 \u221a(1 - x^2) } is \u03c0-1/4", "answer": "No selected answer provided", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "The value of ((log2 9)^2)^(log2 (log2 9) \u00d7 (\u221a7)^(log4 7)) is _______.", "response_choices": "None provided (numerical response required)", "answer": "None provided (numerical response required)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "The number of 5 digit numbers which are divisible by 4, with digits from the set {1, 2, 3, 4, 5} and the repetition of digits is allowed, is _____ .", "response_choices": "None provided (numerical response required)", "answer": "None provided (numerical response required)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let X be the set consisting of the first 2018 terms of the arithmetic progression 1, 6, 11, ... , and Y be the set consisting of the first 2018 terms of the arithmetic progression 9, 16, 23, ... . Then, the number of elements in the set X \u222a Y is _____.", "response_choices": "None provided (numerical response required)", "answer": "None provided (numerical response required)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "The number of real solutions of the equation sin^-1(\u2211(\u221e)(l=1) x^(l+1) - x \u2211(\u221e)(i=1) (x^i)/(i!)) = (\u03c0/2 - cos^-1(\u2211(\u221e)(i=1) ((-x)^i)/2 - \u2211(\u221e)(i=1) (-x)^i)) lying in the interval ((-1/2, 2/1)) is _____ . (Here, the inverse trigonometric functions sin^-1 x and cos^-1 x assume values in [(-\u03c0/2, \u03c0/2)] and [0, \u03c0], respectively.)", "response_choices": "None provided (numerical response required)", "answer": "None provided (numerical response required)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "For each positive integer n, let yn = 1/n ((n + 1)(n + 2)...(n + n))^(1/n). For x \u2208 \u211d, let [x] be the greatest integer less than or equal to x. If lim(n\u2192\u221e) yn = L, then the value of [L] is _____ .", "response_choices": "None provided (numerical response required)", "answer": "None provided (numerical response required)", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let \u00e2 and b\u0302 be two unit vectors such that \u00e2 \u00b7 b\u0302 = 0. For some x, y \u2208 R, let c \u0302 = x \u00e2 + y b\u0302 + (\u00e2 \u00d7 b\u0302). If |\u0109| = 2 and the vector \u0109 is inclined at the same angle \u03b1 to both \u00e2 and b\u0302, then the value of 8 cos^2 \u03b1 is _____.", "response_choices": "No options given", "answer": "No answer given", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let a, b, c be three non-zero real numbers such that the equation \u221a3 a cos x + 2 b sin x = c, x \u2208 [- \u03c0/2, \u03c0/2], has two distinct real roots \u03b1 and \u03b2 with \u03b1 + \u03b2 = \u03c0/3. Then, the value of b/a is _____.", "response_choices": "No options given", "answer": "No answer given", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "A farmer F\u2081 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F\u2082 takes away the region which lies between the side PQ and a curve of the form y = x^n (n > 1). If the area of the region taken away by the farmer F\u2082 is exactly 30% of the area of \u0394PQR, then the value of n is _____.", "response_choices": "No options given", "answer": "No answer given", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Let E1E2 and F1F2 be the chords of S passing through the point P0 (1, 1) and parallel to the x-axis and the y-axis, respectively. Let G1G2 be the chord of S passing through P0 and having slope \u22121. Let the tangents to S at E1 and E2 meet at E3, the tangents to S at F1 and F2 meet at F3, and the tangents to S at G1 and G2 meet at G3. Then, the points E3, F3, and G3 lie on the curve", "response_choices": "(A) x + y = 4\n(B) (x \u2212 4)2 + (y \u2212 4)2 = 16\n(C) (x \u2212 4)(y \u2212 4) = 4\n(D) xy = 4", "answer": "(B) (x \u2212 4)2 + (y \u2212 4)2 = 16", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N. Then, the mid-point of the line segment MN must lie on the curve", "response_choices": "(A) (x + y)2 = 3xy\n(B) x2/3 + y2/3 = 24/3\n(C) x2 + y2 = 2xy\n(D) x2 + y2 = x2 y2", "answer": "(B) x2/3 + y2/3 = 24/3", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "The probability that, on the examination day, the student S1 gets the previously allotted seat R1, and NONE of the remaining students gets the seat previously allotted to him/her is", "response_choices": "(A) 3/40, (B) 1/8, (C) 7/40, (D) 1/5", "answer": "C", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "For i = 1, 2, 3, 4, let Ti denote the event that the students Si and Si+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event T1 \u2229 T2 \u2229 T3 \u2229 T4 is", "response_choices": "(A) 1/15, (B) 1/10, (C) 7/60, (D) 1/5", "answer": "B", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2018_2.jsonl b/JEE_papers/JSON/JEE_2018_2.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..9457349ca76cab4b8fb6234f8cd29cf2552f3cfc --- /dev/null +++ b/JEE_papers/JSON/JEE_2018_2.jsonl @@ -0,0 +1,52 @@ +{"id": 1, "question": "A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as dK/dt = \u03b3t, where \u03b3 is a positive constant of appropriate dimensions. Which of the following statements is (are) true?", "response_choices": "(A) The force applied on the particle is constant\n(B) The speed of the particle is proportional to time\n(C) The distance of the particle from the origin increases linearly with time\n(D) The force is conservative", "answer": "", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)", "response_choices": "A, B, C, D", "answer": "B", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "In a radioactive decay chain, 232Th nucleus decays to 212Pb nucleus. Let N_\u03b1 and N_\u03b2 be the number of \u03b1 and \u03b2^\u2212 particles, respectively, emitted in this decay process. Which of the following statements is (are) true?", "response_choices": "(A) N_\u03b1 = 5 (B) N_\u03b1 = 6 (C) N_\u03b2 = 2 (D) N_\u03b2 = 4", "answer": "(C) N_\u03b2 = 2", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?", "response_choices": "(A) The speed of sound determined from this experiment is 332 m s^-1 (B) The end correction in this experiment is 0.9 cm (C) The wavelength of the sound wave is 66.4 cm (D) The resonance at 50.7 cm corresponds to the fundamental harmonic", "answer": "[Answer not provided]", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass m = 0.4 kg is at rest on this surface. An impulse of 1.0 N s is applied to the block at time t = 0 so that it starts moving along the x-axis with a velocity v(t) = v0e^(-t/\u03c4), where v0 is a constant and \u03c4 = 4 s. The displacement of the block, in metres, at t = \u03c4 is _____________.", "response_choices": "No response choices provided", "answer": "Numerical answer required", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A ball is projected from the ground at an angle of 45\u00b0 with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of 30\u00b0 with the horizontal surface. The maximum height it reaches after the bounce, in metres, is _____________.", "response_choices": "No response choices provided", "answer": "Numerical answer required", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A particle, of mass 10^(-3)kg and charge 1.0 C, is initially at rest. At time t = 0, the particle comes under the influence of an electric field E(t) = E0 sin \u03c9t i, where E0 = 1.0 N C^(-1)and \u03c9 = 10\u00b3 rad s^(-1). Consider the effect of only the electrical force on the particle. Then the maximum speed, in m s^(-1), attained by the particle at subsequent times is _____________.", "response_choices": "No response choices provided", "answer": "Numerical answer required", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A moving coil galvanometer has 50 turns and each turn has an area 2 \u00d7 10^(-4) m\u00b2. The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is 10^(-4) N m rad^(-1). When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is 50 \u03a9. This galvanometer is to be converted into an ammeter capable of measuring current in the range 0 \u2192 1.0 A. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is _____________.", "response_choices": "No response choices provided", "answer": "Numerical answer required", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "A steel wire of diameter 0.5 mm and Young's modulus 2 \u00d7 10\u00b9\u00b9 N m\u207b\u00b2 carries a load of mass M. The length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is _________. Take g = 10 m s\u207b\u00b2 and \u03c0 = 3.2.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant R = 8.0 J mol\u207b\u00b9K\u207b\u00b9, the decrease in its internal energy, in Joule, is________.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "In a photoelectric experiment a parallel beam of monochromatic light with power of 200 W is incident on a perfectly absorbing cathode of work function 6.25 eV. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force F = n x 10\u207b\u2074 N due to the impact of the electrons. The value of n is _________. Mass of the electron m\u2091 = 9 \u00d7 10\u207b\u00b3\u00b9kg and 1.0 eV = 1.6 \u00d7 10\u207b\u00b9\u2079 J.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "Consider a hydrogen-like ionized atom with atomic number Z with a single electron. In the emission spectrum of this atom, the photon emitted in the n = 2 to n = 1 transition has energy 74.8 eV higher than the photon emitted in the n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 eV. The value of Z is _________.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.", "response_choices": "A) P \u2192 5; Q \u2192 3, 4; R \u2192 1; S \u2192 2\nB) P \u2192 5; Q \u2192 3; R \u2192 1, 4; S \u2192 2\nC) P \u2192 5; Q \u2192 3; R \u2192 1, 2; S \u2192 4\nD) P \u2192 4; Q \u2192 2, 3; R \u2192 1; S \u2192 5", "answer": "C) P \u2192 5; Q \u2192 3; R \u2192 1, 2; S \u2192 4", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A planet of mass M has two natural satellites with masses m1 and m2. The radii of their circular orbits are R1 and R2 respectively. Ignore the gravitational force between the satellites. Define v1, L1, K1 and T1 to be, respectively, the orbital speed, angular momentum, kinetic energy and Time period of revolution of satellite 1; and v2, L2, K2 and T2 to be the corresponding quantities of satellite 2. Given m1/m2 = 2 and R1/R2 = 1/4, match the ratios in List-I to the numbers in List-II.", "response_choices": "A) P \u2192 4; Q \u2192 2; R \u2192 1; S \u2192 3\nB) P \u2192 3; Q \u2192 2; R \u2192 4; S \u2192 1\nC) P \u2192 2; Q \u2192 3; R \u2192 1; S \u2192 4\nD) P \u2192 2; Q \u2192 3; R \u2192 4; S \u2192 1", "answer": "D", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PV-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-I with the corresponding statements in List-II.", "response_choices": "A. P \u2192 4; Q \u2192 3; R \u2192 1; S \u2192 2\nB. P \u2192 1; Q \u2192 3; R \u2192 2; S \u2192 4\nC. P \u2192 3; Q \u2192 4; R \u2192 1; S \u2192 2\nD. P \u2192 3; Q \u2192 4; R \u2192 2; S \u2192 1", "answer": "C", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "In the List-I below, four different paths of a particle are given as functions of time. In these functions, \u03b1 and \u03b2 are positive constants of appropriate dimensions and \u03b1 \u2260 \u03b2. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: p\u0302 is the linear momentum, L\u0302 is the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.", "response_choices": "P. r\u20d7(t) = \u03b1t \u00ee + \u03b2t \u0135, Q. r\u20d7(t) = \u03b1 cos \u03c9t \u00ee + \u03b2 sin \u03c9t \u0135, R. r\u20d7(t) = \u03b1 (cos \u03c9t \u00ee + sin \u03c9t \u0135), S. r\u20d7(t) = \u03b1t \u00ee + 1\u20442 t^2 \u0135", "answer": "(A) P \u2192 1, 2, 3, 4, 5; Q \u2192 2, 5; R \u2192 2, 3, 4, 5; S \u2192 5 (B) P \u2192 1, 2, 3, 4, 5; Q \u2192 3, 5; R \u2192 2, 3, 4, 5; S \u2192 2, 5 (C) P \u2192 2, 3, 4; Q \u2192 5; R \u2192 1, 2, 4; S \u2192 2, 5 (D) P \u2192 1, 2, 3, 5; Q \u2192 2, 5; R \u2192 2, 3, 4, 5; S \u2192 2, 5", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "The correct option(s) regarding the complex [Co(en)(NH3)4(H2O)]3+ (en = H2NCH2CH2NH2) is (are)", "response_choices": "(A) It has two geometrical isomers (B) It will have three geometrical isomers if bidentate 'en' is replaced by two cyanide ligands (C) It is paramagnetic (D) It absorbs light at longer wavelength as compared to [Co(en)(NH3)6]3+", "answer": "C", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The correct option(s) to distinguish nitrate salts of Mn2+ and Cu2+ taken separately is (are)", "response_choices": "(A) Mn2+ shows the characteristic green colour in the flame test (B) Only Cu2+ shows the formation of precipitate by passing H2S in acidic medium (C) Only Mn2+ shows the formation of precipitate by passing H2S in faintly basic medium (D) Cu2+/Cu has higher reduction potential than Mn2+/Mn (measured under similar conditions)", "answer": "A,B,D", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Aniline reacts with mixed acid (conc. HNO3 and conc. H2SO4) at 288 K to give P (51 %), Q (47%) and R (2%). The major product(s) of the following reaction sequence is (are)", "response_choices": "(A) (B) (C) (D)", "answer": "(D)", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The Fischer presentation of D-glucose is given below. The correct structure(s) of \u03b2-L-glucopyranose is (are)", "response_choices": "(A), (B), (C), (D)", "answer": "(B)", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "For a first order reaction A(g) \u2192 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are P0 and Pt, respectively. Initially, only A is present with concentration [A]0, and t1/3 is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)", "response_choices": "(A) (B) (C) (D)", "answer": "Graphical response choices, no selected answer marked", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "For a reaction, A \u21cc P, the plots of [A] and [P] with time at temperatures T1 and T2 are given below. If T2 > T1, the correct statement(s) is (are) (Assume \u0394H\u1db1 and \u0394S\u1db1 are independent of temperature and ratio of lnK at T1 to lnK at T2 is greater than T2/T1. Here H, S, G and K are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)", "response_choices": "(A) \u0394H\u1db1 < 0, \u0394S\u1db1 < 0 \n(B) \u0394G\u1db1 < 0, \u0394H\u1db1 > 0 \n(C) \u0394G\u1db1 < 0, \u0394S\u1db1 < 0 \n(D) \u0394G\u1db1 < 0, \u0394S\u1db1 > 0", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The total number of compounds having at least one bridging oxo group among the molecules given below is ____. N2O5, N2O4, P4O6, P4O7, H4P2O5, H3PO10, H2S2O5, H2S2O8", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of O2 consumed is ____. (Atomic weights in g mol^-1: O = 16, S = 32, Pb = 207)", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "To measure the quantity of MnCl2 dissolved in an aqueous solution, it was completely converted to KMnO4 using the reaction, MnCl2 + K2S2O8 + H2O -> KMnO4 + H2SO4 + HCl (equation not balanced). Few drops of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was added in portions till the colour of the permanganate ion disappeared. The quantity of MnCl2 (in mg) present in the initial solution is ____. (Atomic weights in g mol^-1: Mn = 55, Cl = 35.5)", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "For the given compound X, the total number of optically active stereoisomers is ____.", "response_choices": "", "answer": "", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 11, "question": "In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.", "response_choices": "", "answer": "", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 12, "question": "The surface of copper gets tarnished by the formation of copper oxide. N2 gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the N2 gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below: 2Cu(s) + H2O(g) \u2192 Cu2O(s) + H2(g) pH2 is the minimum partial pressure of H2 (in bar) needed to prevent the oxidation at 1250 K. The value of ln(pH2) is _____. (Given: total pressure = 1 bar, R (universal gas constant) = 8 J K-1 mol-1, ln(10) = 2.3, Cu(s) and Cu2O(s) are mutually immiscible. At 1250 K: 2Cu(s) + \u00bd O2(g) \u2192 Cu2O(s); \u0394G^0 = - 78,000 J mol-1 H2(g) + \u00bd O2(g) \u2192 H2O(g); \u0394G^0 = - 1,78,000 J mol-1; G is the Gibbs energy)", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "Consider the following reversible reaction, A(g) + B(g) \u21cc AB(g). The activation energy of the backward reaction exceeds that of the forward reaction by 2RT (in J mol-1). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of \u0394G^0 (in J mol-1) for the reaction at 300 K is _____. (Given: ln(2) = 0.7, RT = 2500 J mol-1 at 300 K and G is the Gibbs energy)", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "Consider an electrochemical cell: A(s) | Am+ (aq, 2 M) || B2m+ (aq, 1 M) | B(s). The value of \u0394H^0 for the cell reaction is twice that of \u0394G^0 at 300 K. If the emf of the cell is zero, the \u0394S^0 (in J K-1 mol-1) of the cell reaction per mole of B formed at 300 K is _____. (Given: ln(2) = 0.7, R (universal gas constant) = 8.3 J K-1 mol-1, H, S and G are enthalpy, entropy and Gibbs energy, respectively.)", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "Match each set of hybrid orbitals from LIST-I with complex(es) given in LIST-II.", "response_choices": "(A) P \u2192 5; Q \u2192 4,6; R \u2192 2,3; S \u2192 1\n(B) P \u2192 5,6; Q \u2192 4; R \u2192 3; S \u2192 1,2\n(C) P \u2192 6; Q \u2192 4,5; R \u2192 1; S \u2192 2,3\n(D) P \u2192 4,6; Q \u2192 5,6; R \u2192 1,2; S \u2192 3", "answer": "(D) P \u2192 4,6; Q \u2192 5,6; R \u2192 1,2; S \u2192 3", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II. (given, order of migratory aptitude: aryl > alkyl > hydrogen)", "response_choices": "(A) P \u2192 1; Q \u2192 2,3; R \u2192 1,4; S \u2192 2,4\n(B) P \u2192 1,5; Q \u2192 3,4; R \u2192 4,5; S \u2192 3\n(C) P \u2192 1,5; Q \u2192 3,4; R \u2192 5; S \u2192 2,4\n(D) P \u2192 1,5; Q \u2192 2,3; R \u2192 1,5; S \u2192 2,3", "answer": "", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "LIST-I contains reactions and LIST-II contains major products. Match each reaction in LIST-I with one or more products in LIST-II and choose the correct option.", "response_choices": "(A) P \u2192 1,5; Q \u2192 2; R \u2192 3; S \u2192 4\n(B) P \u2192 1,4; Q \u2192 2; R \u2192 4; S \u2192 3\n(C) P \u2192 1,4; Q \u2192 1,2; R \u2192 3,4; S \u2192 4\n(D) P \u2192 4,5; Q \u2192 4; R \u2192 4; S \u2192 3,4", "answer": "", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 18, "question": "Dilution processes of different aqueous solutions with water, are given in LIST-I. The effects of dilution of the solutions on [H+] are given in LIST-II. (Note: Degree of dissociation (\u03b1) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; [H+] represents the concentration of H+ ions) Match each process given in LIST-I with one or more effect(s) in LIST-II.", "response_choices": "(A) P \u2192 4; Q \u2192 2; R \u2192 3; S \u2192 1, (B) P \u2192 4; Q \u2192 3; R \u2192 2; S \u2192 3, (C) P \u2192 1; Q \u2192 4; R \u2192 5; S \u2192 3, (D) P \u2192 1; Q \u2192 5; R \u2192 4; S \u2192 1", "answer": "", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "For any positive integer n, define fn: (0, \u221e) \u2192 \u211d as fn(x) = \u2211^n_(j=1) tan^-1 ((1)/((1+(x+j)(x+j-1))) for all x \u2208 (0, \u221e). (Here, the inverse trigonometric function tan^-1 x assumes values in (-\u03c0/2, \u03c0/2).) Then, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) \u2211^5_(j=1) tan^2(fj(0)) = 55 (B) \u2211^10_(j=1) (1 + fj'(0)) sec^2(fj(0)) = 10 (C) For any fixed positive integer n, lim_(x\u2192\u221e) tan (fn(x)) = 1/n (D) For any fixed positive integer n, lim_(x\u2192\u221e) sec^2(fn(x)) = 1", "answer": "", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Let T be the line passing through the points P(-2, 7) and Q(2, -5). Let F1 be the set of all pairs of circles (S1, S2) such that T is tangent to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say, M. Let E1 be the set representing the locus of M as the pair (S1, S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2. Let E2 be the set of the mid-points of the line segments in the set F2. Then, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) The point (-2, 7) lies in E1, (B) The point (4, 7/5) does NOT lie in E2, (C) The point (1/2, 1) lies in E2, (D) The point (0, 3/2) does NOT lie in E1", "answer": "No selected answer visible", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let S be the set of all column matrices [b1, b2, b3] such that b1, b2, b3 \u2208 R and the system of equations (in real variables) -x + 2y + 5z = b1, 2x - 4y + 3z = b2, x - 2y + 2z = b3 has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each [b1, b2, b3] \u2208 S?", "response_choices": "(A) x + 2y + 3z = b1, 4y + 5z = b2 and x + 2y + 6z = b3, (B) x + y + 3z = b1, 5x + 2y + 6z = b2 and -2x - y - 3z = b3, (C) -x + 2y - 5z = b1, 2x - 4y + 10z = b2 and x - 2y + 5z = b3, (D) x + 2y + 5z = b1, 2x + 3z = b2 and x + 4y - 5z = b3", "answer": "No selected answer visible", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Consider two straight lines, each of which is tangent to both the circle x^2 + y^2 = 1/2 and the parabola y^2 = 4x. Let these lines intersect at the point Q. Consider the ellipse whose center is at the origin O(0,0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is \u221a2 , then which of the following statement(s) is (are) TRUE?", "response_choices": "(A) For the ellipse, the eccentricity is 1/\u221a2 and the length of the latus rectum is 1 (B) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (C) The area of the region bounded by the ellipse between the lines x = 1/\u221a2 and x = 1 is 1/4\u221a2 (\u03c0 \u2212 2) (D) The area of the region bounded by the ellipse between the lines x = 1/\u221a2 and x = 1 is 1/16 (\u03c0 \u2212 2)", "answer": "B", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let s, t, r be non-zero complex numbers and L be the set of solutions z = x + iy (x, y \u2208 \u211d, i = \u221a\u22121) of the equation sz + tz + r = 0, where z = x \u2212 iy. Then, which of the following statement(s) is (are) TRUE?", "response_choices": "(A) If L has exactly one element, then |s| \u2260 |t| (B) If |s| = |t|, then L has infinitely many elements (C) The number of elements in L \u2229 {z : |z \u2212 1 + i| = 5} is at most 2 (D) If L has more than one element, then L has infinitely many elements", "answer": "B", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let f: (0, \u03c0) \u2192 \u211d be a twice differentiable function such that lim [(f(x) sin(t-x)/(t-x) - f(t) sin x/(t-x)) / sin^2 x] = 0 for all x \u2208 (0, \u03c0). If f'(\u03c0/2) = - \u03c0/12, then which of the following statement(s) is (are) TRUE?", "response_choices": "A) f(\u03c0/4) = \u03c0/\u221a12\nB) f(x) \u2264 x^4/6 - x^2 for all x \u2208 (0,\u03c0)\nC) There exists \u03b1 \u2208 (0, \u03c0) such that f''(\u03b1) = 0\nD) f''(\u03c0/2) + f'(\u03c0/2) = 0", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "The value of the integral \u222b(0 to (1 + \u221a3)/2) (((x + 1)^2(1 - x))^(-1)) dx", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let P be a matrix of order 3 \u00d7 3 such that all the entries in P are from the set {-1, 0, 1}. Then, the maximum possible value of the determinant of P is _____.", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If \u03b1 is the number of one-one functions from X to Y and \u03b2 is the number of onto functions from Y to X, then the value of (1/5)(\u03b2 - \u03b1) is _____.", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let f: \u211d \u2192 \u211d be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation dy/dx = (2 + 5y)(5y - 2), then the value of lim(x\u21920) f(x) is _____.", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let f: \u211d \u2192 \u211d be a differentiable function with f(0) = 1 and satisfying the equation f(x + y) = f(x)f'(y) + f'(x)f(y) for all x, y \u2208 \u211d. Then, the value of loge(f(4)) is _____.", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let P be a point in the first octant, whose image Q in the plane x + y = 3 (that is, the line segment PQ is perpendicular to the plane x + y = 3 and the mid-point of PQ lies in the plane x + y = 3) lies on the z-axis. Let the distance of P from the x-axis be 5. If R is the image of P in the xy-plane, then the length of PR is _____.", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where O(0,0,0) is the origin. Let S(1/2, 1/2, 1/2) be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If p\u20d7 = 5i\u20d7, q\u20d7 = 5j\u20d7, r\u20d7 = 5k\u20d7 and t\u20d7 = 5T\u20d7, then the value of |(p\u20d7\u00d7q\u20d7)\u00d7(r\u20d7\u00d7t\u20d7)| is _____.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Let X = (^10C_1 )^2 + 2(^10C_2 )^2 + 3(^10C_3 )^2 + ... + 10(^10C_10 )^2, where ^nC_r, r \u2208 {1, 2, ..., 10} denote binomial coefficients. Then, the value of 1/1430 X is _____.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Let E1 = {x \u2208 \u211d : x \u2260 1 and x^-1 > 0} and E2 = {x \u2208 E1 : sin^-1 (log_e (x^-1)) is a real number}. (Here, the inverse trigonometric function sin^-1 x assumes values in [-\u03c0/2, \u03c0/2]). Let f: E1 \u2192 \u211d be the function defined by f(x) = log_e (x^-1) and g: E2 \u2192 \u211d be the function defined by g(x) = sin^-1 (log_e (x^-1)).", "response_choices": "P. The range of f is\nQ. The range of g contains\nR. The domain of f contains\nS. The domain of g is", "answer": "A", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "In a high school, a committee has to be formed from a group of 6 boys M1, M2, M3, M4, M5, M6 and 5 girls G1, G2, G3, G4, G5. (i) Let \u03b11 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls. (ii) Let \u03b12 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls. (iii) Let \u03b13 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls. (iv) Let \u03b14 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M1 and G1 are NOT in the committee together.", "response_choices": "LIST-I: P. The value of \u03b11 is, Q. The value of \u03b12 is, R. The value of \u03b13 is, S. The value of \u03b14 is; LIST-II: 1. 136, 2. 189, 3. 192, 4. 200, 5. 381, 6. 461", "answer": "(A) P \u2192 4; Q \u2192 6; R \u2192 2; S \u2192 1", "page_number": 31, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Let H: x^2/a^2 - y^2/b^2 = 1, where a > b > 0, be a hyperbola in the xy-plane whose conjugate axis LM subtends an angle of 60\u00b0 at one of its vertices N. Let the area of the triangle LMN be 4\u221a3.", "response_choices": "(A) P \u2192 4; Q \u2192 2; R \u2192 1; S \u2192 3\n(B) P \u2192 4; Q \u2192 3; R \u2192 1; S \u2192 2\n(C) P \u2192 4; Q \u2192 1; R \u2192 3; S \u2192 2\n(D) P \u2192 3; Q \u2192 4; R \u2192 2; S \u2192 1", "answer": "(A) P \u2192 4; Q \u2192 2; R \u2192 1; S \u2192 3", "page_number": 32, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "Let f1: R -> R, f2: (\u03c0/2, \u03c0/2) -> R, f3: (-1, e^2 - 2) -> R and f4: R -> R be functions defined by (i) f1(x) = sin(sqrt(1 - e^(-x^2))), (ii) f2(x) = { sin x / tan^-1 x if x \u2260 0, 1 if x = 0 }, where the inverse trigonometric function tan^-1 x assumes values in (- \u03c0/2, \u03c0/2), (iii) f3(x) = [ sin(log_e(x + 2))], where, for t \u2208 R, [t] denotes the greatest integer less than or equal to t, (iv) f4(x) = { x^2 sin (1/x) if x \u2260 0, 0 if x = 0 }", "response_choices": "LIST-I: P. The function f1 is, Q. The function f2 is, R. The function f3 is, S. The function f4 is. LIST-II: 1. NOT continuous at x = 0, 2. continuous at x = 0 and NOT differentiable at x = 0, 3. differentiable at x = 0 and its derivative is NOT continuous at x = 0, 4. differentiable at x = 0 and its derivative is continuous at x = 0. The correct option is: (A) P -> 2; Q -> 3; R -> 1; S -> 4, (B) P -> 4; Q -> 1; R -> 2; S -> 3, (C) P -> 4; Q -> 2; R -> 1; S -> 3, (D) P -> 2; Q -> 1; R -> 4; S -> 3", "answer": "(C) P -> 4; Q -> 2; R -> 1; S -> 3", "page_number": 33, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2019_1_English.jsonl b/JEE_papers/JSON/JEE_2019_1_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..f5be154b6855aad045a693b7210580f79562af9a --- /dev/null +++ b/JEE_papers/JSON/JEE_2019_1_English.jsonl @@ -0,0 +1,54 @@ +{"id": 1, "question": "Consider a spherical gaseous cloud of mass density \u03c1(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particles is their mutual gravitational force. If \u03c1(r) is constant in time, the particle number density n(r) = \u03c1(r)/m is [G is universal gravitational constant]", "response_choices": "(A) K/2\u03c0r^2m^2G, (B) K/\u03c0r^2m^2G, (C) 3K/\u03c0r^2m^2G, (D) K/6\u03c0r^2m^2G", "answer": "(B) K/\u03c0r^2m^2G", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "A thin spherical insulating shell of radius R carries a uniformly distributed charge such that the potential at its surface is V0. A hole with a small area \u03b14\u03c0R^2 (\u03b1 \u226a 1) is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?", "response_choices": "(A) The potential at the center of the shell is reduced by 2\u03b1V0, (B) The magnitude of electric field at the center of the shell is reduced by \u03b1V0/2R, (C) The ratio of the potential at the center of the shell to that of the point at 1/2R from center towards the hole will be 1-\u03b1/1-2\u03b1, (D) The magnitude of electric field at a point, located on a line passing through the hole and shell's center, on a distance 2R from the center of the spherical shell will be reduced by \u03b1V0/2R", "answer": "(C) The ratio of the potential at the center of the shell to that of the point at 1/2R from center towards the hole will be 1-\u03b1/1-2\u03b1", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as T(t) = T0(1 + \u03b2t^2), where \u03b2 is a constant with appropriate dimension while T0 is a constant with dimension of temperature. The heat capacity of the metal is,", "response_choices": "(A) 4P(T(t)-T0)^3/\u03b2^4T03, (B) 4P(T(t)-T0)^4/\u03b2^4T03, (C) 4P(T(t)-T0)^2/\u03b2^4T03, (D) 4P(T(t)-T0)/\u03b2^4T03", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "In a radioactive sample, 40K nuclei either decay into stable 40Ca nuclei with decay constant 4.5 x 10^-10 per year or into stable 40Ar nuclei with decay constant 0.5 x 10^-10 per year. Given that in this sample all the stable 40Ca and 40Ar nuclei are produced by the 40K nuclei only. In time t x 10^5 years, if the ratio of the sum of stable 40Ca and 40Ar nuclei to the radioactive 40K nuclei is 99, the value of t will be, [Given: ln 10 = 2.3]", "response_choices": "(A) 1.15, (B) 9.2, (C) 2.3, (D) 4.6", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A cylindrical capillary tube of 0.2 mm radius is made by joining two capillaries T1 and T2 of different materials having water contact angles of 0\u00b0 and 60\u00b0, respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure. Which of the following option(s) is(are) correct? [Surface tension of water = 0.075 N/m, density of water = 1000 kg/m\u00b3, take g = 10 m/s\u00b2]", "response_choices": "(A) The correction in the height of water column raised in the tube, due to weight of water contained in the meniscus, will be different for both cases. \n(B) For case II, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be 3.75 cm. (Neglect the weight of the water in the meniscus) \n(C) For case I, if the joint is kept at 8 cm above the water surface, the height of water column in the tube will be 7.5 cm. (Neglect the weight of the water in the meniscus) \n(D) For case I, if the capillary joint is 5 cm above the water surface, the height of water column raised in the tube will be more than 8.75 cm. (Neglect the weight of the water in the meniscus)", "answer": "", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A conducting wire of parabolic shape, initially y = x^2, is moving with velocity V = Vot in a non-uniform magnetic field B = B0 (1 + (\u03b3)^\u03b2) k, as shown in figure. If V0, B0, L and \u03b2 are positive constants and \u0394\u03c6 is the potential difference developed between the ends of the wire, then the correct statement(s) is/are:", "response_choices": "(A) |\u0394\u03c6| = 1/4 B0V0L for \u03b2 = 0
(B) |\u0394\u03c6| = 3/5 B0V0L for \u03b2 = 2
(C) |\u0394\u03c6| remains the same if the parabolic wire is replaced by a straight wire, y = x initially, of length \u221a(2L)
(D) |\u0394\u03c6| is proportional to the length of the wire projected on the y-axis.", "answer": "B", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "In the circuit shown, initially there is no charge on capacitors and keys S1 and S2 are open. The values of the capacitors are C1 = 10 \u03bcF, C2 = 30 \u03bcF and C3 = C4 = 80 \u03bcF. Which of the statement(s) is/are correct?", "response_choices": "A) At time t = 0, the key S1 is closed, the instantaneous current in the closed circuit will be 25 mA.\n\nB) If key S1 is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor C1 will be 4 V.\n\nC) The key S1 is kept closed for long time such that capacitors are fully charged. Now key S2 is closed, at this time, the instantaneous current across 30 \u03a9 resistor (between points P and Q) will be 0.2 A (round off to 1* decimal place).\n\nD) If key S1 is kept closed for long time such that capacitors are fully charged, the voltage difference between points P and Q will be 10 V.", "answer": "", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "A charged shell of radius R carries a total charge Q. Given \u03a6 as the flux of electric field through a closed cylindrical surface of height h, radius r and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct? [\u03b50 is the permittivity of free space]", "response_choices": "A) If h > 2R and r > R then \u03a6 = Q/\u03b50\n\nB) If h < 8R/5 and r = 3R/5 then \u03a6 = 0\n\nC) If h > 2R and r = 3R/5 then \u03a6 = Q/5\u03b50\n\nD) If h > 2R and r = 4R/5 then \u03a6 = Q/5\u03b50", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are: [R is the gas constant]", "response_choices": "(A) Work done in this thermodynamic cycle (1 \u2192 2 \u2192 3 \u2192 4 \u2192 1) is |W| = 1/2 RT0, (B) The above thermodynamic cycle exhibits only isochoric and adiabatic processes, (C) The ratio of heat transfer during processes 1 \u2192 2 and 2 \u2192 3 is |Q1\u21922|/|Q2\u21923| = 5/3, (D) The ratio of heat transfer during processes 1 \u2192 2 and 3 \u2192 4 is |Q1\u21922|/|Q3\u21924| = 1/2", "answer": "", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "A thin convex lens is made of two materials with refractive indices n1 and n2, as shown in figure. The radius of curvature of the left and right spherical surfaces are equal. f is the focal length of the lens when n1 = n2 = n. The focal length is f + \u0394f when n1 = n and n2 = n + \u0394n. Assuming \u0394n << (n - 1) and 1 < n < 2, the correct statement(s) is/are.", "response_choices": "A) |f| < |\u0394n|\nB) For n = 1.5, \u0394n = 10^-3 and f = 20 cm, the value of |\u0394f| will be 0.02 cm (round off to 2nd decimal place).\nC) If \u0394n < 0 then \u0394f > 0\nD) The relation between \u0394f and \u0394n remains unchanged if both the convex surfaces are replaced by concave surfaces of the same radius of curvature.", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?", "response_choices": "(A) The dimension of linear momentum is L^-1\n(B) The dimension of energy is L^-2\n(C) The dimension of force is L^-3\n(D) The dimension of power is L^-5", "answer": "", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "Two identical moving coil galvanometers have 10 \u03a9 resistance and full scale deflection at 2 \u03bcA current. One of them is converted into a voltmeter of 100 mV full scale reading and the other into an Ammeter of 1mA full scale current using appropriate resistors. These are then used to measure the voltage and current in the Ohm's law experiment with R = 1000 \u03a9 resistor by using an ideal cell. Which of the following statement(s) is/are correct?", "response_choices": "(A) The resistance of the Voltmeter will be 100 k\u03a9\n(B) The resistance of the Ammeter will be 0.02 \u03a9 (round off to 2nd decimal place)\n(C) The measured value of R will be 978 \u03a9 < R < 982 \u03a9\n(D) If the ideal cell is replaced by a cell having internal resistance of 5 \u03a9 then the measured value of R will be more than 1000 \u03a9", "answer": "", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force F\u20d7 = (\u03b1y)i\u02c6 + 2(\u03b1x)j\u02c6 N, where x and y are in meter and \u03b1 = \u22121 Nm\u207b\u00b9. The work done on the particle by this force F\u20d7 will be ___ Joule.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "A block of weight 100 N is suspended by copper and steel wires of same cross sectional area 0.5 cm\u00b2 and, length \u221a3 m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30\u00b0 and 60\u00b0, respectively. If elongation in copper wire is (\u0394L\u2082) and elongation in steel wire is (\u0394L\u2085), then the ratio \u0394L\u2085/\u0394L\u2082 is ___. [Young's modulus for copper and steel are 1\u00d710\u00b9\u00b9 N/m\u00b2 and 2\u00d710\u00b9\u00b9 N/m\u00b2, respectively.]", "response_choices": "", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is __________. [Speed of the sound = 330 m/s]", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A parallel plate capacitor of capacitance C has spacing d between two plates having area A. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness \u03b4 = (d/N). The dielectric constant of the mth layer is Km = K (1 + m/N). For a very large N (> 10^3), the capacitance C is \u03b1 (K\u03f5oA/d ln 2). The value of \u03b1 will be _______. [\u03f5o is the permittivity of free space]", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "A liquid at 30\u00b0C is poured very slowly into a Calorimeter that is at temperature of 110\u00b0C. The boiling temperature of the liquid is 80\u00b0C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50\u00b0C. The ratio of the Latent heat of the liquid to its specific heat will be ______\u00b0C. [Neglect the heat exchange with surrounding]", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "A planar structure of length L and width W is made of two different optical media of refractive indices n1 = 1.5 and n2 = 1.44 as shown in figure. If L >> W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For L = 9.6 m, if the incident angle \u03b8 is varied, the maximum time taken by a ray to exit the plane CD is t x 10^-9 s, where t is _______. [Speed of light c = 3 x 10^8 m/s]", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "The green colour produced in the borax bead test of a chromium(III) salt is due to", "response_choices": "(A) Cr(BO2)3 (B) Cr2(B4O7)3 (C) Cr2O3 (D) CrI3", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "Calamine, malachite, magneite and cryolite, respectively, are", "response_choices": "(A) ZnSO4, CuCO3, Fe2O3, AlP3 (B) ZnSO4, Cu(OH)2, Fe3O4, Na3AlF6 (C) ZnCO3, CuCO3,Cu(OH)2, Fe3O4, Na3AlF6 (D) ZnCO3, CuCO3, Fe2O3, Na3AlF6", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Molar conductivity (Am) of aqueous solution of sodium stearate, which behaves as a strong electrolyte, is recorded at varying concentrations (c) of sodium stearate. Which one of the following plots provides the correct representation of micelle formation in the solution? (critical micelle concentration (CMC) is marked with an arrow in the figures)", "response_choices": "(A) (B) (C) (D)", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The correct order of acid strength of the following carboxylic acids is", "response_choices": "A) III > II > I > IV, B) I > II > III > IV, C) I > III > II > IV, D) II > I > IV > III", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "A tin chloride Q undergoes the following reactions (not balanced) Q + Cl- \u2192 X Q + Mg3N2 \u2192 Y Q + CuCl2 \u2192 Z + CuCl X is a monoanion having pyramidal geometry. Both Y and Z are neutral compounds. Choose the correct option(s)", "response_choices": "(A) The central atom in X is sp3 hybridized (B) There is a coordinate bond in Y (C) The oxidation state of the central atom in Z is +2 (D) The central atom in Z has one lone pair of electrons", "answer": "", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "Fusion of MnO2 with KOH in presence of O2 produces a salt W. Alkaline solution of W upon electrolytic oxidation yields another salt X. The manganese containing ions present in W and X, respectively, are Y and Z. Correct statement(s) is(are)", "response_choices": "(A) In aqueous acidic solution, Y undergoes disproportionation reaction to give Z and MnO2, (B) Both Y and Z are coloured and have tetrahedral shape, (C) Y is diamagnetic in nature while Z is paramagnetic, (D) In both Y and Z, \u03c0-bonding occurs between p-orbitals of oxygen and d-orbitals of manganese", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "Choose the reaction(s) from the following options, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation.", "response_choices": "(A) 2H2(g) + O2(g) \u2192 2H2O (l), (B) 2C(g) + 3H2(g) \u2192 C2H6(g), (C) \u00bdO2(g) \u2192 O3(g), (D) \u00bdNa(S) + O2(g) \u2192 SO2(g)", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "Which of the following statement(s) is(are) correct regarding the root mean square speed (urms) and average translational kinetic energy (\u03f5av) of a molecule in a gas at equilibrium ?", "response_choices": "(A) urms is doubled when its temperature is increased four times, (B) \u03f5av is doubled when its temperature is increased four times, (C) \u03f5av at a given temperature does not depend on its molecular mass, (D) urms is inversely proportional to the square root of its molecular mass", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "Each of the following options contains a set of four molecules. Identify the option(s) where all four molecules possess permanent dipole moment at room temperature.", "response_choices": "(A) BeCl2, CO2, BCl3, CHCl3, (B) NO2, NH3, POCl3, CH3Cl, (C) BF3, O2, SF6, XeF6, (D) SO2, C2H5Cl, H2Se, BrF5", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "In the decay sequence, 238U \u2192 234Th \u2192 234Pa \u2192 234U \u2192 230Th, x1, x2, x3 and x4 are particles/radiation emitted by the respective isotopes. The correct option(s) is(are)", "response_choices": "(A) x1 will deflect towards negatively charged plate, (B) x2 is \u03b2\u207b, (C) x3 is \u03b3-ray, (D) Z is an isotope of uranium", "answer": "B,C,D", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "Which of the following statement(s) is(are) true?", "response_choices": "(A) Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones, (B) Oxidation of glucose with bromine water gives glutamic acid, (C) Hydrolysis of sucrose gives dextrorotatory glucose and laevorotatory fructose, (D) The two six-membered cyclic hemiacetal forms of D-(+)-glucose are called anomers", "answer": "C,D", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "Choose the correct option(s) for the following set of reactions", "response_choices": "(A) (B) (C) (D)", "answer": "(B) (D)", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "Among B2H6, B3N3H6, N2O, N2O4, H2S2O3 and H2S2O8, the total number of molecules containinng covalent bond between two atoms of the same kind is______", "response_choices": "NUMERICAL VALUE", "answer": "NUMERICAL VALUE", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "At 143 K, the reaction of XeF4 with O2F2 produces a xenon compound Y. The total number of lone pair(s) of electrons present on the whole molecule of Y is______", "response_choices": "NUMERICAL VALUE", "answer": "NUMERICAL VALUE", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "For the following reaction, the equilibrium constant Kc at 298 K is 1.6 \u00d7 10^17. Fe^2+ (aq) + S^2- (aq) \u21cc FeS (s) When equal volumes of 0.06 M Fe^3 (aq) and 0.2 M S^2- (aq) solutions are mixed, the equilibrium concentration of Fe^2 (aq) is found to be Y \u00d7 10^-17 M. The value of Y is_______", "response_choices": "NUMERICAL VALUE", "answer": "NUMERICAL VALUE", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "On dissolving 0.5 g of a non-volatile non-ionic solute to 39 g of benzene, its vapor pressure decreases from 650 mm Hg to 640 mm Hg. The depression of freezing point of benzene (in K) upon addition of the solute is______ (Given data: Molar mass and the molal freezing point depression constant of benzene are 78 g mol^-1 and 5.12 K kg mol^-1, respectively)", "response_choices": "NUMERICAL VALUE", "answer": "NUMERICAL VALUE", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "Consider the kinetic data given in the following table for the reaction A + B + C \u2192 Product. [TABLE DATA] The rate of the reaction for [A] = 0.15 mol dm^-3, [B] = 0.25 mol dm^-3 and [C] = 0.15 mol dm^-3 is found to be Y \u00d7 10^-5 mol dm^-3 s^-1. The value of Y is______", "response_choices": "MATRIX RESPONSE", "answer": "NUMERICAL VALUE", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 18, "question": "Schemes 1 and 2 describe the conversion of P to Q and R to S, respectively. Scheme 3 describes the synthesis of T from Q and S. The total number of Br atoms in a molecule of T is _______", "response_choices": "No response choices provided", "answer": "(major)", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 1, "question": "Let S be the set of all complex numbers z satisfying |z - 2 + i| \u2265 \u221a5. If the complex number z0 is such that (1/|z0 - 1|) is the maximum of the set {1/|z - 1| : z \u2208 S}, then the principal argument of (A - z0 - z\u03040)/(z0 - z\u03040 + 2i) is", "response_choices": "(A) -(\u03c0/2), (B) \u03c0/4, (C) \u03c0/2, (D) 3\u03c0/4", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Let M = [sin^4\u03b8 -1 - sin^2\u03b8]/[1 + cos^2\u03b8 cos^4\u03b8] = \u03b1I + \u03b2M^-1, where \u03b1 = \u03b1(\u03b8) and \u03b2 = \u03b2(\u03b8) are real numbers, and I is the 2 x 2 identity matrix. If \u03b1* is the minimum of the set {\u03b1(\u03b8): \u03b8 \u2208 [0,2\u03c0)} and \u03b2* is the minimum of the set {\u03b2(\u03b8): \u03b8 \u2208 [0,2\u03c0)}, then the value of \u03b1* + \u03b2* is", "response_choices": "(A) -37/16, (B) -31/16, (C) -29/16, (D) -17/16", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "A line y = mx + 1 intersects the circle (x - 3)^2 + (y + 2)^2 = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate = -2, then which one of the following options is correct?", "response_choices": "(A) -3 \u2264 m < -1, (B) 2 \u2264 m < 4, (C) 4 \u2264 m < 6, (D) 6 \u2264 m < 8", "answer": "B", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "The area of the region {(x, y) : xy \u2264 8, 1 \u2264 y \u2264 x\u00b2} is", "response_choices": "(A) 16 log\u2082 2 - 14/3, (B) 8 log\u2082 2 - 14/3, (C) 16 log\u2082 2 - 6, (D) 8 log\u2082 2 - 7/3", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let \u03b1 and \u03b2 be the roots of x^2 - x - 1 = 0, with \u03b1 > \u03b2. For all positive integers n, define a_n = (\u03b1^n - \u03b2^n) / (\u03b1 - \u03b2), n \u2265 1, b_1 = 1 and b_n = a_n-1 + a_n+1, n \u2265 2. Then which of the following options is/are correct?", "response_choices": "A) a_1 + a_2 + a_3 + ... + a_n = a_n+2 - 1 for all n \u2265 1\nB) \u03a3 a_n = 10/89 from n=1 to infinity\nC) b_n = \u03b1^n + \u03b2^n for all n \u2265 1\nD) \u03a3 b_n = 8/89 from n=1 to infinity", "answer": "A, B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let M = [[0, 1, a], [1, 2, 3], [3, b, 1]] and adjM = [[-1, 1, -1], [8, -6, 2], [-5, 3, -1]] where a and b are real numbers. Which of the following options is/are correct?", "response_choices": "(A) a + b = 3\n(B) (adjM)^-1 + adjM^-1 = -M\n(C) det(adjM^2) = 81\n(D) If M [[\u03b1], [\u03b2], [\u03b3]] = [[1], [2], [3]], then \u03b1 - \u03b2 + \u03b3 = 3", "answer": "Not enough information to determine answer", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and 3 green balls. Bags B1, B2 and B3 have probabilities 3/10, 3/10 and 4/10 respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?", "response_choices": "(A) Probability that the chosen ball is green, given that the selected bag is B3, equals 3/8\n(B) Probability that the chosen ball is green equals 39/80\n(C) Probability that the selected bag is B3, given that the chosen ball is green, equals 5/13\n(D) Probability that the selected bag is B3 and the chosen ball is green equals 3/10", "answer": "Not enough information to determine answer", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "In a non-right-angled triangle \u0394PQR, let p, q, r denote the lengths of the sides opposite to the angles at P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. If p = \u221a3, q = 1, and the radius of the circumcircle of the \u0394PQR equals 1, then which of the following options is/are correct?", "response_choices": "(A) Length of RS = \u221a7/2 \n(B) Area of \u0394SOE = \u221a3/12 \n(C) Length of OE = 1/6 \n(D) Radius of incircle of \u0394PQR = \u221a3/2 (2 - \u221a3)", "answer": "(C) Length of OE = 1/6", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Define the collections {E1, E2, E3, ...} of ellipses and {R1, R2, R3, ...} of rectangles as follows: \nE3: x^2/9 + y^2/4 = 1; \nR3: rectangle of largest area, with sides parallel to the axes, inscribed in E3; \nEn: ellipse x^2/a^2 + y^2/b^2 = 1 of largest area inscribed in Rn-1, n > 1; \nRn: rectangle of largest area, with sides parallel to the axes, inscribed in En, n > 1. \nThen which of the following options is/are correct?", "response_choices": "(A) The eccentricities of E18 and E19 are NOT equal \n(B) \u2211 (area of Rn) < 24, for each positive integer N \n n=1 \n(C) The length of latus rectum of E9 is 1/6 \n(D) The distance of a focus from the centre in E9 is \u221a5/32", "answer": "(B) \u2211 (area of Rn) < 24, for each positive integer N", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let f: R \u2192 R be given by the piecewise function shown in the image.", "response_choices": "(A) f is increasing on (\u2212\u221e, 0); (B) f' has a local maximum at x = 1; (C) f is onto; (D) f' is NOT differentiable at x = 1", "answer": "B", "page_number": 25, "image_available": "yes", "question_subject": "mathematics"} +{"id": 11, "question": "Let \u0393 denote a curve y = y(x) which is in the first quadrant and let the point (1,0) lie on it. Let the tangent to \u0393 at a point P intersect the y-axis at Yp. If PYp has length 1 for each point P on \u0393, then which of the following options is/are correct?", "response_choices": "(A) y = log\u2081\u2081(1 + \u221a(1 - x\u00b2)/x) - \u221a(1 - x\u00b2); (B) xy' + \u221a(1 - x\u00b2) = 0; (C) y = -log\u2081\u2081((1 + \u221a(1 - x\u00b2))/x) + \u221a(1 - x\u00b2); (D) xy' - \u221a(1 - x\u00b2) = 0", "answer": "A, B, C", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let l\u2081 and l\u2082 denote the lines r\u20d7 = i\u20d7 + \u03bb (\u2212i\u20d7 + 2j\u20d7 + 2k\u20d7), \u03bb \u2208 \u211d and r\u20d7 = \u03bc (2i\u20d7 \u2212 j\u20d7 + 2k\u20d7), \u03bc \u2208 \u211d respectively. If l\u2083 is a line which is perpendicular to both l\u2081 and l\u2082 and cuts both of them, then which of the following options describe(s) l\u2083?", "response_choices": "(A) r\u20d7 = \u00bd (4i\u20d7 + j\u20d7 + k\u20d7) + t(2i\u20d7 + 2j\u20d7 \u2212 k\u20d7), t \u2208 \u211d\n(B) r\u20d7 = \u00bd (2i\u20d7 \u2212 j\u20d7 + 2k\u20d7) + t (2i\u20d7 + 2j\u20d7 \u2212 k\u20d7), t \u2208 \u211d\n(C) r\u20d7 = \u2153 (2i\u20d7 + k\u20d7) + t(2i\u20d7 + 2j\u20d7 \u2212 k\u20d7), t \u2208 \u211d\n(D) r\u20d7 = t(2i\u20d7 + 2j\u20d7 \u2212 k\u20d7), t \u2208 \u211d", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let \u03c9 \u2260 1 be a cube root of unity. Then the minimum of the set {|a + b\u03c9 + c\u03c9^2|^2 : a, b, c distinct non-zero integers} equals", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Let AP(a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d > 0. If AP(1; 3) \u2229 AP(2; 5) \u2229 AP(3; 7) = AP(a; d) then a + d equals", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Let S be the sample space of all 3 \u00d7 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by E1 = {A \u2208 S : det A = 0} and E2 = {A \u2208 S : sum of entries of A is 7}. If a matrix is chosen at random from S, then the conditional probability P(E1|E2) equals", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let the point B be the reflection of the point A(2, 3) with respect to the line 8x \u2212 6y \u2212 23 = 0. Let \u0393A and \u0393B be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles \u0393A and \u0393B such that both the circles are on the same side of T. If C is the point of intersection of T and the line passing through A and B, then the length of the line segment AC is", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "If I = (2/\u03c0) * \u222b(\u03c0/4)(-\u03c0/4) (dx / (1 + e^(sin x))(2 - cos 2x)) then 27 I^2 equals___", "response_choices": "", "answer": "", "page_number": 28, "image_available": "yes", "question_subject": "mathematics"} +{"id": 18, "question": "Three lines are given by r = \u03bbi, \u03bb \u2208 R r = \u03bc (i + j), \u03bc \u2208 R and r = v(i + j + k), v \u2208 R. Let the lines cut the plane x + y + z = 1 at the points A, B and C respectively. If the area of the triangle ABC is A then the value of (6A)^2 equals___", "response_choices": "", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2019_2_English.jsonl b/JEE_papers/JSON/JEE_2019_2_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..5c65a6958f15c21c783330d17c407dfe8059744d --- /dev/null +++ b/JEE_papers/JSON/JEE_2019_2_English.jsonl @@ -0,0 +1,59 @@ +{"id": 1, "question": "A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle 60\u00b0 with vertical? [g is the acceleration due to gravity]", "response_choices": "(A) The angular speed of the rod will be \u221a(3g/2), (B) The angular acceleration of the rod will be 2g/L, (C) The radial acceleration of the rod's center of mass will be 3g/4, (D) The normal reaction force from the floor on the rod will be Mg/16", "answer": "B, C", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "A block of mass 2M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a1, a2 and a3 as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x0. Which of the following option(s) is/are correct? [g is the acceleration due to gravity. Neglect friction]", "response_choices": "A) x0 = 4Mg/k\nB) When spring achieves an extension of x0/2 for the first time, the speed of the block connected to the spring is 3g sqrt(M/5k)\nC) At an extension of x0/4 of the spring, the magnitude of acceleration of the block connected to the spring is 3g/10\nD) a2 - a1 = a1 - a3", "answer": "A, D", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is L = L0, the particle speed is v = v0. The piston is moved inward at a very low speed V such that V << dL/v0 , where dL is the infinitesimal displacement of the piston. Which of the following statement(s) is/are correct?", "response_choices": "(A) The rate at which the particle strikes the piston is v/L\n(B) After each collision with the piston, the particle speed increases by 2V\n(C) If the piston moves inward by dL, the particle speed increases by 2 v dL/L\n(D) The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from L0 to 1/2 L0", "answer": "C", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "An electric dipole with dipole moment p0/(i + j) is held fixed at the origin O in the presence of an uniform electric field of magnitude E0. If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are: (e0 is permittivity of free space. R >> dipole size)", "response_choices": "(A) R = ( p0 )^(1/3) (4\u03c0\u03b50E0) (B) Total electric field at point A is BA = \u221a2 E0 (i + j) (C) Total electric field at point B is BB = 0 (D) The magnitude of total electric field on any two points of the circle will be same.", "answer": "A", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P0, volume V0, and temperature T0. If the gas mixture is adiabatically compressed to a volume V0/4, then the correct statement(s) is/are, (Given \u03b3^(1/2) = 2.3; \u03b3^(3/2) = 9.2; R is gas constant)", "response_choices": "(A) The work |W| done during the process is 13RT0 (B) The average kinetic energy of the gas mixture after compression is in between 18RT0 and 19RT0 (C) The final pressure of the gas mixture after compression is in between 9P0 and 10P0 (D) Adiabatic constant of the gas mixture is 1.6", "answer": "B", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same ( R = 3m). If H2, H2, and H3 are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are:", "response_choices": "A) H2 > H1, B) H3 > H1, C) H2 > H3, D) 0.8 cm < (H2 - H1) < 0.9 cm", "answer": "D", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle \u03b1 as shown in figure. On the screen, the point O is equidistant from the slits and distance P O is 11.0 mm. Which of the following statement(s) is/are correct?", "response_choices": "(A) For \u03b1 = 0.3\u03b1 degree, there will be destructive interference at point O. (B) For \u03b1 = 0, there will be constructive interference at point P. (C) For \u03b1 = 0.3\u03b1 \u03bb degree, there will be destructive interference at point P. (D) Fringe spacing depends on \u03b1.", "answer": "", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "A free hydrogen atom after absorbing a photon of wavelength \u03bbin gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength \u03bbe. Let the change in momentum of atom due to the absorption and the emission are \u0394p\u2090 and \u0394pe, respectively. If \u03bb\u2090/\u03bbe = 1/5, which of the option(s) is/are correct? [Use hc = 1242 eV nm ; 1 nm = 10\u207b\u2079 m, h and c are Planck's constant and speed of light, respectively]", "response_choices": "(A) m = 2 (B) \u03bbe = 418 nm (C) \u0394p\u2090/\u0394pe = 1/2 (D) The ratio of kinetic energy of the electron in the state n = m to the state n = 1 is 1/4", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A ball is thrown from ground at an angle \u03b8 with horizontal and with an initial speed u0. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is V1. After hitting the ground, the ball rebounds at the same angle \u03b8 but with a reduced speed of u0/\u03b1. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is 0.8 V1, the value of \u03b1 is __________.", "response_choices": "", "answer": "", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1 \u03a9 as shown in figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field \ud835\udc35\u20d7 = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is x \u00d7 10^-3 A, where the value of x is _______. [Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given: e^-1 = 0.37, where e is base of the natural logarithm]", "response_choices": "No options provided", "answer": "Blank", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "A monochromatic light is incident from air on a refracting surface of a prism of angle 75\u2070 and refractive index n\u2080 = \u221a3. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of \u03b8 \u2264 60\u2070. The value of n^2 is _______.", "response_choices": "No options provided", "answer": "Blank", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency \u03a9 such that 4\u03c0M\u03a9/h = 10^24 m^-2 with h as Planck's constant. N photons of wavelength \u03bb = 8\u03c0 x 10^-6 m strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1 \u03bcm. If the value of N is x \u00d7 10^12, then the value of x is _____. [Consider the spring as massless]", "response_choices": "", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "Suppose a \u00b2\u00b2\u2076Ra nucleus at rest and in ground state undergoes \u03b1-decay to a \u00b2\u00b2\u00b2Rn nucleus in its excited state. The kinetic energy of the emitted \u03b1 particle is found to be 4.44 MeV. \u00b2\u00b2\u00b2Rn nucleus then goes to its ground state by \u03b3-decay. The energy of the emitted \u03b3 photon is ____ keV. [Given: atomic mass of \u00b2\u00b2\u2076Ra = 226.005 u, atomic mass of \u00b2\u00b2\u00b2Rn = 222.000 u, atomic mass of \u03b1 particle = 4.000 u, 1 u = 931 MeV/c\u00b2, c is speed of the light]", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is _____.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "If the tension in each string is T0, the correct match for the highest fundamental frequency in f0 units will be,", "response_choices": "(A) I \u2192 P, II \u2192 Q, III \u2192 T, IV \u2192 S\n(B) I \u2192 P, II \u2192 R, III \u2192 S, IV \u2192 Q\n(C) I \u2192 Q, II \u2192 S, III \u2192 R, IV \u2192 P\n(D) I \u2192 Q, II \u2192 P, III \u2192 R, IV \u2192 T", "answer": "(B) I \u2192 P, II \u2192 R, III \u2192 S, IV \u2192 Q", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "The length of the strings 1, 2, 3 and 4 are kept fixed at L0, 3L0/2 , 5L0/4 and 7L0/4 , respectively. Strings 1, 2, 3, and 4 are vibrated at their 1st, 3rd , 5th, and 14th harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of T0 will be,", "response_choices": "(A) I \u2192 P, II \u2192 R, III \u2192 T, IV \u2192 U\n(B) I \u2192 P, II \u2192 Q, III \u2192 T, IV \u2192 U\n(C) I \u2192 P, II \u2192 Q, III \u2192 R, IV \u2192 T\n(D) I \u2192 T, II \u2192 Q, III \u2192 R, IV \u2192 U", "answer": "(B) I \u2192 P, II \u2192 Q, III \u2192 T, IV \u2192 U", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Answer Q.17 and Q.18 by appropriately matching the lists based on the information given in the paragraph", "response_choices": "", "answer": "", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by TdX, where T is the temperature of the system and dX is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas X = (3/2)R ln (Vd/Va) + R ln (Vd/Va). Here, R is gas constant, V is volume of gas, Td and Va are constants.", "response_choices": "", "answer": "", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.", "response_choices": "List-I: (I) Work done by the system in process 1->2->3, (II) Change in internal energy in process 1->2->3, (III) Heat absorbed by the system in process 1->2->3, (IV) Heat absorbed by the system in process 1->2; List-II: (P) 1/2 RTo ln 2, (Q) 1/3 RTo, (R) RTo, (S) 4/3 RTo, (T) 1/3 RTo(3 + ln 2), (U) 5/3 RTo", "answer": "(I) P, (II) Q, (III) R, (IV) S", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "If the process carried out on one mole of monatomic ideal gas is as shown in figure in the PV-diagram with P0V0 = 4/3 RT0, the correct match is,", "response_choices": "(A) I \u2192 Q, II \u2192 R, III \u2192 P, IV \u2192 U; (B) I \u2192 Q, II \u2192 R, III \u2192 S, IV \u2192 U; (C) I \u2192 S, II \u2192 R, III \u2192 Q, IV \u2192 T; (D) I \u2192 Q, II \u2192 S, III \u2192 R, IV \u2192 U", "answer": "(D) I \u2192 Q, II \u2192 S, III \u2192 R, IV \u2192 U", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with P0V0 = 1/3 RT0, the correct match is,", "response_choices": "(A) I \u2192 P, II \u2192 R, III \u2192 T, IV \u2192 S; (B) I \u2192 P, II \u2192 T, III \u2192 Q, IV \u2192 T; (C) I \u2192 P, II \u2192 R, III \u2192 T, IV \u2192 P; (D) I \u2192 S, II \u2192 T, III \u2192 Q, IV \u2192 U", "answer": "(C) I \u2192 P, II \u2192 R, III \u2192 T, IV \u2192 P", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "The cyanide process of gold extraction involves leaching out gold from its ore with CN\u207b in the presence of O in water to form R. Subsequently, R is treated with T to obtain Au and Z. Choose the correct option(s)", "response_choices": "(A) O is O\u2082, (B) T is Zn, (C) Z is [Zn(CN)\u2084]\u00b2\u207b, (D) R is [Au(CN)\u2082]\u207b", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "With reference to aqua regia, choose the correct option(s)", "response_choices": "(A) Aqua regia is prepared by mixing conc. HCl and conc. HNO\u2083 in 3:1 (v/v) ratio, (B) Reaction of gold with aqua regia produces an anion having Au in +3 oxidation state, (C) Reaction of gold with aqua regia produces NO\u2082 in the absence of air, (D) The yellow colour of aqua regia is due to the presence of NOCl and Cl\u2082", "answer": "A,B,D", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Consider the following reactions (unbalanced)\n\nZn + hot conc. H\u2082SO\u2084 \u2192 G + R + X\nZn + conc. NaOH \u2192 T + Q\nG + H\u2082S + NH\u2084OH \u2192 Z (a precipitate) + X + Y", "response_choices": "(A) Z is dirty white in colour\n\n(B) The oxidation state of Zn in T is +1\n\n(C) R is a V-shaped molecule\n\n(D) Bond order of Q is 1 in its ground state", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "The ground state energy of hydrogen atom is -13.6 eV. Consider an electronic state \u03a8'of He\u207a whose energy, azimuthal quantum number and magnetic quantum number are -3.4 eV, 2 and 0, respectively. Which of the following statement(s) is(are) true for the state \u03a8'?", "response_choices": "(A) It is a 4d state\n\n(B) It has 2 angular nodes\n\n(C) It has 3 radial nodes\n\n(D) The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "Which of the following reactions produce(s) propane as a major product?", "response_choices": "(A)\n\nH\u2083C\u23bb\u23bb\u23bbCOONa NaOH, CaO, \u0394\n\n(B)\n\nH\u2083C\u23bb\u23bb\u23bbCOONa + H\u2082O electrolysis\n\n(C)\n\nH\u2083C\u23bb\u23bb\u23bbCl Zn, dil. HCl\n\n(D)\n\nBr\n| \nH\u2083C\u23bb\u23bb\u23bbBr Zn", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "Choose the correct option(s) that give(s) an aromatic compound as the major product", "response_choices": "(A) i) alc. KOH, ii) NaNH2, iii) red hot iron tube, 873 K, (B) NaOMe, (C) Br, NaOEt, (D) + Cl2 (excess), UV, 500 K", "answer": "D", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "Choose the correct option(s) for the following reaction sequence", "response_choices": "A) \n\nMeO Q\n\nMeO S\n\nB) \n\nMeO R\n\nMeO S\n\nC) \n\nMeO Q\n\nMeO R\n\nD) \n\nMeO R\n\nMeO S", "answer": "B", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "Choose the correct option(s) from the following", "response_choices": "A) Natural rubber is polyisoprene containing trans alkene units\n\nB) Nylon-6 has amide linkages\n\nC) Teflon is prepared by heating tetrafluoroethene in presence of a persulphate catalyst at high pressure\n\nD) Cellulose has only \u03b1-D-glucose units that are joined by glycosidic linkages", "answer": "", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by conc. HNO3 to a compound with the highest oxidation state of sulphur is _____\n(Given data: Molar mass of water = 18 g mol^-1)", "response_choices": "", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Total number of cis N-Mn-Cl bond angles (that is, Mn-N and Mn-Cl bonds in cis positions) present in a molecule of cis-[Mn(en)2Cl2] complex is _____\n(en = NH2CH2CH2NH2)", "response_choices": "", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "The decomposition reaction 2N2O5(g) \u2192 2N2O4(g) + O2(g) is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After Y \u00d7 10^8 s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is 5 \u00d7 10^-4 s^-1, assuming ideal gas behavior, the value of Y is _____", "response_choices": "", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the solution is 1.2 g cm^-3, the molarity of urea solution is _____\n(Given data: Molar masses of urea and water are 60 g mol^-1 and 18 g mol^-1, respectively)", "response_choices": "", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "Total number of hydroxyl groups present in a molecule of the major product P is ____", "response_choices": "No multiple choice options provided", "answer": "No answer marked", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with the molecular formula C4H8O is ____", "response_choices": "No multiple choice options provided", "answer": "No answer marked", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "Which of the following options has the correct combination considering List-I and List-II?", "response_choices": "(A) (I), (P) (B) (I), (T) (C) (II), (Q) (D) (II), (R)", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "Which of the following options has the correct combination considering List-I and List-II?", "response_choices": "(A) (III), (P) (B) (III), (S) (C) (IV), (Q) (D) (IV), (U)", "answer": "B", "page_number": 20, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "Answer Q.17 and Q.18 by appropriately matching the lists based on the information given in the paragraph", "response_choices": "", "answer": "", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 18, "question": "List-I includes starting materials and reagents of selected chemical reactions. List-II gives structures of compounds that may be formed as intermediate products and/or final products from the reactions of List-I.", "response_choices": "(I) i) DIBAL-H, ii) dil. HCl, iii) NaBH4, iv) conc. H2SO4; (II) i) O3, ii) Zn, H2O, iii) NaBH4, iv) conc. H2SO4; (III) i) KCN, ii) H3O+, \u0394, iii) LiAlH4, iv) conc. H2SO4; (IV) i) LiAlH4, ii) conc. H2SO4; (P) CHO-CO2H; (Q) OH-OH; (R) O; (S) OH-CO2H; (T) CO2H-CO2H; (U) O-O", "answer": "(I) P, (II) Q, (III) R, (IV) S, (V) T", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "Which of the following options has correct combination considering List-I and List-II?", "response_choices": "(A) (I), (Q), (T), (U) | (B) (II), (P), (S), (T) | (C) (II), (P), (S), (U) | (D) (I), (S), (Q), (R)", "answer": "(B) (II), (P), (S), (T)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "Which of the following options has correct combination considering List-I and List-II?", "response_choices": "(A) (III), (S), (R) | (B) (IV), (Q), (U) | (C) (III), (T), (U) | (D) (IV), (Q), (R)", "answer": "(B) (IV), (Q), (U)", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "Let P1 = I = [1 0 0; 0 1 0; 0 0 1], P2 = [1 0 0; 0 0 1; 0 1 0], P3 = [0 1 0; 1 0 0; 0 0 1], P4 = [0 1 0; 0 0 1; 1 0 0], P5 = [0 0 1; 1 0 0; 0 1 0], P6 = [0 0 1; 0 1 0; 1 0 0] and X = \u2211(6 k=1) Pk [2 1 3; 1 0 2; 2 2 1]PkT where PkT denotes the transpose of the matrix Pk. Then which of the following options is/are correct? (A) If X [1 1 1]T = \u03b1 [1 1 1]T, then \u03b1 = 30 (B) X is a symmetric matrix (C) The sum of diagonal entries of X is 18 (D) X \u2212 30I is an invertible matrix", "response_choices": "(A) If X [1 1 1]T = \u03b1 [1 1 1]T, then \u03b1 = 30, (B) X is a symmetric matrix, (C) The sum of diagonal entries of X is 18, (D) X \u2212 30I is an invertible matrix", "answer": "", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Let x \u2208 \u211d and let P = [1 1 1, 0 2 2, 0 0 3], Q = [2 x x, 0 4 0] and R = PQP^(-1). Then which of the following options is/are correct?", "response_choices": "(A) There exists a real number x such that PQ = QP, (B) det R = det [0 4 0] + 8, for all x \u2208 \u211d, (C) For x = 0, if R [a] = 6 [a], then a + b = 5, (D) For x = 1, there exists a unit vector \u03b1\u200bi + \u03b2\u200bj + \u03b3k\u200b\u200b for which R [\u03b2] = [0]", "answer": "(B)", "page_number": 24, "image_available": "yes", "question_subject": "mathematics"} +{"id": 3, "question": "For non-negative integers n, let f(n) = (\u03a3 from k=0 to n) sin((k+1)\u03c0/(n+2)\u03c0) sin((k+2)/(n+2)\u03c0) / (\u03a3 from k=0 to n) sin^2((k+1)\u03c0/(n+2)\u03c0). Assuming cos^(-1)x takes values in [0,\u03c0], which of the following options is/are correct?", "response_choices": "(A) f(4) = \u221a3/2, (B) lim f(n) = 1/2, n->\u221e, (C) If \u03b1 = tan(cos^(-1)f(6)), then \u03b1^2 + 2\u03b1 - 1 = 0, (D) sin(7 cos^(-1)f(5)) = 0", "answer": "(B),(D)", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let f: R \u2192 R be a function. We say that f has PROPERTY 1 if lim [f(h) - f(0)]/sqrt(|h|) exists and is finite, and PROPERTY 2 if lim [f(h) - f(0)]/h^2 exists and is finite. Then which of the following options is/are correct?", "response_choices": "(A) f(x) = |x| has PROPERTY 1, (B) f(x) = x^(2/3) has PROPERTY 1, (C) f(x) = x|x| has PROPERTY 2, (D) f(x) = sin x has PROPERTY 2", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let f(x) = sin \u03c0x/x^2, x > 0. Let x1 < x2 < x3 < ... < xn < ... be all the points of local maximum of f and y1 < y2 < y3 < ... < yn < ... be all the points of local minimum of f. Then which of the following options is/are correct?", "response_choices": "(A) x1 < y1, (B) xn+1 - xn > 2 for every n, (C) xn \u2208 (2n,2n + 1) for every n, (D) |xn - yn| > 1 for every n", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "For a \u2208 R, |a| > 1, let lim (1 + sqrt(2) + ... + sqrt(n))/(n^(7/3) ((an+1)^2 + (an+2)^2 + ... + (an+n)^2)) = 54. Then the possible value(s) of a is/are", "response_choices": "(A) -9, (B) -6, (C) 7, (D) 8", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let f: \u211d \u2192 \u211d be given by f(x) = (x - 1)(x - 2)(x - 5). Define F(x) = \u222b[x to \u221e] f(t) dt, x > 0. Then which of the following options is/are correct?", "response_choices": "(A) F has a local minimum at x = 1 \n(B) F has a local maximum at x = 2 \n(C) F has two local maxima and one local minimum in (0, \u221e) \n(D) F(x) \u2260 0 for all x \u2208 (0, 5)", "answer": "C", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Three lines l1: r\u20d7 = \u03bbi\u20d7, \u03bb \u2208 \u211d, l2: r\u20d7 = k\u20d7 + \u03bcj\u20d7, \u03bc \u2208 \u211d and l3: r\u20d7 = i\u20d7 + j\u20d7 + \u03bdk\u20d7, \u03bd \u2208 \u211d are given. For which point(s) Q on l2 can we find a point P on l1 and a point R on l3 so that P, Q and R are collinear?", "response_choices": "(A) k\u20d7 - 1/2j\u20d7 \n(B) k\u20d7 \n(C) k\u20d7 + 1/2j\u20d7 \n(D) k\u20d7 + j\u20d7", "answer": "C", "page_number": 26, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Suppose det [ (Sum from k=0 to n) k, (Sum from k=0 to n) nCk k^2 ] = 0 [ (Sum from k=0 to n) nCk k, (Sum from k=0 to n) nCk 3k ] holds for some positive integer n. Then (Sum from k=0 to n) nCk / (k + 1) equals _", "response_choices": "", "answer": "", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 10, "question": "Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is _", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let |X| denote the number of elements in a set X. Let S = {1, 2, 3, 4, 5, 6} be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A, B) such that 1 \u2264 |B| < |A|, equals _", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "The value of sec^-1 (1/4 (sum from k=0 to 10) sec (2\u03c0/12 + k\u03c0/2) + sec (7\u03c0/12 + (k + 1)\u03c0/2)) in the interval [-\u03c0 3\u03c0/4, \u03c0/4] equals ___", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 28, "image_available": "yes", "question_subject": "mathematics"} +{"id": 13, "question": "The value of the integral from 0 to \u03c0/2 of (3 \u221a(cos \u03b8)) / ((\u221a(cos \u03b8) + \u221a(sin \u03b8))^2) d\u03b8 equals ___", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 28, "image_available": "yes", "question_subject": "mathematics"} +{"id": 14, "question": "Let \u00e2 = 2\u00ee + j - k\u0302 and b\u0302 = \u00ee + 2j + k be two vectors. Consider a vector \u0109 = a\u00e2 + \u03b2b\u0302, \u03b1, \u03b2 \u2208 \u211d. If the projection of \u0109 on the vector (\u00e2 + b\u0302) is 3\u221a2, then the minimum value of (\u0109 - (\u00e2 \u00d7 b\u0302)) \u22c5 \u0109 equals___", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Which of the following is the only CORRECT combination?", "response_choices": "A) (I), (P), (R) B) (II), (Q), (T) C) (I), (Q), (U) D) (II), (R), (S)", "answer": "B", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Which of the following is the only CORRECT combination?", "response_choices": "A) (III), (R), (U) B) (IV), (P), (R), (S) C) (III), (P), (Q), (U) D) (IV), (Q), (T)", "answer": "B", "page_number": 30, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Which of the following is the only CORRECT combination?", "response_choices": "(A) (I), (S) (B) (I), (U) (C) (II), (Q) (D) (II), (T)", "answer": "(C) (II), (Q)", "page_number": 31, "image_available": "yes", "question_subject": "mathematics"} +{"id": 18, "question": "Which of the following is the only INCORRECT combination?", "response_choices": "(A) (I), (P) (B) (IV), (U) (C) (III), (R) (D) (IV), (S)", "answer": "(D) (IV), (S)", "page_number": 31, "image_available": "yes", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2020_1_English.jsonl b/JEE_papers/JSON/JEE_2020_1_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..670e3c8973b6fc44e54a453532b14ffd8ae8b1f5 --- /dev/null +++ b/JEE_papers/JSON/JEE_2020_1_English.jsonl @@ -0,0 +1,51 @@ +{"id": 1, "question": "A football of radius R is kept on a hole of radius r (r < R) made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle \u03b8 from the horizontal as shown in the figure below. The maximum value of \u03b8 so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale)", "response_choices": "(A) sin\u03b8 = r/R, (B) tan\u03b8 = r/R, (C) sin\u03b8 = r/2R, (D) cos\u03b8 = r/2R", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)", "response_choices": "(A) rotate in the direction opposite to the direction of magnet's motion, (B) rotate in the same direction as the direction of magnet's motion, (C) not rotate and its temperature will remain unchanged, (D) not rotate but its temperature will slowly rise", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)", "response_choices": "A, B, C, D", "answer": "B", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge Q through a switch. The coil is in a horizontal uniform magnetic field Bo parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)", "response_choices": "A) nNQBoR2/2, B) \u03c0NQBoR2, C) 2\u03c0NQBoR2, D) 4\u03c0NQBoR2", "answer": "C", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)", "response_choices": "A, B, C, D", "answer": "C", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "An open-ended U-tube of uniform cross-sectional area contains water (density 10^3kg m^-3). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg m^-3 is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio (h1/h2) of the heights of the liquid in the two arms is", "response_choices": "A) 15/14, B) 35/33, C) 7/6, D) 5/4", "answer": "C", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the nth orbit (here h is the Planck's constant)", "response_choices": "A) R \u221d n^(1/3) and v \u221d n^(2/3), B) R \u221d n^(2/3) and v \u221d n^(1/3), C) E = 3\u20442 (n^2\u210f^2E^2)^(1/3) / (4\u03c0^2m), D) E = 2 (n^2\u210f^2E^2)^(1/3) / (4\u03c0^2m)", "answer": "D", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "The filament of a light bulb has surface area 64 mm2. The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take Stefan-Boltzmann constant = 5.67 \u00d7 10^-8 Wm^-2K^-4, Wien's displacement constant = 2.90 \u00d7 10^-3 m-K, Planck's constant = 6.63 \u00d7 10^-34 Js, speed of light in vacuum = 3.00 \u00d7 10^8 ms^-1)", "response_choices": "A) power radiated by the filament is in the range 642 W to 645 W, B) radiated power entering into one eye of the observer is in the range 3.15 \u00d7 10^-8 W to 3.25 \u00d7 10^-8 W, C) the wavelength corresponding to the maximum intensity of light is 1160 nm, D) taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range 2.75 \u00d7 10^11 to 2.85 \u00d7 10^11", "answer": "D", "page_number": 5, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [X\u03b1]; [speed] = [X\u03b2]; [acceleration] =[X\u03b3]; [linear momentum] = [X\u03b4]; [force] = [X\u03b5]. Then", "response_choices": "(A) \u03b1 + p = 2\u03b2\n(B) p + q - r = \u03b2\n(C) p - q + r = \u03b1\n(D) p + q + r = \u03b2", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A uniform electric field, E = -400\u221a3\u221a NC\u207b\u00b9 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2\u221a10 \u00d7 10\u2076 ms\u207b\u00b9. This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure. Take q = 10\u00b9\u2070 Ckg\u02c9\u00b9. Then", "response_choices": "(A) the particle will hit T if projected at an angle 45\u00b0 from the horizontal\n(B) the particle will hit T if projected either at an angle 30\u00b0 or 60\u00b0 from the horizontal\n(C) time taken by the particle to hit T could be \u221a5/5 \u03bcs as well as \u221a5/2 \u03bcs\n(D) time taken by the particle to hit T is \u221a5/3 \u03bcs", "answer": "", "page_number": 6, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "Shown in the figure is a semicircular metallic strip that has thickness t and resistivity \u03c1. Its inner radius is R1 and outer radius is R2. If a voltage V0 is applied between its two ends, a current I flows in it. In addition, it is observed that a transverse voltage \u0394V develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)", "response_choices": "(A) I = vt/n\u03c1 ln (R2/R1) (B) the outer surface is at a higher voltage than the inner surface (C) the outer surface is at a lower voltage than the inner surface (D) \u0394V \u221d I^2", "answer": "B", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per unit volume with \u0394n = (n1 \u2212 n2) \u226a n1. When they are connected by a tube of small length l and cross-sectional area S, KMnO4 starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force \u2212\u03b2v on each molecule, where \u03b2 is a constant. Neglecting all terms of the order (\u0394n)2, which of the following is/are correct? (kB is the Boltzmann constant)", "response_choices": "A) the force causing the molecules to move across the tube is \u0394nkBTS, B) force balance implies n1\u03b2vl = \u0394nkBT, C) total number of molecules going across the tube per sec is (\u0394n/T)(kBT/\u03b2)S, D) rate of molecules getting transferred through the tube does not change with time", "answer": "C", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance xR from the center (50.00 cm) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are 0.40 and 0.32, respectively, the value of xR (in cm) is _______.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are 103kg m\u22123, 0.07 Nm\u22121 and 10 ms\u22122, respectively, the value of h (in mm) is _______.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0,0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole p pointing towards the charge q is fixed at the origin, the spring gets stretched to a length l and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by \u0394l << l from its equilibrium position and released, it is found to oscillate at frequency 1/2 \u221a(k/m). The value of \u03b4 is _____.", "response_choices": "No response choices provided.", "answer": "No answer provided.", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "Consider one mole of helium gas enclosed in a container at initial pressure P1 and volume V1. It expands isothermally to volume 4V1. After this, the gas expands adiabatically and its volume becomes 32V1. The work done by the gas during isothermal and adiabatic expansion processes are Wiso and Wadia, respectively. If the ratio Wadia/Wiso = f ln2, then f is _______.", "response_choices": "No response choices provided.", "answer": "No answer provided.", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 ms\u22121 in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 ms\u22121, the smallest value of the percentage change required in the length of the pipe is _______.", "response_choices": "No response choices provided.", "answer": "No answer provided.", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "A circular disc of radius R carries surface charge density \u03c3(r) = \u03c30 (1 - r/R), where \u03c30 is a constant and r is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is \u03a60. Electric flux through another spherical surface of radius R/4 and concentric with the disc is \u03a6. Then the ratio \u03a60/\u03a6 is _______.", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is", "response_choices": "(A) 1 : 1 : 1 (B) 1 : 1 : 1.224 (C) 1 : 1.128 : 1.224 (D) 1 : 1.128 : 1", "answer": "C", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "Which of the following liberates O2 upon hydrolysis?", "response_choices": "(A) Pb3O4 (B) KO2 (C) Na2O2 (D) Li2O2", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "A colorless aqueous solution contains nitrates of two metals, X and Y. When it was added to an aqueous solution of NaCl, a white precipitate was formed. This precipitate was found to be partly soluble in hot water to give a residue P and a solution Q. The residue P was soluble in aq. NH3 and also in excess sodium thiosulfate. The hot solution Q gave a yellow precipitate with KI. The metals X and Y, respectively, are", "response_choices": "(A) Ag and Pb (B) Ag and Cd (C) Cd and Pb (D) Cd and Zn", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "Which one of the following options represents identical molecules?", "response_choices": "(A) P and Q, (B) Q and S, (C) Q and R, (D) R and S", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "Which one of the following structures has the IUPAC name 3-ethynyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid?", "response_choices": "(A), (B), (C), (D)", "answer": "B", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "The Fischer projection of D-erythrose is shown below. D-Erythrose and its isomers are listed as P, Q, R, and S in Column-I. Choose the correct relationship of P, Q, R, and S with D-erythrose from Column II.", "response_choices": "A) P->2, Q->3, R->2, S->2\nB) P->3, Q->1, R->1, S->2\nC) P->2, Q->1, R->1, S->3\nD) P->2, Q->3, R->3, S->1", "answer": "B", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "In thermodynamics, the P \u2013 V work done is given by w = \u2013 \u222b dV Pext . For a system undergoing a particular process, the work done is, w = \u2013 \u222b dV (RT/v \u2013 b \u2013 a/v2). This equation is applicable to a", "response_choices": "(A) system that satisfies the van der Waals equation of state, (B) process that is reversible and isothermal, (C) process that is reversible and adiabatic, (D) process that is irreversible and at constant pressure.", "answer": "(B) process that is reversible and isothermal", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "With respect to the compounds I-V, choose the correct statement(s).", "response_choices": "(A) The acidity of compound I is due to delocalization in the conjugate base, (B) The conjugate base of compound IV is aromatic, (C) Compound II becomes more acidic, when it has a -NO2 substituent, (D) The acidity of compounds follows the order I > IV > V > II > III.", "answer": "(D) The acidity of compounds follows the order I > IV > V > II > III.", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "In the reaction scheme shown below, Q, R, and S are the major products. The correct structure of (A) S is, (B) Q is, (C) R is, (D) S is", "response_choices": "A, B, C, D", "answer": "B", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 10, "question": "Choose the correct statement(s) among the following:", "response_choices": "(A) [FeCl4]- has tetrahedral geometry. (B) [Co(en)(NH3)2Cl2]+ has 2 geometrical isomers. (C) [FeCl4]- has higher spin-only magnetic moment than [Co(en)(NH3)2Cl2]+. (D) The cobalt ion in [Co(en)(NH3)2Cl2]+ has sp3d2 hybridization.", "answer": "(B)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "With respect to hypochlorite, chlorate and perchlorate ions, choose the correct statement(s).", "response_choices": "(A) The hypochlorite ion is the strongest conjugate base. (B) The molecular shape of only chlorate ion is influenced by the lone pair of electrons of Cl. (C) The hypochlorite and chlorate ions disproportionate to give rise to identical set of ions. (D) The hypochlorite ion oxidizes the sulfite ion.", "answer": "(B)", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).", "response_choices": "(A) The empirical formula of the compound is MX. (B) The cation M and anion X have different coordination geometries. (C) The ratio of M-X bond length to the cubic unit cell edge length is 0.866. (D) The ratio of the ionic radii of cation M to anion X is 0.414.", "answer": "(D)", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "5.00 mL of 0.10 M oxalic acid solution taken in a conical flask is titrated against NaOH from a burette using phenolphthalein indicator. The volume of NaOH required for the appearance of permanent faint pink color is tabulated below for five experiments. What is the concentration, in molarity, of the NaOH solution?", "response_choices": "Exp. No.\tVol. of NaOH (mL)\n1\t12.5\n2\t10.5\n3\t9.0\n4\t9.0\n5\t9.0", "answer": "The question does not provide the selected answer choice.", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "Consider the reaction A \u21cc B at 1000 K. At time t', the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at 1 bar. Given below is the plot of the partial pressure of B with time. What is the ratio of the standard Gibbs energy of the reaction at 1000 K to that at 2000 K?", "response_choices": "The question does not contain multiple choice options.", "answer": "The plot shows a decrease in partial pressure of B, indicating an endothermic reaction. Based on the graph, the ratio of standard Gibbs energy at 1000 K to 2000 K should be greater than 1.", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 15, "question": "Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is H2(g) + 1/2 O2 (g) \u2192 H2O (l). The work derived from the cell on the consumption of 1.0 \u00d7 10^-3 mol of H2(g) is used to compress 1.00 mol of a monoatomic ideal gas in a thermally insulated container. What is the change in the temperature (in K) of the ideal gas?", "response_choices": "No multiple choice options provided.", "answer": "No answer provided.", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulfuric acid are combined for the reaction? (Use molar mass of aluminium as 27.0 g mol^-1, R = 0.082 atm L mol^-1 K^-1)", "response_choices": "No multiple choice options provided.", "answer": "No answer provided.", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "238U is known to undergo radioactive decay to form 206Pb by emitting alpha and beta particles. A rock initially contained 68 \u00d7 10^-6 g of 238U. If the number of alpha particles that it would emit during its radioactive decay of 238U to 206Pb in three half-lives is Z \u00d7 10^18, then what is the value of Z?", "response_choices": "No multiple choice options provided.", "answer": "No answer provided.", "page_number": 19, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "In the following reaction, compound Q is obtained from compound P via an ionic intermediate. [Chemical structure image] What is the degree of unsaturation of Q?", "response_choices": "No multiple choice options provided.", "answer": "No answer provided.", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 1, "question": "Suppose a, b denote the distinct real roots of the quadratic polynomial x^2 + 20x \u2013 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x^2 \u2013 20x + 2020. Then the value of ac(a \u2013 c) + ad(a \u2013 d) + bc(b \u2013 c) + bd(b \u2013 d)", "response_choices": "(A) 0, (B) 8000, (C) 8080, (D) 16000", "answer": "(C) 8080", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "If the function f: \u211d \u2192 \u211d is defined by f(x) = |x|(x \u2013 sin x), then which of the following statements is TRUE?", "response_choices": "(A) f is one-one, but NOT onto, (B) f is onto, but NOT one-one, (C) f is BOTH one-one and onto, (D) f is NEITHER one-one NOR onto", "answer": "(D) f is NEITHER one-one NOR onto", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let the functions f: \u211d \u2192 \u211d and g: \u211d \u2192 \u211d be defined by f(x) = e^(x-1) \u2013 e^(-x-1) and g(x) = 1/2 (e^(x-1) + e^(-x)). Then the area of the region in the first quadrant bounded by the curves y = f(x), y = g(x) and x = 0 is", "response_choices": "(A) (2 \u2013 \u221a3) + 1/2 (e \u2013 e^(-1)), (B) (2 + \u221a3) + 1/2 (e \u2013 e^(-1)), (C) (2 \u2013 \u221a3) + 1/2 (e + e^(-1)), (D) (2 + \u221a3) + 1/2 (e + e^(-1))", "answer": "(B) (2 + \u221a3) + 1/2 (e \u2013 e^(-1))", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let a,b and \u03bb be positive real numbers. Suppose P is an end point of the latus rectum of the parabola y^2 = 4\u03bbx, and suppose the ellipse (x^2/a^2) + (y^2/b^2) = 1 passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is", "response_choices": "(A) 1/\u221a2, (B) 1/2, (C) 1/3, (D) 2/5", "answer": "C", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let C1 and C2 be two biased coins such that the probabilities of getting head in a single toss are 2/3 and 1/3, respectively. Suppose \u03b1 is the number of heads that appear when C1 is tossed twice, independently, and suppose \u03b2 is the number of heads that appear when C2 is tossed twice, independently. Then the probability that the roots of the quadratic polynomial x^2 - \u03b1x + \u03b2 are real and equal, is", "response_choices": "(A) 40/81, (B) 20/81, (C) 1/2, (D) 1/4", "answer": "C", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Consider all rectangles lying in the region {(x,y) \u2208 \u211d x \u211d : 0 \u2264 x \u2264 \u03c0/2 and 0 \u2264 y \u2264 2 sin(2x)} and having one side on the x-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is", "response_choices": "(A) 3\u03c0/2, (B) \u03c0, (C) \u03c0/2\u221a3, (D) \u03c0\u221a3/2", "answer": "D", "page_number": 21, "image_available": "yes", "question_subject": "mathematics"} +{"id": 7, "question": "Let the function f: R \u2192 R be defined by f(x) = x^3 - x^2 + (x - 1) sin x and let g: R \u2192 R be an arbitrary function. Let f g: R \u2192 R be the product function defined by (f g)(x) = f(x)g(x). Then which of the following statements is/are TRUE?", "response_choices": "A) If g is continuous at x = 1, then f g is differentiable at x = 1\nB) If f g is differentiable at x = 1, then g is continuous at x = 1\nC) If g is differentiable at x = 1, then f g is differentiable at x = 1\nD) If f g is differentiable at x = 1, then g is differentiable at x = 1", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let M be a 3 \u00d7 3 invertible matrix with real entries and let I denote the 3 \u00d7 3 identity matrix. If M^-1 = adj (adj M), then which of the following statements is/are ALWAYS TRUE?", "response_choices": "A) M = I\nB) det M = 1\nC) M^2 = I\nD) (adj M)^2 = I", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let S be the set of all complex numbers z satisfying |z^2 + z + 1| = 1. Then which of the following statements is/are TRUE?", "response_choices": "A) |z + 1| \u2264 1/2 for all z \u2208 S\nB) |z| \u2264 2 for all z \u2208 S\nC) |z + 1| \u2265 1/2 for all z \u2208 S\nD) The set S has exactly four elements", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y and Z, respectively. If\n\nX/tan z + Y/tan z = 2y/(x + y + z),\n\nthen which of the following statements is/are TRUE?", "response_choices": "A) 2Y = X + Z\nB) Y = X + Z\nC) tan z = x/y+z\nD) x^2 + z^2 - y^2 = xz", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference 2. Also, let b1, b2, b3, ... be a sequence of positive integers in geometric progression with common ratio 2. If a1 = b1 = c, then the number of all possible values of c, for which the equality 2(a1 + a2 + ... + an) = b1 + b2 + ... + bn holds for some positive integer n, is _____", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Let f: [0, 2] \u2192 \u211d be the function defined by f(x) = (3 \u2212 sin(2\u03c0x)) sin (\u03c0x \u2212 \u03c0/4) \u2212 sin (3\u03c0x + \u03c0/4). If \u03b1, \u03b2 \u2208 [0, 2] are such that {x \u2208 [0, 2] : f(x) \u2265 0} = [\u03b1, \u03b2], then the value of \u03b2 \u2212 \u03b1 is _____", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "In a triangle PQR, let \\vec{a} = \\overrightarrow{QR}, \\vec{b} = \\overrightarrow{RP} and \\vec{c} = \\overrightarrow{PQ}. If |\\vec{a}| = 3, |\\vec{b}| = 4 and \\vec{a} \\cdot (\\vec{c} - \\vec{b}) = (|\\vec{a}|) / (\\vec{c} \\cdot (\\vec{a} - \\vec{b})) |\\vec{a}| + |\\vec{b}|, then the value of |\\vec{a} \\times \\vec{b}| is _____", "response_choices": "", "answer": "", "page_number": 24, "image_available": "yes", "question_subject": "mathematics"} +{"id": 17, "question": "For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by S = {(x^2 - 1)^2 (a0 + a1x + a2x^2 + a3x^3) : a0, a1, a2, a3 \u2208 \u211d}. For a polynomial f, let f' and f'' denote its first and second order derivatives, respectively. Then the minimum possible value of (mf' + mf''), where f \u2208 S, is _____", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit lim x\u21920+ ((1 - x)^(1 - e^-1) / x^a) is equal to a nonzero real number, is _____", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2020_2_English.jsonl b/JEE_papers/JSON/JEE_2020_2_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..fdef0058dde44f5b83d44c50af023b8c743a1e7b --- /dev/null +++ b/JEE_papers/JSON/JEE_2020_2_English.jsonl @@ -0,0 +1,54 @@ +{"id": 1, "question": "A large square container with thin transparent vertical walls and filled with water (refractive index 4/3) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is __________.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A train with cross-sectional area St is moving with speed vt inside a long tunnel of cross-sectional area S0 (S0 = 4St). Assume that almost all the air (density \u03c1) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be p0. If the pressure in the region between the sides of the train and the tunnel walls is p, then: p0 \u2013 p = \u03c0\u03bf\u03c4/2 \u03c1vt2. The value of N is ______.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 1, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Two large circular discs separated by a distance of 0.01 m are connected to a battery via a switch as shown in the figure. Charged oil drops of density 900 kg m^-3 are released through a tiny hole at the center of the top disc. Once some oil drops achieve terminal velocity, the switch is closed to apply a voltage of 200 V across the discs. As a result, an oil drop of radius 8 \u00d7 10^-7 m stops moving vertically and floats between the discs. The number of electrons present in this oil drop is _______ (neglect the buoyancy force, take acceleration due to gravity = 10 m/s^-2 and charge on an electron (e) = 1.6\u00d710^-19 C)", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height h from the ground is \u03c1(h) = \u03c10e^(-h/h0), where \u03c10 = 1.25 kg m^-3 and h0 = 6000 m, the value of N is _________.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A point charge q of mass m is suspended vertically by a string of length l. A point dipole of dipole moment 'p' is now brought towards q from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is N \u00d7 (mg h), where g is the acceleration due to gravity, then the value of N is _______. (Note that for three coplanar forces keeping a point mass in equilibrium, F/sin \u03b8 is the same for all forces, where F is any one of the forces and \u03b8 is the angle between the other two forces)", "response_choices": "No multiple choice options provided.", "answer": "No answer provided.", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8.3 kg. Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0.1 mole of an ideal gas at temperature 300 K. The partition is now released and moves without any gas leaking from one part of the vessel to the other. When equilibrium is reached, the distance of the partition from the top (in m) will be _______. (take the acceleration due to gravity = 10 ms^-2 and the universal gas constant = 8.3 J mol^-1 K^-1).", "response_choices": "No multiple choice options provided.", "answer": "No answer provided.", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "A beaker of radius r is filled with water (refractive index 4/3) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed \u03c9. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is h (h << H, h << r), as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature R. Which of the following is/are correct? (g is the acceleration due to gravity)", "response_choices": "(A) R = h^2+r^2/2h, (B) R = 3r^2/2h, (C) Apparent depth of the bottom of the beaker is close to 3H/2 (1+\u03c9^2H)/2g, (D) Apparent depth of the bottom of the beaker is close to 3H/4 (1+\u03c9^2H)/4g", "answer": "D", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "A student skates up a ramp that makes an angle 30\u00b0 with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v0 and wants to turn around over a semicircular path xyz of radius R during which he/she reaches a maximum height h (at point y) from the ground as shown in the figure. Assume that the energy loss is negligible and the force required for this turn at the highest point is provided by his/her weight only. Then (g is the acceleration due to gravity)", "response_choices": "(A) v02 \u2013 2gh = \u00bd gR\n(B) v02 \u2013 2gh = v02/2 gR\n(C) the centripetal force required at points x and z is zero\n(D) the centripetal force required is maximum at points x and z", "answer": "", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed \u03c9 about the pivot. The maximum angular speed \u03c9M is achieved for x = xM. Then", "response_choices": "(A) \u03c9 = 3vx/L\u00b2+3x\u00b2\n(B) \u03c9 = 12vx/L\u00b2+12x\u00b2\n(C) xM = L/\u221a3\n(D) \u03c9M = v/\u221a3L", "answer": "", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "In an X-ray tube, electrons emitted from a filament (cathode) carrying current I hit a target (anode) at a distance d from the cathode. The target is kept at a potential V higher than the cathode resulting in emission of continuous and characteristic X-rays. If the filament current I is decreased to I/2, the potential difference V is increased to 2V, and the separation distance d is reduced to d/2, then", "response_choices": "A) the cut-off wavelength will reduce to half, and the wavelengths of the characteristic X-rays will remain the same\nB) the cut-off wavelength as well as the wavelengths of the characteristic X-rays will remain the same\nC) the cut-off wavelength will reduce to half, and the intensities of all the X-rays will decrease\nD) the cut-off wavelength will become two times larger, and the intensity of all the X-rays will decrease", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is \u03b1. The spheres are now immersed in a dielectric liquid of density 800 kg m^-3 and dielectric constant 21. If the angle between the strings remains the same after the immersion, then", "response_choices": "(A) electric force between the spheres remains unchanged\n(B) electric force between the spheres reduces\n(C) mass density of the spheres is 840 kg m^-3\n(D) the tension in the strings holding the spheres remains unchanged", "answer": "", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "Starting at time t = 0 from the origin with speed 1 ms^-1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation y = x^2/2. The x and y components of its acceleration are denoted by ax and ay, respectively. Then", "response_choices": "(A) ax = 1 ms^-2 implies that when the particle is at the origin, ay = 1 ms^-2\n(B) ax = 0 implies ay = 1 ms^-2 at all times\n(C) at t = 0, the particle's velocity points in the x-direction\n(D) ax = 0 implies that at t = 1 s, the angle between the particle's velocity and the x axis is 45\u00b0", "answer": "", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "A spherical bubble inside water has radius R. Take the pressure inside the bubble and the water pressure to be p0. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes (R - a). For a << R the magnitude of the work done in the process is given by (4\u03c0p0Ra^2)X, where X is a constant and \u03b3 = Cp/Cv = 41/30. The value of X is______.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "In the balanced condition, the values of the resistances of the four arms of a Wheatstone bridge are shown in the figure below. The resistance R3 has temperature coefficient 0.0004 \u00b0C\u207b\u00b9. If the temperature of R3 is increased by 100 \u00b0C, the voltage developed between S and T will be _________volt.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "Two capacitors with capacitance values C1 = 2000 \u00b1 10 pF and C2 = 3000 \u00b1 15 pF are connected in series. The voltage applied across this combination is V = 5.00 \u00b1 0.02 V. The percentage error in the calculation of the energy stored in this combination of capacitors is _______.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "A cubical solid aluminium (bulk modulus = -V(dP/dV) = 70 GPa) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10^3 kg m^-3 and 10 ms^-2, respectively, the change in the edge length of the block in mm is _______.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced EMF in the inductors by the time the currents reach their steady state values is_________ mJ.", "response_choices": "N/A", "answer": "N/A", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "A container with 1 kg of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is 700 Wm^-2 and it is absorbed by the water over an effective area of 0.05 m^2. Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in \u00b0C) in the temperature of water and the surroundings after a long time will be____________. (Ignore effect of the container, and take constant for Newton's law of cooling = 0.001 s^-1, Heat capacity of water = 4200 J kg^-1 K^-1)", "response_choices": "N/A", "answer": "N/A", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "The 1st, 2nd, and the 3rd ionization enthalpies, I1, I2, and I3, of four atoms with atomic numbers n, n + 1, n + 2, and n + 3 , where n < 10, are tabulated below. What is the value of n?", "response_choices": "The question does not provide explicit multiple choice options.", "answer": "The question requires determining the value of n based on the tabulated ionization enthalpy values.", "page_number": 10, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "Consider the following compounds in the liquid form: O2, HF, H2O, NH3, H2O2, CCl4, CHCl3, C6H6, C6H5Cl. When a charged comb is brought near their flowing stream, how many of them show deflection as per the following figure?", "response_choices": "The question does not provide explicit multiple choice options.", "answer": "The question requires analyzing the given compounds and the provided figure to determine how many of them show deflection.", "page_number": 10, "image_available": "yes", "question_subject": "chemistry"} +{"id": 3, "question": "In the chemical reaction between stoichiometric quantities of KMnO4 and KI in weakly basic solution, what is the number of moles of I2 released for 4 moles of KMnO4 consumed?", "response_choices": "The question does not provide explicit multiple choice options.", "answer": "The question requires calculating the number of moles of I2 released based on the given stoichiometric quantities.", "page_number": 10, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "An acidified solution of potassium chromate was layered with an equal volume of amyl alcohol. When it was shaken after the addition of 1 mL of 3% H2O2, a blue alcohol layer was obtained. The blue color is due to the formation of a chromium (VI) compound 'X'. What is the number of oxygen atoms bonded to chromium through only single bonds in a molecule of 'X'?", "response_choices": "The question does not provide explicit multiple choice options.", "answer": "The question requires determining the number of oxygen atoms bonded to chromium through single bonds in the chromium (VI) compound 'X' formed.", "page_number": 10, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "The structure of a peptide is given below. If the absolute values of the net charge of the peptide at pH = 2, pH = 6, and pH = 11 are |z1|, |z2|, and |z3|, respectively, then what is |z1| + |z2| + |z3|?", "response_choices": "", "answer": "", "page_number": 11, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "An organic compound (C8H16O3) rotates plane-polarized light . It produces pink color with neutral FeCl3 solution. What is the total number of all the possible isomers for this compound?", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "In an experiment, m grams of a compound X (gas/liquid/solid) taken in a container is loaded in a balance as shown in figure 1 below. In the presence of a magnetic field, the pan with X is either deflected upwards (figure II), or deflected downwards (figure III), depending on the compound X. Identify the correct statement(s).", "response_choices": "(A) If X is H\u2082O(l), deflection of the pan is upwards. (B) If X is K\u2084[Fe(CN)\u2086](s), deflection of the pan is upwards. (C) If X is O\u2082 (g), deflection of the pan is downwards. (D) If X is C\u2086H\u2086(l), deflection of the pan is downwards.", "answer": "", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "Which of the following plots is(are) correct for the given reaction? ([P]0 is the initial concentration of P)", "response_choices": "(A) (B) (C) (D)", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "Which among the following statement(s) is(are) true for the extraction of aluminium from bauxite?", "response_choices": "(A) Hydrated Al2O3 precipitates, when CO2 is bubbled through a solution of sodium aluminate. (B) Addition of Na3AlF6 lowers the melting point of alumina. (C) CO2 is evolved at the anode during electrolysis. (D) The cathode is a steel vessel with a lining of carbon.", "answer": "", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Choose the correct statement(s) among the following.", "response_choices": "(A) SnCl2.2H2O is a reducing agent. (B) SnO2 reacts with KOH to form K2[Sn(OH)6]. (C) A solution of PbCl2 in HCl contains Pb2+ and Cl- ions. (D) The reaction of Pb3O4 with hot dilute nitric acid to give PbO2 is a redox reaction.", "answer": "", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "Consider the following four compounds I, II, III, and IV.", "response_choices": "(A) The order of basicity is II > I > III > IV. (B) The magnitude of pKa difference between I and II is more than that between III and IV. (C) Resonance effect is more in III than in IV. (D) Steric effect makes compound IV more basic than III.", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 12, "question": "Consider the following transformations of a compound P.", "response_choices": "(A) P is (B) X is Pd-C/quinoline/H2 (C) P is (D) R is", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "A solution of 0.1 M weak base (B) is titrated with 0.1 M of a strong acid (HA). The variation of pH of the solution with the volume of HA added is shown in the figure below. What is the pKb of the base? The neutralization reaction is given by B + HA \u2192 BH+ + A\u207b.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "Liquids A and B form ideal solution for all compositions of A and B at 25 \u00b0C. Two such solutions with 0.25 and 0.50 mole fractions of A have the total vapor pressures of 0.3 and 0.4 bar, respectively. What is the vapor pressure of pure liquid B in bar?", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "The figure below is the plot of potential energy versus internuclear distance (d) of H\u2082 molecule in the electronic ground state. What is the value of the net potential energy E\u2080 (as indicated in the figure) in kJ mol\u207b\u00b9, for d = d\u2080 at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart. Use Avogadro constant as 6.023 \u00d7 10\u00b2\u00b3 mol\u207b\u00b9.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 16, "question": "Consider the reaction sequence from P to Q shown below. The overall yield of the major product Q from P is 75%. What is the amount in grams of Q obtained from 9.3 mL of P? (Use density of P = 1.00 g mL^-1; Molar mass of C = 12.0, H =1.0, O =16.0 and N = 14.0 g mol^-1)", "response_choices": "", "answer": "", "page_number": 16, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K) at which the reduction of cassiterite by coke would take place. At 298 K: \u0394r H^0(SnO2(s)) = \u2212581.0 kJ mol^-1, \u0394r H^0(CO2(g)) = \u2212394.0 kJ mol^-1, S^0(SnO2(s)) = 56.0 J K^-1 mol^-1, S^0(Sn(s)) = 52.0 J K^-1 mol^-1, S^0(C(s)) = 6.0 J K^-1 mol^-1, S^0(CO2(g)) = 210.0 J K^-1 mol^-1. Assume that the enthalpies and the entropies are temperature independent.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "An acidified solution of 0.05 M Zn^2+ is saturated with 0.1 M H2S. What is the minimum molar concentration (M) of H+ required to prevent the precipitation of ZnS? Use KSP (ZnS) = 1.25 \u00d7 10^\u221222 and overall dissociation constant of H2S, KNET = K1 K2 = 1 \u00d7 10^\u221221.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "For a complex number z, let Re(z) denote the real part of z. Let S be the set of all complex numbers z satisfying z^4 - |z|^4 = 4 i z^2, where i = \u221a(-1) . Then the minimum possible value of |z1 - z2|^2, where z1,z2 \u2208 S with Re(z1) > 0 and Re(z2) < 0, is _____", "response_choices": "NO CHOICES PROVIDED", "answer": "NO ANSWER MARKED", "page_number": 17, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "The probability that a missile hits a target successfully is 0.75. In order to destroy the target completely, at least three successful hits are required. Then the minimum number of missiles that have to be fired so that the probability of completely destroying the target is NOT less than 0.95, is _____", "response_choices": "NO CHOICES PROVIDED", "answer": "NO ANSWER MARKED", "page_number": 17, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let O be the centre of the circle x^2 + y^2 = r^2, where r > \u221a5. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle OPQ lies on the line x + 2y = 4, then the value of r is _____", "response_choices": "NO CHOICES PROVIDED", "answer": "NO ANSWER MARKED", "page_number": 17, "image_available": "yes", "question_subject": "mathematics"} +{"id": 4, "question": "The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 \u00d7 2 matrix such that the trace of A is 3 and the trace of A^3 is \u221218, then the value of the determinant of A is _____", "response_choices": "NO CHOICES PROVIDED", "answer": "NO ANSWER MARKED", "page_number": 17, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let the functions f : (\u22121, 1) \u2192 \u211d and g: (\u22121, 1) \u2192 (\u22121, 1) be defined by f(x) = |2x \u2212 1| + |2x + 1| and g(x) = x \u2212 [x], where [x] denotes the greatest integer less than or equal to x. Let f \u2218 g: (\u22121, 1) \u2192 \u211d be the composite function defined by (f \u2218 g)(x) = f(g(x)). Suppose c is the number of points in the interval (\u22121, 1) at which f \u2218 g is NOT continuous, and suppose d is the number of points in the interval (\u22121, 1) at which f \u2218 g is NOT differentiable. Then the value of c + d is _____", "response_choices": "NO CHOICES PROVIDED", "answer": "NO ANSWER MARKED", "page_number": 17, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "The value of the limit lim_{x\u2192\u03c0/2} (2 sin 2x sin 3x/2 + cos 8x/2) / (\u221a2(sin 3x + sin x) / (\u221a2 + \u221a2 cos 2x + cos 2x/2)) is _____", "response_choices": "NO CHOICES PROVIDED", "answer": "NO ANSWER MARKED", "page_number": 17, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let b be a nonzero real number. Suppose f : IR \u2192 IR is a differentiable function such that f (0) = 1. If the derivative f ' of f satisfies the equation f '(x) = f(x) / (b^2 + x^2) for all x \u2208 IR, then which of the following statements is/are TRUE?", "response_choices": "(A) If b > 0, then f is an increasing function\n\n(B) If b < 0, then f is a decreasing function\n\n(C) f (x)f (\u2212x) = 1 for all x \u2208 IR\n\n(D) f (x) \u2212 f (\u2212x) = 0 for all x \u2208 IR", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let a and b be positive real numbers such that a > 1 and b < a. Let P be a point in the first quadrant that lies on the hyperbola x^2/a^2 - y^2/b^2 = 1. Suppose the tangent to the hyperbola at P passes through the point (1,0), and suppose the normal to the hyperbola at P cuts off equal intercepts on the coordinate axes. Let \u0394 denote the area of the triangle formed by the tangent at P, the normal at P and the x-axis. If e denotes the eccentricity of the hyperbola, then which of the following statements is/are TRUE?", "response_choices": "(A) 1 < e < \u221a2\t\t(B) \u221a2 < e < 2\t\t(C) \u0394= a^4\t\t(D) \u0394= b^4", "answer": "", "page_number": 18, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let f: R \u2192 R and g: R \u2192 R be functions satisfying \n\n f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) \n\n for all x, y \u2208 R. If lim g(x) = 1, then which of the following statements is/are TRUE?", "response_choices": "A) f is differentiable at every x \u2208 R \n\nB) If g(0) = 1, then g is differentiable at every x \u2208 R \n\nC) The derivative f'(1) is equal to 1 \n\nD) The derivative f'(0) is equal to 1", "answer": "", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let \u03b1, \u03b2, \u03b3, \u03b4 be real numbers such that \u03b12 + \u03b22 + \u03b32 \u2260 0 and \u03b1 + \u03b3 = 1. Suppose the point (3, 2, \u22121) is the mirror image of the point (1, 0, \u22121) with respect to the plane \u03b1x + \u03b2y + \u03b3z = \u03b4. Then which of the following statements is/are TRUE?", "response_choices": "A) \u03b1 + \u03b2 = 2 \n\nB) \u03b4 \u2212 \u03b3 = 3 \n\nC) \u03b4 + \u03b2 = 4 \n\nD) \u03b1 + \u03b2 + \u03b3 = \u03b4", "answer": "", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let a and b be positive real numbers. Suppose PQ = ai + bj and PS = ai - bj are adjacent sides of a parallelogram PQRS. Let u and v be the projection vectors of w = j + i along PQ and PS, respectively. If |u| + |v| = |w| and if the area of the parallelogram PQRS is 8, then which of the following statements is/are TRUE?", "response_choices": "A) a + b = 4 \n\nB) a - b = 2 \n\nC) The length of the diagonal PR of the parallelogram PQRS is 4 \n\nD) w is an angle bisector of the vectors PQ and PS", "answer": "", "page_number": 19, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "For nonnegative integers s and r, let (s over r) = (s! / r! (s - r)!) if r <= s, 0 if r > s. For positive integers m and n, let g(m, n) = (sum from p=0 to m+n) f(m, n, p) / (m + n over p) where for any nonnegative integer p, f(m, n, p) = (sum from i=0 to p) (m over i) (n + i over p - i) (p + n over p - i). Then which of the following statements is/are TRUE? (A) g(m, n) = g(n, m) for all positive integers m, n (B) g(m, n + 1) = g(m + 1, n) for all positive integers m, n (C) g(2m, 2n) = 2 g(m, n) for all positive integers m, n (D) g(2m, 2n) = (g(m, n))^2 for all positive integers m, n", "response_choices": "A) g(m, n) = g(n, m) for all positive integers m, n\nB) g(m, n + 1) = g(m + 1, n) for all positive integers m, n\nC) g(2m, 2n) = 2 g(m, n) for all positive integers m, n\nD) g(2m, 2n) = (g(m, n))^2 for all positive integers m, n", "answer": "No answer provided", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "An engineer is required to visit a factory for exactly four days during the first 15 days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during 1-15 June 2021 is _____", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "In a hotel, four rooms are available. Six persons are to be accommodated in these four rooms in such a way that each of these rooms contains at least one person and at most two persons. Then the number of all possible ways in which this can be done is _____", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Two fair dice, each with faces numbered 1, 2, 3, 4, 5 and 6, are rolled together and the sum of the numbers on the faces is observed. This process is repeated till the sum is either a prime number or a perfect square. Suppose the sum turns out to be a perfect square before it turns out to be a prime number. If p is the probability that this perfect square is an odd number, then the value of 14p is _____", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let the function f: [0, 1] \u2192 R be defined by f(x) = 4x / (4x + 2). Then the value of f(1/40) + f(2/40) + f(3/40) + ... + f(39/40) - f(1/2) is _____", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Let f: R \u2192 R be a differentiable function such that its derivative f' is continuous and f(\u03c0) = -6. If F: [0,\u03c0] \u2192 R is defined by F(x) = \u222b(0 to x) f(t)dt, and if \u222b(0 to \u03c0) (f'(x) + F(x)) cos x dx = 2, then the value of f(0) is _____", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "Let the function f: (0, \u03c0) \u2192 \u211d be defined by f(\u03b8) = (sin \u03b8 + cos \u03b8)\u00b2 + (sin \u03b8 - cos \u03b8)\u2074. Suppose the function f has a local minimum at \u03b8 precisely when \u03b8 \u2208 {\u03bb\u2081\u03c0, ..., \u03bbr\u03c0}, where 0 < \u03bb\u2081 < ... < \u03bbr < 1. Then the value of \u03bb\u2081 + ... + \u03bbr is _____", "response_choices": "No response choices given", "answer": "Open-ended numerical response", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2021_1_English.jsonl b/JEE_papers/JSON/JEE_2021_1_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..4983f83440f185517a6e6043b2446e0ab85d02ac --- /dev/null +++ b/JEE_papers/JSON/JEE_2021_1_English.jsonl @@ -0,0 +1,57 @@ +{"id": 1, "question": "The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is", "response_choices": "(A) 3.07 cm (B) 3.11 cm (C) 3.15 cm (D) 3.17 cm", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "An ideal gas undergoes a four step cycle as shown in the P \u2013 V diagram below. During this cycle, heat is absorbed by the gas in", "response_choices": "(A) steps 1 and 2 (B) steps 1 and 3 (C) steps 1 and 4 (D) steps 2 and 4", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is", "response_choices": "(A) 0.4, (B) 0.8, (C) 1.3, (D) 1.6", "answer": "(C) 1.3", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is", "response_choices": "(A) 50, (B) 75, (C) 350, (D) 525", "answer": "(C) 350", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "The value of t is ___ .", "response_choices": "", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "The value of x is ___ .", "response_choices": "", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \u03bcC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \u03bcC.", "response_choices": "", "answer": "", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \u03bcC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \u03bcC.", "response_choices": "", "answer": "", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "The magnitude of q1 is ___ .", "response_choices": "", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "The magnitude of q2 is ___ .", "response_choices": "", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "The value of R is ___ meter.", "response_choices": "", "answer": "", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "The value of b is ___ meter.", "response_choices": "", "answer": "", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 13, "question": "A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = -l, y = -h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s^2 along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by L and \u03c4, respectively. i, j and k are unit vectors along the positive x, y and z-directions, respectively. If k = i \u00d7 j then which of the following statement(s) is(are) correct?", "response_choices": "(A) The particle arrives at the point (x = l, y = -h) at time t = 2 s \n\n(B) \u03c4 = 2 k when the particle passes through the point (x = l, y = -h) \n\n(C) L = 4 k when the particle passes through the point (x = l, y = -h) \n\n(D) \u03c4 = k when the particle passes through the point (x = 0, y = -h)", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?", "response_choices": "(A) The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5 \n\n(B) There is an overlap between the wavelength ranges of Balmer and Paschen series \n\n(C) The wavelengths of Lyman series are given by (1 + m^2/n^2) \u03bb0, where \u03bb0 is the shortest wavelength of Lyman series and m is an integer \n\n(D) The wavelength ranges of Lyman and Balmer series do not overlap", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure). A resistor R = 1.4 \u03a9 and a capacitor Co = 5.0 \u03bcF are connected in series between the rails. At time t = 0, Co is uncharged. Which of the following statement(s) is(are) correct? [\u03bco = 4\u03c0 \u00d7 10^-7 SI units. Take ln 2 = 0.7]", "response_choices": "(A) Maximum current through R is 1.2 \u00d7 10^-6 ampere\n\n(B) Maximum current through R is 3.8 \u00d7 10^-6 ampere\n\n(C) Maximum charge on capacitor Co is 8.4 \u00d7 10^-12 coulomb\n\n(D) Maximum charge on capacitor Co is 2.4 \u00d7 10^-12 coulomb", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle \u03b8 = 45\u00b0. P1 and P2 are pressures at points 1 and 2, respectively, located at the base of the tube. Let \u03b2 = (P1 \u2212 P2)/(\u03c1gd), where \u03c1 is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?", "response_choices": "A) \u03b2 = 0 when a = g/\u221a2, B) \u03b2 > 0 when a = g/\u221a2, C) \u03b2 = \u221a2-1/\u221a2 when a = g/2, D) \u03b2 = 1/\u221a2 when a = g/2", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "An \u03b1-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the \u03b1-particle and the sulfur ion move in circular orbits of radii r\u03b1 and rS, respectively. The ratio (rS/r\u03b1) is ___.", "response_choices": "", "answer": "", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "A thin rod of mass M and length a is free to rotate in horizontal plane about a fixed vertical axis passing through point O. A thin circular disc of mass M and of radius a/4 is pivoted on this rod with its center at a distance a/4 from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity \u03a9 and the disc rotating about its vertical axis with angular velocity 4\u03a9. The total angular momentum of the system about the point O is (Ma^2\u03a9)/48 n. The value of n is ___.", "response_choices": "", "answer": "", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 19, "question": "A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t = t1 and 50 K at t = t2. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio (t2/t1) is ____.", "response_choices": "No response choices provided.", "answer": "____", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = packing efficiency/100)", "response_choices": "(A) 0.74, (B) 0.63, (C) 0.52, (D) 0.48", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The calculated spin only magnetic moments of [Cr(NH3)6]3+ and [CuF6]3- in BM, respectively, are (Atomic numbers of Cr and Cu are 24 and 29, respectively)", "response_choices": "(A) 3.87 and 2.84, (B) 4.90 and 1.73, (C) 3.87 and 1.73, (D) 4.90 and 2.84", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "The value of x is ___.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 6, "question": "The value of y is ___.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The value of standard enthalpy, \u0394H\u00b0 (in kJ mol\u207b\u00b9) for the given reaction is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "The value of \u0394S\u00b0 (in J K\u207b\u00b9 mol\u207b\u00b9) for the given reaction, at 1000 K is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "The boiling point of water in a 0.1 molal silver nitrate solution (solution A) is x \u00b0C. To this solution A, an equal volume of 0.1 molal aqueous barium chloride solution is added to make a new solution B. The difference in the boiling points of water in the two solutions A and B is y \u00d7 10\u207b\u00b2 \u00b0C.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Follow up from Question 9, no additional details provided.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The value of x is ___.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "The value of |y| is ___.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "The compound(s), which on reaction with HNO3 will give the product having degree of rotation, [\u03b1]D = \u221252.7\u00b0 is(are)", "response_choices": "(A), (B), (C), (D)", "answer": "(D)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 12, "question": "The reaction of Q with PhSNa yields an organic compound (major product) that gives positive Carius test on treatment with Na2O2 followed by addition of BaCl2. The correct option(s) for Q is(are)", "response_choices": "(A), (B), (C), (D)", "answer": "(C)", "page_number": 18, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "The correct statement(s) related to colloids is(are)", "response_choices": "(A) The process of precipitating colloidal sol by an electrolyte is called peptization. (B) Colloidal solution freezes at higher temperature than the true solution at the same concentration. (C) Surfactants form micelle above critical micelle concentration (CMC). CMC depends on temperature. (D) Micelles are macromolecular colloids.", "answer": "", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "An ideal gas undergoes a reversible isothermal expansion from state I to state II followed by a reversible adiabatic expansion from state II to state III. The correct plot(s) representing the changes from state I to state III is(are)", "response_choices": "(A) (B) (C) (D)", "answer": "B", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 15, "question": "The correct statement(s) related to the metal extraction processes is(are)", "response_choices": "(A) A mixture of PbS and PbO undergoes self-reduction to produce Pb and SO2. (B) In the extraction process of copper from copper pyrites, silica is added to produce copper silicate. (C) Partial oxidation of sulphide ore of copper by roasting, followed by self-reduction produces blister copper. (D) In cyanide process, zinc powder is utilized to precipitate gold from Na[Au(CN)2].", "answer": "", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "A mixture of two salts is used to prepare a solution S, which gives the following results:", "response_choices": "(A) Pb(NO3)2 and Zn(NO3)2 (B) Pb(NO3)2 and Bi(NO3)3 (C) AgNO3 and Bi(NO3)3 (D) Pb(NO3)2 and Hg(NO3)2", "answer": "", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 17, "question": "The maximum number of possible isomers (including stereoisomers) which may be formed on mono-bromination of 1-methylcyclohex-1-ene using Br2 and UV light is ___.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "In the reaction given below, the total number of atoms having sp2 hybridization in the major product P is ___.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 19, "question": "The total number of possible isomers for [Pt(NH3)4Cl2]Br2 is ___.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "Consider a triangle A whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of A is (1, 1), then the equation of the circle passing through the vertices of the triangle A is", "response_choices": "(A) x^2 + y^2 - 3x + y = 0, (B) x^2 + y^2 + x + 3y = 0, (C) x^2 + y^2 + 2y - 1 = 0, (D) x^2 + y^2 + x + y = 0", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "The area of the region {(x, y) : 0 \u2264 x \u2264 9/4, 0 \u2264 y \u2264 1, x \u2265 3y, x + y \u2265 2} is", "response_choices": "(A) 11/32, (B) 35/96, (C) 37/96, (D) 13/32", "answer": "C", "page_number": 22, "image_available": "yes", "question_subject": "mathematics"} +{"id": 3, "question": "Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 - S1 and F2 = F1 \u222a S1. Now two elements are chosen at random, without replacement, from the set F2 and let S2 denote the set of these chosen elements. Let G2 = G1 \u222a S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements. Let E3 = E2 \u222a S3. Given that E1= E3, let p be the conditional probability of the event S1 = {1, 2}. Then the value of p is", "response_choices": "(A) 1/5, (B) 2/5, (C) 1/2, (D) 2/5", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "The value of (625/4) * p1 is ___.", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "The value of (125/4) * p2 is ___.", "response_choices": "No multiple choice options provided", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "The value of |M| is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "The value of D is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "The value of \u03bb2 is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "The value of D is __ .", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "For any 3 \u00d7 3 matrix M, let |M| denote the determinant of M. Let E = [1 2 3; 2 3 4; 8 13 18], P = [1 0 0; 0 0 1; 0 1 0] and F = [1 3 2; 8 18 13; 2 4 3]. If Q is a nonsingular matrix of order 3 \u00d7 3, then which of the following statements is (are) TRUE?", "response_choices": "Options A, B, C, D (not provided in the image)", "answer": "Not provided", "page_number": 26, "image_available": "yes", "question_subject": "mathematics"} +{"id": 1, "question": "(A) F = PEP and P^2 = [1 0 0; 0 1 0; 0 0 1] (B) |EQ + PFQ^-1| = |EQ| + |PFQ^-1| (C) |(EF)^3| > |EF|^2 (D) Sum of the diagonal entries of P^-1FP + F is equal to the sum of diagonal entries of E + P^-1FP", "response_choices": "No options given", "answer": "No answer given", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 2, "question": "Let f: R \u2192 R be defined by f(x) = (x^2 - 3x - 6) / (x^2 + 2x + 4). Then which of the following statements is (are) TRUE? (A) f is decreasing in the interval (-2, -1) (B) f is increasing in the interval (1, 2) (C) f is onto (D) Range of f is [-3/2, 2]", "response_choices": "(A), (B), (C), (D)", "answer": "No answer given", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let E, F and G be three events having probabilities P(E) = 1/8, P(F) = 1/6 and P(G) = 1/4, and let P(E \u2229 F \u2229 G) = 1/10. For any event H, if H^c denotes its complement, then which of the following statements is (are) TRUE? (A) P(E \u2229 F \u2229 G^c) \u2264 1/40 (B) P(E^c \u2229 F \u2229 G) \u2264 1/15 (C) P(E \u222a F \u222a G) \u2264 13/24 (D) P(E^c \u2229 F^c \u2229 G^c) \u2264 5/12", "response_choices": "(A), (B), (C), (D)", "answer": "No answer given", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "For any 3 \u00d7 3 matrix M, let |M| denote the determinant of M. Let I be the 3 \u00d7 3 identity matrix. Let E and F be two 3 \u00d7 3 matrices such that (I - EF) is invertible. If G = (I - EF)^-1, then which of the following statements is (are) TRUE? (A) |FE| = |I - FE||FGE| (B) (I - FE)(I + FGE) = I", "response_choices": "(A), (B)", "answer": "No answer given", "page_number": 27, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "For any positive integer n, let Sn: (0,\u221e) \u2192 \u211d be defined by Sn(x) = \u2211(n)(k=1) cot^(-1)((1 + k(k + 1)x^2)/x), where for any x \u2208 \u211d, cot^(-1)(x) \u2208 (0,\u03c0) and tan^(-1)(x) \u2208 (-\u03c0/2,\u03c0/2). Then which of the following statements is (are) TRUE?", "response_choices": "(A) S10(x) = \u03c0/2 = tan^(-1)((1+11x^2)/(10x)), for all x > 0\n(B) lim cot(Sn(x)) = x, for all x > 0\nn\u2192\u221e\n(C) The equation S3(x) = \u03c0/4 has a root in (0,\u221e)\n(D) tan(Sn(x)) \u2264 1/2, for all n \u2265 1 and x > 0", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "For any complex number w = c + id, let arg(w) \u2208 (-\u03c0,\u03c0], where i = \u221a(-1) . Let \u03b1 and \u03b2 be real numbers such that for all complex numbers z = x + iy satisfying arg((z+\u03b1)/(z+\u03b2)) = \u03c0/4, the ordered pair (x,y) lies on the circle x^2 + y^2 + 5x - 3y + 4 = 0. Then which of the following statements is (are) TRUE?", "response_choices": "(A) \u03b1 = -1\n(B) \u03b1\u03b2 = 4\n(C) \u03b1\u03b2 = -4\n(D) \u03b2 = 4", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "For x \u2208 \u211d, the number of real roots of the equation 3x^2 - 4|x^2 - 1| + x - 1 = 0 is ___.", "response_choices": "None provided", "answer": "Must enter an integer", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "In a triangle ABC, let AB = \u221a23, BC = 3 and CA = 4. Then the value of (cot A + cot C) / cot B is ___.", "response_choices": "None provided", "answer": "Must enter an integer", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 19, "question": "Let \u20d7u, \u20d7v and \u20d7w be vectors in three-dimensional space, where \u20d7u and \u20d7v are unit vectors which are not perpendicular to each other and \u20d7u \u00b7 \u20d7w = 1, \u20d7v \u00b7 \u20d7w = 1, \u20d7w \u00b7 \u20d7w = 4 If the volume of the parallelopiped, whose adjacent sides are represented by the vectors \u20d7u, \u20d7v and \u20d7w, is \u221a2 , then the value of |3 \u20d7u +5 \u20d7v | is ___.", "response_choices": "None provided", "answer": "Must enter an integer", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2021_2_English.jsonl b/JEE_papers/JSON/JEE_2021_2_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..c4957d1982268cb9b5d3b127e77358410254e634 --- /dev/null +++ b/JEE_papers/JSON/JEE_2021_2_English.jsonl @@ -0,0 +1,70 @@ +{"id": 1, "question": "One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight \u03b1W is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2\u221a2)W. Which of the following statement(s) is(are) correct?", "response_choices": "A) The vertical component of reaction force at O does not depend on \u03b1\nB) The horizontal component of reaction force at O is equal to W for \u03b1 = 0.5\nC) The tension in the rope is 2W for \u03b1 = 0.5\nD) The rope breaks if \u03b1 > 1.5", "answer": "", "page_number": 2, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the pipe is closed. The speed of sound in air is v and fo is the fundamental frequency of the pipe. For which of the following combination(s) of u and fs, will the sound reaching the pipe lead to a resonance?", "response_choices": "A) u = 0.8v and fs = fo\nB) u = 0.8v and fs = 2fo\nC) u = 0.8v and fs = 0.5fo\nD) u = 0.5v and fs = 1.5fo", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "For a prism of prism angle \u03b8 = 60\u00b0, the refractive indices of the left half and the right half are, respectively, n\u2081 and n\u2082 (n\u2082 \u2265 n\u2081) as shown in the figure. The angle of incidence i is chosen such that the incident light rays will have minimum deviation if n\u2081 = n\u2082 = n = 1.5. For the case of unequal refractive indices, n\u2081 = n and n\u2082 = n + \u0394n (where \u0394n << n), the angle of emergence e = i + \u0394e. Which of the following statement(s) is(are) correct?", "response_choices": "(A) The value of \u0394e (in radians) is greater than that of \u0394n\n\n(B) \u0394e is proportional to \u0394n\n\n(C) \u0394e lies between 2.0 and 3.0 milliradians, if \u0394n = 2.8 \u00d7 10^-3\n\n(D) \u0394e lies between 1.0 and 1.6 milliradians, if \u0394n = 2.8 \u00d7 10^-3", "answer": "", "page_number": 3, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A physical quantity S is defined as S = (E \u00d7 B)/\u03bc\u2080, where E is electric field, B is magnetic field and \u03bc\u2080 is the permeability of free space. The dimensions of S are the same as the dimensions of which of the following quantity(ies) ?", "response_choices": "(A) Energy/Charge \u00d7 Current\n\n(B) Force/Length \u00d7 Time\n\n(C) Energy/Volume\n\n(D) Power/Area", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A heavy nucleus N, at rest, undergoes fission N \u2192 P + Q, where P and Q are two lighter nuclei. Let \u03b4 = MN \u2212 MP \u2212 MQ, where MP, MQ and MN are the masses of P, Q and N, respectively. EP and EQ are the kinetic energies of P and Q, respectively. The speeds of P and Q are vP and vQ, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?", "response_choices": "", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I2 in the clockwise direction, with I2 > 2I1. B(x,y) denotes the magnetic field at a point (x,y) in the xy-plane. Which of the following statement(s) is(are) correct?", "response_choices": "(A) B(x,y) is perpendicular to the xy-plane at any point in the plane (B) |B(x,y)| depends on x and y only through the radial distance r = \u221a(x^2 + y^2) (C) |B (x,y)| is non-zero at all points for r < R (D) B (x,y) points normally outward from the xy-plane for all the points between the two loops", "answer": "B,C", "page_number": 4, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "(D) The magnitude of momentum for P as well as Q is c\u221a(2\u03bc\u03b4), where \u03bc = (MpMq)/(Mp+Mq)", "response_choices": "Statement only", "answer": "Statement only", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "(C) vq/vq = Mq/Mp", "response_choices": "Statement only", "answer": "Statement only", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "(B) Ep = (Mp/(Mp+Mq))c^2\u03b4", "response_choices": "Statement only", "answer": "Statement only", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "(A) Ep + Eq = c^2\u03b4", "response_choices": "Statement only", "answer": "Statement only", "page_number": 4, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmospheric pressure p0 = 10^5 Pa so that the volume of the trapped air is v0 = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p0 + \u0394p without changing its orientation. At this pressure, the volume of the trapped air is v0 \u2212 \u0394v. Let \u0394v = X cc and \u0394p = Y \u00d7 10^5 Pa.", "response_choices": "NUMERICAL VALUE", "answer": "", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmospheric pressure p0 = 10^5 Pa so that the volume of the trapped air is v0 = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p0 + \u0394p without changing its orientation. At this pressure, the volume of the trapped air is v0 \u2212 \u0394v. Let \u0394v = X cc and \u0394p = Y \u00d7 10^5 Pa.", "response_choices": "NUMERICAL VALUE", "answer": "", "page_number": 5, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "The value of X is ____.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "The value of Y is ____.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "The value of J is ____.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "The value of K is ____.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "The value of C is ____.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "The value of \u03c6 is ____.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "When the dipole m is placed at a distance r from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to", "response_choices": "(A) m/r^3, (B) m^2/r^2, (C) m/r^2, (D) m^2/r", "answer": "B", "page_number": 7, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "The work done in bringing the dipole from infinity to a distance r from the center of the loop by the given process is proportional to", "response_choices": "(A) m/r^5 (B) m^2/r^5 (C) m^2/r^6 (D) m^2/r^7", "answer": "(C) m^2/r^6", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "The value of TR/T0 is", "response_choices": "(A) \u221a2 (B) \u221a3 (C) 2 (D) 3", "answer": "(B) \u221a3", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "The value of Q/RTo is", "response_choices": "(A) 4(2\u221a2 + 1) (B) 4(2\u221a2 - 1) (C) (5\u221a2 + 1) (D) (5\u221a2 - 1)", "answer": "(B) 4(2\u221a2 - 1)", "page_number": 8, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "In order to measure the internal resistance r1 of a cell of emf E, a meter bridge of wire resistance R0 = 50 \u03a9, a resistance R0/2, another cell of emf E/2 (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at l =72 cm, then the value of r1 is __ \u03a9.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "The distance between two stars of masses 3Msand 6Ms is 9R. Here R is the mean distance between the centers of the Earth and the Sun, and Ms is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period \u03c0T, where T is the period of Earth's revolution around the Sun. The value of \u03c0 is ___.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals P, Q and R are EP, EQ and ER, respectively, and they are related by EP = 2EQ = 2ER. In this experiment, the same source of monochromatic light is used for metals P and Q while a different source of monochromatic light is used for the metal R. The work functions for metals P, Q and R are 4.0 eV, 4.5 eV and 5.5 eV, respectively. The energy of the incident photon used for metal R, in eV, is ___.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "The reaction sequence(s) that would lead to o-xylene as the major product is(are)", "response_choices": "(A), (B), (C) and (D)", "answer": "(B) 1. Mg, CO2, H3O+ 2. SOCl2 3. H2, Pd-BaSO4 4. Zn-Hg, HCl", "page_number": 10, "image_available": "yes", "question_subject": "chemistry"} +{"id": 2, "question": "Correct option(s) for the following sequence of reactions is(are)", "response_choices": "(A) Q = KNO2, W = LiAlH4\\n(B) R = benzenamine, V = KCN\\n(C) Q = AgNO2, R = phenylmethanamine\\n(D) W = LiAlH4, V = AgCN", "answer": "D", "page_number": 11, "image_available": "yes", "question_subject": "chemistry"} +{"id": 3, "question": "For the following reaction\\n2X + Y \u2014> P\\nthe rate of reaction is d[P]/dt = k[X]. Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the reaction mixture. The correct statement(s) about the reaction is(are)\\n\\n(Use: ln 2 = 0.693)", "response_choices": "(A) The rate constant, k, of the reaction is 13.86 \u00d7 10^-4 s^-1.\\n(B) Half-life of X is 50 s.\\n(C) At 50 s, \u2212 d[X]/dt = 13.86 \u00d7 10^-3 mol L^-1 s^-1.\\n(D) At 100 s, \u2212 d[Y]/dt = 3.46 \u00d7 10^-3 mol L^-1 s^-1.", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "Some standard electrode potentials at 298 K are given below:\n\nPb2+/Pb\t\u22120.13 V\nNi2+/Ni\t\u22120.24 V\nCd2+/Cd\t\u22120.40 V\nFe2+/Fe\t\u22120.44 V\n\nTo a solution containing 0.001 M of X2+ and 0.1 M of Y2+, the metal rods X and Y are inserted (at 298 K) and connected by a conducting wire. This resulted in dissolution of X. The correct combination(s) of X and Y, respectively, is(are)\n\n(Given: Gas constant, R = 8.314 J K\u22121 mol\u22121,\nFaraday constant, F = 96500 C mol\u22121)", "response_choices": "(A) Cd and Ni\n\n(B) Cd and Fe\n\n(C) Ni and Pb\n\n(D) Ni and Fe", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "The pair(s) of complexes wherein both exhibit tetrahedral geometry is(are)\n\n(Note: py = pyridine\nGiven: Atomic numbers of Fe, Co, Ni and Cu are 26, 27, 28 and 29, respectively)", "response_choices": "(A) [FeCl4]\u2212 and [Fe(CO)4]2\u2212\t\t(B) [Co(CO)4]\u2212 and [CoCl4]2\u2212\n\n(C) [Ni(CO)4] and [Ni(CN)4]2\u2212\t\t(D) [Cu(py)4]+ and [Cu(CN)4]3\u2212", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "The correct statement(s) related to oxoacids of phosphorous is(are)", "response_choices": "", "answer": "", "page_number": 12, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "Upon heating, H3PO3 undergoes disproportionation reaction to produce H3PO4 and PH3.", "response_choices": "A) , B) , C) , D) ", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "While H3PO3 can act as reducing agent, H3PO4 cannot.", "response_choices": "A) , B) , C) , D) ", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "H3PO3 is a monobasic acid.", "response_choices": "A) , B) , C) , D) ", "answer": "C", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "The H atom of P-H bond in H3PO3 is not ionizable in water.", "response_choices": "A) , B) , C) , D) ", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 \u00d7 10^2 S cm^2 mol^-1. At 298 K, for an aqueous solution of the acid the degree of dissociation is \u03b1 and the molar conductivity is y \u00d7 10^2 S cm^2 mol^-1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y \u00d7 10^2 S cm^2 mol^-1. The value of \u03b1 is ___.", "response_choices": "No response choices provided.", "answer": "Numeric value to be entered.", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "The value of y is ___.", "response_choices": "No response choices provided.", "answer": "Numeric value to be entered.", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "Reaction of x g of Sn with HCl quantitatively produced a salt. Entire amount of the salt reacted with y g of nitrobenzene in the presence of required amount of HCl to produce 1.29 g of an organic salt (quantitatively). (Use Molar masses (in g mol^-1) of H, C, N, O, Cl and Sn as 1, 12, 14, 16, 35 and 119, respectively).", "response_choices": "No response choices provided.", "answer": "Numeric values for x and y to be entered.", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Same as question 9.", "response_choices": "No response choices provided.", "answer": "Numeric values for x and y to be entered.", "page_number": 14, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "The value of x is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "The value of y is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "A sample (5.6 g) containing iron is completely dissolved in cold dilute HCl to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M KMnO4 solution to reach the end point. Number of moles of Fe2+ present in 250 mL solution is x \u00d7 10^-7 (consider complete dissolution of FeCl2). The amount of iron present in the sample is y% by weight. (Assume: KMnO4 reacts only with Fe2+ in the solution Use: Molar mass of iron as 56 g mol^-1) The value of x is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "A sample (5.6 g) containing iron is completely dissolved in cold dilute HCl to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M KMnO4 solution to reach the end point. Number of moles of Fe2+ present in 250 mL solution is x \u00d7 10^-7 (consider complete dissolution of FeCl2). The amount of iron present in the sample is y% by weight. (Assume: KMnO4 reacts only with Fe2+ in the solution Use: Molar mass of iron as 56 g mol^-1) The value of y is ___.", "response_choices": "", "answer": "", "page_number": 15, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond Strength. BDE is affected by s-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. BDEs for some bonds are given below:", "response_choices": "There are no multiple choice options provided.", "answer": "The question shows values for 4 different bond dissociation energies: H3C-H (105 kcal mol^-1), Cl-Cl (58 kcal mol^-1), H3C-Cl (85 kcal mol^-1), H-Cl (103 kcal mol^-1).", "page_number": 16, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "Correct match of the C-H bonds (shown in bold) in Column J with their BDE in Column K is", "response_choices": "A) P - iii, Q - iv, R - ii, S - i\nB) P - i, Q - ii, R - iii, S - iv\nC) P - iii, Q - ii, R - i, S - iv\nD) P - ii, Q - i, R - iv, S - iii", "answer": "B) P - i, Q - ii, R - iii, S - iv", "page_number": 17, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "For the following reaction\n\nCH4(g) + Cl2(g) \u2192 CH3Cl(g) + HCl(g)\n\nthe correct statement is", "response_choices": "A) Initiation step is exothermic with \u0394H\u00b0 = -58 kcal mol-1.\nB) Propagation step involving \u2022CH3 formation is exothermic with \u0394H\u00b0 = -2 kcal mol-1.\nC) Propagation step involving CH3Cl formation is endothermic with \u0394H\u00b0 = +27 kcal mol-1.\nD) The reaction is exothermic with \u0394H\u00b0 = -25 kcal mol-1.", "answer": "D) The reaction is exothermic with \u0394H\u00b0 = -25 kcal mol-1", "page_number": 17, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "Precipitate X is", "response_choices": "(A) Fe4[Fe(CN)6]3 | (B) Fe[Fe(CN)6] | (C) K3Fe[Fe(CN)6] | (D) KFe[Fe(CN)6]", "answer": "B", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "Among the following, the brown ring is due to the formation of", "response_choices": "(A) [Fe(NO)2(SO4)2]2- | (B) [Fe(NO)2(H2O)6]3+ | (C) [Fe(NO)4(SO4)2] | (D) [Fe(NO)(H2O)5]2+", "answer": "B", "page_number": 18, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of ln V2/V1 is ___.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 18, "question": "Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s^-1) of He atom after the photon absorption is ___.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 19, "image_available": "no", "question_subject": "physics"} +{"id": 19, "question": "Ozonolysis of ClO2 produces an oxide of chlorine. The average oxidation state of chlorine in this oxide is ___.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "Let S1 = {(i, j, k) : i, j, k \u2208 {1,2, ...,10}}, S2 = {(i, j) : 1 \u2264 i < j + 2 \u2264 10, i, j \u2208 {1,2, ..., 10}}, S3 = {(i, j, k, l) : 1 \u2264 i < j < k < l, i, j, k, l \u2208 {1,2, ...,10}} and S4 = {(i, j, k, l) : i, j, k and l are distinct elements in {1,2, ...,10}}. If the total number of elements in the set Sr is nr, r = 1,2,3,4, then which of the following statements is (are) TRUE ?", "response_choices": "(A) n1 = 1000 (B) n2 = 44 (C) n3 = 220 (D) n4 = 420", "answer": "(D) n4 = 420", "page_number": 20, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE ?", "response_choices": "(A) cos P \u2265 1 - p^2/2qr, (B) cos R \u2265 (q-r)/(q+r) cos P + (p-r)/(p+r) cos Q, (C) (q+r)/p < 2 \u221a(sin Q sin R/sin P), (D) If p < q and p < r, then cos Q > p/r and cos R > p/q", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let f: [- \u03c0/2, \u03c0] \u2192 \u211d be a continuous function such that f(0) = 1 and \u222b(\u03c0/2)^0 f(t)dt = 0. Then which of the following statements is (are) TRUE ?", "response_choices": "(A) The equation f(x) - 3 cos 3x = 0 has at least one solution in (0, \u03c0/3), (B) The equation f(x) - 3 sin 3x = - 6/\u03c0 has at least one solution in (0, \u03c0/3), (C) lim x\u21921- \u222bx/0 f(t)dt/(1-e^x^2) = -1, (D) lim x\u21920 sin x \u222b0^x f(t)dt/x^2 = -1", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "For any real numbers \u03b1 and \u03b2, let y\u03b1,\u03b2(x), x \u2208 \u211d, be the solution of the differential equation dy/dx + \u03b1y = xe\u03b2x, y(1) = 1. Let S = {y\u03b1,\u03b2 (x) : \u03b1,\u03b2 \u2208 \u211d}. Then which of the following functions belong(s) to the set S?", "response_choices": "(A) f(x) = (x\u00b2/2) e^-x + (e - 1/2) e^-x, (B) f(x) = -x\u00b2 e^-x + (e + 1/2) e^-x, (C) f(x) = e^x (x - 1/2) + (e - e\u00b2/4) e^-x, (D) f(x) = e^x (1 - x)/2 + (e + e\u00b2/4) e^-x", "answer": "", "page_number": 22, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let O be the origin and OA\u20d7 = 2i\u20d7 + 2j\u20d7 + k\u20d7, OB\u20d7 = i\u20d7 - 2j\u20d7 + 2k\u20d7 and OC\u20d7 = 1/\u03bb (OB\u20d7 - \u03bb OA\u20d7) for some \u03bb > 0. If |OB\u20d7 \u00d7 OC\u20d7| = 9/2 , then which of the following statements is (are) TRUE?", "response_choices": "(A) Projection of OC\u20d7 on OA\u20d7 is -3/2, (B) Area of the triangle OAB is 9/2, (C) Area of the triangle ABC is 9/2, (D) The acute angle between the diagonals of the parallelogram with adjacent sides OA\u20d7 and OC\u20d7 is \u03c0/3", "answer": "", "page_number": 22, "image_available": "yes", "question_subject": "mathematics"} +{"id": 6, "question": "Let E denote the parabola y^2 = 8x. Let P = (-2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is (are) TRUE ?", "response_choices": "(A) The triangle PFQ is a right-angled triangle\n\n(B) The triangle QPQ' is a right-angled triangle\n\n(C) The distance between P and F is 5\u221a2\n\n(D) F lies on the line joining Q and Q'", "answer": "", "page_number": 23, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "The radius of the circle C is ____.", "response_choices": "Requires a numerical value to be entered", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "The value of \u03b1 is ____.", "response_choices": "Requires a numerical value to be entered", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "The value of 2m1 + 3n1 + m1n1 is ___.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "The value of 6m2 + 4n2 + 8m2n2 is ___.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "The value of (165/\u03c0) is ___.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "The value of (485/\u03c0^2) is ___.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Consider M with r = 1025/513. Let k be the number of all those circles Cn that are inside M. Let l be the maximum possible of circles among these k circles such that no two circles intersect. Then", "response_choices": "(A) k + 2l = 22, (B) 2k + l = 26, (C) 2k + 3l = 34, (D) 3k + 2l = 40", "answer": "(B) 2k + l = 26", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 14, "question": "Consider M with r = (2^199 - 1)^(1/2) / 2^198. The number of all those circles Dn that are inside M is", "response_choices": "(A) 198, (B) 199, (C) 200, (D) 201", "answer": "(C) 200", "page_number": 27, "image_available": "yes", "question_subject": "mathematics"} +{"id": 15, "question": "Which of the following statements is TRUE ?", "response_choices": "(A) f(\u221aln 3) + g(\u221aln 3) = 1\u20442\n(B) For every x > 1, there exists an \u03b1 \u2208 (1, x) such that \u03c81(x) = 1 + \u03b1x\n(C) For every x > 0, there exists a \u03b2 \u2208 (0, x) such that \u03c82(x) = 2x(\u03c81(\u03b2) \u2212 1)\n(D) f is an increasing function on the interval [0, 2]", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Which of the following statements is TRUE ?", "response_choices": "(A) \u03c81(x) \u2264 1, for all x > 0\n(B) \u03c82(x) \u2264 0, for all x > 0\n(C) f(x) \u2265 1 \u2212 e^(-x^2) \u2212 2\u20443 x^3 + 2\u20445 x^5, for all x \u2208 (0, 1\u20442)\n(D) g(x) \u2264 3\u20444 x^3 \u2212 2\u20445 x^5 + 1\u20447 x^7, for all x \u2208 (0, 1\u20442)", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "A number is chosen at random from the set {1, 2, 3, ..., 2000}. Let p be the probability that the chosen number is a multiple of 3 or a multiple of 7. Then the value of 500p is ___.", "response_choices": "", "answer": "", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "Let E be the ellipse (x^2)/16 + (y^2)/9 = 1. For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and M(P, Q') be the mid-point of the line segment joining P and Q'. Then the maximum possible value of the distance between M(P, Q) and M(P, Q'), as P, Q and Q' vary on E, is ___.", "response_choices": "", "answer": "", "page_number": 29, "image_available": "yes", "question_subject": "mathematics"} +{"id": 19, "question": "For any real number x, let [x] denote the largest integer less than or equal to x. If I = \u2776[0 to 10] ( (10x)/sqrt(x + 1) ) dx , then the value of 9I is ___.", "response_choices": "", "answer": "", "page_number": 29, "image_available": "no", "question_subject": "mathematics"} diff --git a/JEE_papers/JSON/JEE_2022_1_English.jsonl b/JEE_papers/JSON/JEE_2022_1_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..796a29ae3db762823389f850027da72055f332c7 --- /dev/null +++ b/JEE_papers/JSON/JEE_2022_1_English.jsonl @@ -0,0 +1,51 @@ +{"id": 1, "question": "Considering only the principal values of the inverse trigonometric functions, the value of (3/2)cos^(-1)((2/sqrt(2+pi^2))+(1/4)sin^(-1)(2sqrt(2)pi/2+pi^2)+tan^(-1)(sqrt(2)/pi)) is _________.", "response_choices": "", "answer": "", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Let \u03b1 be a positive real number. Let f: \u211d \u2192 \u211d and g: (\u03b1, \u221e) \u2192 \u211d be the functions defined by f(x) = sin((\u03c0x/12)) and g(x) = (2 log\u2090(sqrt(x) - sqrt(\u03b1)))/log\u2090(e^(sqrt(x)) - e^sqrt(\u03b1)). Then the value of lim[x\u2192\u03b1+] f(g(x)) is _________.", "response_choices": "", "answer": "", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of breathing problem, 330 persons had symptom of fever or cough or both, 350 persons had symptom of cough or breathing problem or both, 340 persons had symptom of fever or breathing problem or both, 30 persons had all three symptoms (fever, cough and breathing problem). If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is _________.", "response_choices": "", "answer": "", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let z be a complex number with non-zero imaginary part. If (2 + 3z + 4z^2) / (2 - 3z + 4z^2) is a real number, then the value of |z|^2 is _________.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let z\u0304 denote the complex conjugate of a complex number z and let i = \u221a-1 . In the set of complex numbers, the number of distinct roots of the equation z - z^2 = i(z\u0304 + z^2) is _________.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let l1, l2 ..., l100 be consecutive terms of an arithmetic progression with common difference d1, and let w1, w2, ..., w100 be consecutive terms of another arithmetic progression with common difference d2 , where d1d2 = 10. For each i = 1, 2, ..., 100, let Ri be a rectangle with length li, width wi and area Ai. If A51 - A50 = 1000, then the value of A100 - A99 is _________.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits 0, 2, 3, 4, 6, 7 is _________.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let ABC be the triangle with AB = 1, AC = 3 and \u2220BAC = \u03c0/2. If a circle of radius r > 0 touches the sides AB, AC and also touches internally the circumcircle of the triangle ABC, then the value of r is _________.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "yes", "question_subject": "mathematics"} +{"id": 9, "question": "Consider the equation \u222b[e/(1 \u00d7 (a \u2013 (log\u2080 x)^\u00bd)^2)] \u00d7 (log\u2080 x)^(1/2) dx = 1, a \u2208 (-\u221e, 0) \u222a (1, \u221e). Which of the following statements is/are TRUE?", "response_choices": "(A) No a satisfies the above equation, (B) An integer a satisfies the above equation, (C) An irrational number a satisfies the above equation, (D) More than one a satisfy the above equation", "answer": "D", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let a1, a2, a3, ... be an arithmetic progression with a1 = 7 and common difference 8. Let T1, T2, T3, ... be such that T1 = 3 and Tn+1 - Tn = an for n \u2265 1. Then, which of the following is/are TRUE ?", "response_choices": "(A) T20 = 1604, (B) \u03a320k=1 Tk = 10510, (C) T30 = 3454, (D) \u03a330k=1 Tk = 35610", "answer": "(B) \u03a320k=1 Tk = 10510", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let P1 and P2 be two planes given by P1: 10x + 15y + 12z - 60 = 0, P2: - 2x + 5y + 4z - 20 = 0. Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on P1 and P2 ?", "response_choices": "(A) x-1=y-1=z-1/5, (B) x-6/-5=y=z/3, (C) x/2=y-4/5=z/4, (D) x=y-4/-2=z/3", "answer": "(B) x-6/-5=y=z/3", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let S be the reflection of a point Q with respect to the plane given by r = -(t + p)i + tj + (1 + p)k where t, p are real parameters and i, j, k are the unit vectors along the three positive coordinate axes. If the position vectors of Q and S are 10i + 15j + 20k and \u03b1i + \u03b2j + \u03b3k respectively, then which of the following is/are TRUE ?", "response_choices": "(A) 3(\u03b1 + \u03b2) = -101, (B) 3(\u03b2 + \u03b3) = -71, (C) 3(\u03b3 + \u03b1) = -86, (D) 3(\u03b1 + \u03b2 + \u03b3) = -121", "answer": "(B) 3(\u03b2 + \u03b3) = -71", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Consider the parabola y^2 = 4x. Let S be the focus of the parabola. A pair of tangents drawn to the parabola from the point P = (\u22122, 1) meet the parabola at P1 and P2. Let Q1 and Q2 be points on the lines SP1 and SP2 respectively such that PQ1 is perpendicular to SP1 and PQ2 is perpendicular to SP2. Then, which of the following is/are TRUE ?", "response_choices": "(A) SQ1 = 2 (B) Q1Q2 = 3\u221a10/5 (C) PQ1 = 3 (D) SQ2 = 1", "answer": "C", "page_number": 5, "image_available": "yes", "question_subject": "mathematics"} +{"id": 14, "question": "Let |M| denote the determinant of a square matrix M. Let g: [0, \u03c0] \u2192 \u211d be the function defined by g(\u03b8) = \u221a(f(\u03b8) \u2212 1 + \u221a((\u03c0 \u2212 \u03b8)/2 \u2212 \u03b8) \u2212 1) where f(\u03b8) = 1/2 [1 -sin \u03b8 sin \u03b8 1; -sin \u03b8 -1 sin \u03b8; 1 -sin \u03b8 1] + [sin \u03c0 cos (\u03b8 + \u03c0/4) tan (\u03b8 - \u03c0/4); -cos \u03c0/4 -logE (\u03c0/4) tan \u03c0; cot (\u03b8 + \u03c0/4) logB (\u03c0/4)] Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g(\u03b8), and p(2) = 2 - \u221a2 . Then, which of the following is/are TRUE ?", "response_choices": "(A) p (3+\u221a2/4) < 0 (B) p (1+3\u221a2/4) > 0 (C) p (5\u221a2-1/4) > 0 (D) p (5-\u221a2/4) < 0", "answer": "C", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Consider the following lists: [List-I with four sets of equations given] [List-II with descriptions of set sizes P, Q, R, S, T]", "response_choices": "(A) (I) \u2192 (P); (II) \u2192 (S); (III) \u2192 (P); (IV) \u2192 (S) \n(B) (I) \u2192 (P); (II) \u2192 (P); (III) \u2192 (T); (IV) \u2192 (R) \n(C) (I) \u2192 (Q); (II) \u2192 (P); (III) \u2192 (T); (IV) \u2192 (S) \n(D) (I) \u2192 (Q); (II) \u2192 (S); (III) \u2192 (P); (IV) \u2192 (R)", "answer": "(B) (I) \u2192 (P); (II) \u2192 (P); (III) \u2192 (T); (IV) \u2192 (R)", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Two players, P1 and P2, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by P1 and P2, respectively. If x > y, then P1 scores 5 points and P2 scores 0 point. If x = y, then each player scores 2 points. If x < y, then P1 scores 0 point and P2 scores 5 points. Let Xl and Yl be the total scores of P1 and P2, respectively, after playing the lth round.", "response_choices": "(A) (I) \u2192 (Q); (II) \u2192 (R); (III) \u2192 (T); (IV) \u2192 (S) \n (B) (I) \u2192 (Q); (II) \u2192 (R); (III) \u2192 (T); (IV) \u2192 (T) \n (C) (I) \u2192 (P); (II) \u2192 (R); (III) \u2192 (Q); (IV) \u2192 (S) \n (D) (I) \u2192 (P); (II) \u2192 (R); (III) \u2192 (Q); (IV) \u2192 (T)", "answer": "(C) (I) \u2192 (P); (II) \u2192 (R); (III) \u2192 (Q); (IV) \u2192 (S)", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Let p, q, r be nonzero real numbers that are, respectively, the 10th, 100th and 1000th terms of a harmonic progression. Consider the system of linear equations x + y + z = 1, 10x + 100y + 1000z = 0, qr x + pr y + pq z = 0.", "response_choices": "(A) (I) \u2192 (T); (II) \u2192 (R); (III) \u2192 (S); (IV) \u2192 (T) | (B) (I) \u2192 (Q); (II) \u2192 (S); (III) \u2192 (S); (IV) \u2192 (R) | (C) (I) \u2192 (Q); (II) \u2192 (R); (III) \u2192 (P); (IV) \u2192 (R) | (D) (I) \u2192 (T); (II) \u2192 (S); (III) \u2192 (P); (IV) \u2192 (T)", "answer": "(C) (I) \u2192 (Q); (II) \u2192 (R); (III) \u2192 (P); (IV) \u2192 (R)", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "Consider the ellipse (x^2)/4 + (y^2)/3 = 1. Let H(\u03b1, 0), 0 < \u03b1 < 2, be a point. A straight line drawn through H parallel to the y-axis crosses the ellipse and its auxiliary circle at points E and F respectively, in the first quadrant. The tangent to the ellipse at the point E intersects the positive x-axis at a point G. Suppose the straight line joining F and the origin makes an angle \u03d5 with the positive x-axis.", "response_choices": "List-I: (I) If \u03d5 = \u03c0/4, then the area of the triangle FGH is, (II) If \u03d5 = \u03c0/3, then the area of the triangle FGH is, (III) If \u03d5 = \u03c0/6, then the area of the triangle FGH is, (IV) If \u03d5 = \u03c0/12, then the area of the triangle FGH is; List-II: (P) (\u221a3-1)^4/8, (Q) 1, (R) 3/4, (S) 1/2\u221a3, (T) 3\u221a3/2", "answer": "D", "page_number": 9, "image_available": "yes", "question_subject": "mathematics"} +{"id": 1, "question": "Two spherical stars A and B have densities \u03c1A and \u03c1B, respectively. A and B have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an interaction process, star A loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains \u03c1A. The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being \u03c1A. If vA and vB are the escape velocities from A and B after the interaction process, the ratio vB/vA = \u221a[10n/(3\u221a\u03c0)]. The value of n is _____.", "response_choices": "No response choices provided", "answer": "Numerical Value", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction 15N + 4He \u2192 3H + 18O in a laboratory frame is n (in MeV). Assume that 15N is at rest in the laboratory frame. The masses of 15N, 4He, 3H and 18O can be taken to be 16.006 u, 4.003 u, 1.008 u and 19.003 u, respectively, where 1 u = 930 MeV/c^2. The value of n is _____.", "response_choices": "No response choices provided", "answer": "Numerical Value", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "In the following circuit C1 = 12 \u03bcF, C2 = C3 = 4 \u03bcF and C4 = C5 = 2 \u03bcF. The charge stored in C5 is ___ \u03bcC.", "response_choices": "No response choices provided", "answer": "Numerical Value", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A rod of length 2 cm makes an angle 2\u03c0/3 rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of 40/3 cm from the object as shown in the figure. The height of the image is 30\u221a3/13 cm and the angle made by it with respect to the principal axis is \u03b1 rad. The value of \u03b1 is \u03c0/n rad, where n is _______.", "response_choices": "No response choices provided", "answer": "Numerical Value", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "At time t = 0, a disk of radius 1 m starts to roll without slipping on a horizontal plane with an angular acceleration of \u03b1 = 5 rad s^-2. A small stone is stuck to the disk. At t = 0, it is at the contact point of the disk and the plane. Later, at time t = \u221a6 s, the stone detaches itself and flies off tangentially from the disk. The maximum height (in m) reached by the stone measured from the plane is \u00bd + \u221a6/10. The value of x is _____. [Take g = 10 m s^-2.]", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with an angle of inclination \u03b8 = 30\u00b0 from the horizontal. Two forces of magnitude 1 N each, parallel to the incline, act on the sphere, both at distance r = 0.5 m from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ___ ms^-2. (Take g = 10 m s^-2.)", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "Consider an LC circuit, with inductance L = 0.1 H and capacitance C = 10^-3 F, kept on a plane. The area of the circuit is 1 m\u00b2. It is placed in a constant magnetic field of strength B0 which is perpendicular to the plane of the circuit. At time t = 0, the magnetic field strength starts increasing linearly as B = B0 + \u03b2t with \u03b2 = 0.04 Ts^-1. The maximum magnitude of the current in the circuit is ___ mA.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A projectile is fired from horizontal ground with speed v and projection angle \u03b8. When the acceleration due to gravity is g, the range of the projectile is d. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is g' = v\u00b2/g.\u03c0\u00b2, then the new range is d' = \u03c0.d. The value of n is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A medium having dielectric constant K >1 fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is d. The capacitor is connected to a battery of voltage V, as shown in Figure (a). Now, both the plates are moved by a distance of d/2 from their original positions, as shown in Figure (b). In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?", "response_choices": "(A) The electric field inside the dielectric material is reduced by a factor of 2K. (B) The capacitance is decreased by a factor of (1+d/2)/(1+d). (C) The voltage between the capacitor plates is increased by a factor of (K + 1). (D) The work done in the process DOES NOT depend on the presence of the dielectric material.", "answer": "B", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "An ideal gas of density \u03c1 = 0.2 kg m^-3 enters a chimney of height h at the rate of \u03b1 = 0.8 kg s^-1 from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is A1 = 0.1 m^2 and the upper end is A2 = 0.4 m^2. The pressure and the temperature of the gas at the lower end are 600 Pa and 300 K, respectively, while its temperature at the upper end is 150 K. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take g = 10 m s^-2 and the ratio of specific heats of the gas \u03b3 = 2. Ignore atmospheric pressure. Which of the following statement(s) is(are) correct?", "response_choices": "(A) The pressure of the gas at the upper end of the chimney is 300 Pa.\n(B) The velocity of the gas at the lower end of the chimney is 40 m s^-1 and at the upper end is 20 m s^-1.\n(C) The height of the chimney is 590 m.\n(D) The density of the gas at the upper end is 0.05 kg m^-3.", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "Three plane mirrors form an equilateral triangle with each side of length L. There is a small hole at a distance l > 0 from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle \u03b8 and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane. Which of the following statement(s) is(are) correct?", "response_choices": "(A) The ray of light will come out for \u03b8 = 30\u00b0, for 0 < l < L.\n(B) There is an angle for l = L/2 at which the ray of light will come out after two reflections.\n(C) The ray of light will NEVER come out for \u03b8 = 60\u00b0, and l = L/3.\n(D) The ray of light will come out for \u03b8 = 60\u00b0, and 0 < l < L/2 after six reflections.", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "A small circular loop of area A and resistance R is fixed on a horizontal xy-plane with the center of the loop always on the axis n\u0302 of a long solenoid. The solenoid has m turns per unit length and carries current I counterclockwise as shown in the figure. The magnetic field due to the solenoid is in n\u0302 direction. List-I gives time dependences of n\u0302 in terms of a constant angular frequency \u03c9. List-II gives the torques experienced by the circular loop at time t = \u03c0/\u03c9. Let \u03b1 = A^2R^2nm^2/2R.", "response_choices": "(A) I->Q, II->P, III->S, IV->T \n(B) I->S, II->T, III->Q, IV->P \n(C) I->Q, II->P, III->S, IV->R \n(D) I->T, II->Q, III->P,IV->R", "answer": "(C) I->Q, II->P, III->S, IV->R", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities (in m s^-1) at time t = \u03c0/3 s.", "response_choices": "(A) I \u2192 R, II \u2192 T, III \u2192 P, IV \u2192 S\n(B) I \u2192 S, II \u2192 P, III \u2192 Q, IV \u2192 R\n(C) I \u2192 S, II \u2192 T, III \u2192 P, IV \u2192 R\n(D) I \u2192 T, II \u2192 P, III \u2192 R, IV \u2192 S", "answer": "C", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process. Which one of the following options is correct?", "response_choices": "(A) I \u2192 T, II \u2192 R, III \u2192 S, IV \u2192 Q, (B) I \u2192 S, II \u2192 P, III \u2192 T, IV \u2192 P, (C) I \u2192 P, II \u2192 R, III \u2192 T, IV \u2192 Q, (D) I \u2192 Q, II \u2192 R, III \u2192 S, IV \u2192 T,", "answer": "(D)", "page_number": 19, "image_available": "no", "question_subject": "physics"} +{"id": 18, "question": "Which one of the following options is correct?", "response_choices": "(A) (I) \u2192 P; (II) \u2192 R; (III) \u2192 Q; (IV) \u2192 T\n(B) (I) \u2192 Q; (II) \u2192 P; (III) \u2192 T; (IV) \u2192 S\n(C) (I) \u2192 P; (II) \u2192 T; (III) \u2192 R; (IV) \u2192 Q\n(D) (I) \u2192 T; (II) \u2192 S; (III) \u2192 Q; (IV) \u2192 R", "answer": "(C)", "page_number": 20, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of O2 at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of Hg(g) are 20.00 kJ K^-1 and 61.32 kJ mol^-1 at 298 K, respectively, the calculated standard molar enthalpy of formation of HgO(s) at 298 K is X kJ mol^-1. The value of [X] is _____. [Given: Gas constant R = 8.3 J K^-1 mol^-1]", "response_choices": "Numerical Value", "answer": "Numerical Value", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The reduction potential (E\u00b0, in V) of MnO4^-(aq)/Mn(s) is _______.", "response_choices": "Numerical Value", "answer": "Numerical Value", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "A solution is prepared by mixing 0.01 mol each of H\u2082CO\u2083, NaHCO\u2083, Na\u2082CO\u2083, and NaOH in 100 mL of water. pH of the resulting solution is _______.", "response_choices": "", "answer": "", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 4, "question": "The treatment of an aqueous solution of 3.74 g of Cu(NO\u2083)\u2082 with excess KI results in a brown solution along with the formation of a precipitate. Passing H\u2082S through this brown solution gives another precipitate X. The amount of X (in g) is _______.", "response_choices": "", "answer": "", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "Dissolving 1.24 g of white phosphorous in boiling NaOH solution in an inert atmosphere gives a gas Q. The amount of CuSO\u2084 (in g) required to completely consume the gas Q is _______.", "response_choices": "", "answer": "", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "Consider the following reaction. On estimation of bromine in 1.00 g of R using Carius method, the amount of AgBr formed (in g) is _______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The weight percentage of hydrogen in Q, formed in the following reaction sequence, is _______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "If the reaction sequence given below is carried out with 15 moles of acetylene, the amount of the product D formed (in g) is _______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two 2pz orbitals is(are)", "response_choices": "(A) \u03c3 orbital has a total of two nodal planes.\n(B) \u03c3* orbital has one node in the xz-plane containing the molecular axis.\n(C) \u03c0 orbital has one node in the plane which is perpendicular to the molecular axis and goes through the center of the molecule.\n(D) \u03c0* orbital has one node in the xy-plane containing the molecular axis.", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "The correct option(s) related to adsorption processes is(are)", "response_choices": "(A) Chemisorption results in a unimolecular layer.\n(B) The enthalpy change during physisorption is in the range of 100 to 140 kJ mol\u00af\u00b9.\n(C) Chemisorption is an endothermic process.\n(D) Lowering the temperature favors physisorption processes.", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 1, "question": "The electrochemical extraction of aluminum from bauxite ore involves", "response_choices": "(A) the reaction of Al2O3 with coke (C) at a temperature > 2500 \u00b0C. (B) the neutralization of aluminate solution by passing CO2 gas to precipitate hydrated alumina (Al2O3\u00b73H2O). (C) the dissolution of Al2O3 in hot aqueous NaOH. (D) the electrolysis of Al2O3 mixed with Na3AlF6 to give Al and CO2.", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The treatment of galena with HNO3 produces a gas that is", "response_choices": "(A) paramagnetic (C) an acidic oxide (B) bent in geometry (D) colorless", "answer": "A", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Considering the reaction sequence given below, the correct statement(s) is(are)", "response_choices": "(A) P can be reduced to a primary alcohol using NaBH4. (B) Treating P with conc. NH4OH solution followed by acidification gives Q. (C) Treating Q with a solution of NaNO2 in aq. HCl liberates N2. (D) P is more acidic than CH3CH2COOH.", "answer": "B", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "Considering the following reaction sequence, the correct option(s) is(are)", "response_choices": "A) P = H2/Pd, ethanol R = NaNO2/HCl U = 1. H3PO2 2. KMnO4 - KOH, heat B) P = Sn/HCl R = HNO2 S = (image) C) S = (image) T = (image) U = 1. CH3CH2OH 2. KMnO4 - KOH, heat D) Q = (image) R = H2/Pd, ethanol T = (image)", "answer": "C", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"} +{"id": 15, "question": "Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. X, and k are constants having appropriate units.", "response_choices": "A) I \u2192 P, II \u2192 Q, III \u2192 S, IV \u2192 T\nB) I \u2192 R, II \u2192 S, III \u2192 S, IV \u2192 T\nC) I \u2192 P, II \u2192 Q, III \u2192 Q, IV \u2192 R\nD) I \u2192 R, II \u2192 S, III \u2192 Q, IV \u2192 R", "answer": "B", "page_number": 29, "image_available": "yes", "question_subject": "chemistry"} +{"id": 16, "question": "LIST-I contains compounds and LIST-II contains reactions\n\nLIST-I\n(I) H\u2082O\u2082\n(II) Mg(OH)\u2082\n(III) BaCl\u2082\n(IV) CaCO\u2083\n\nLIST-II\n(P) Mg(HCO\u2083)\u2082 + Ca(OH)\u2082 \u2192\n(Q) BaO\u2082 + H\u2082SO\u2084 \u2192\n(R) Ca(OH)\u2082 + MgCl\u2082 \u2192\n(S) BaO\u2082 + HCl \u2192\n(T) Ca(HCO\u2083)\u2082 + Ca(OH)\u2082 \u2192\n\nMatch each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option", "response_choices": "(A) I \u2192 Q; II \u2192 P; III \u2192 S; IV \u2192 R\n(B) I \u2192 T; II \u2192 P; III \u2192 Q; IV \u2192 R\n(C) I \u2192 T; II \u2192 R; III \u2192 Q; IV \u2192 P\n(D) I \u2192 Q; II \u2192 R; III \u2192 S; IV \u2192 P", "answer": "D", "page_number": 30, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "LIST-I contains metal species and LIST-II contains their properties.\n\nLIST-I\n(I) [Cr(CN)\u2086]\u00b3\u207b\n(II) [RuCl\u2086]\u00b2\u207b\n(III) [Cr(H\u2082O)\u2086]\u00b3\u207a\n(IV) [Fe(H\u2082O)\u2086]\u00b3\u207a\n\nLIST-II\n(P) t\u2082g orbitals contain 4 electrons\n(Q) \u03bc (spin-only) = 4.9 BM\n(R) low spin complex ion\n(S) metal ion in 4+ oxidation state\n(T) d\u00b3 species\n\n[Given: Atomic number of Cr = 24, Ru = 44, Fe = 26]\n\nMatch each metal species in LIST-I with their properties in LIST-II, and choose the correct option", "response_choices": "(A) I \u2192 R, T; II \u2192 P, S; III \u2192 Q, T; IV \u2192 P, Q\n(B) I \u2192 R, S; II \u2192 P, T; III \u2192 P, Q; IV \u2192 Q, T\n(C) I \u2192 P, R; II \u2192 R, S; III \u2192 R, T; IV \u2192 P, T\n(D) I \u2192 Q, T; II \u2192 S, T; III \u2192 P, T; IV \u2192 Q, R", "answer": "B", "page_number": 30, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option.", "response_choices": "(A) I\u2192P,Q; II\u2192S; III\u2192Q,R; IV\u2192P\n(B) I\u2192P; II\u2192R,S; III\u2192R; IV\u2192Q,S\n(C) I\u2192Q,S; II\u2192P,T; III\u2192P; IV\u2192S\n(D) I\u2192P,S; II\u2192T; III\u2192Q,R; IV\u2192P", "answer": "", "page_number": 31, "image_available": "no", "question_subject": "chemistry"} diff --git a/JEE_papers/JSON/JEE_2022_2_English.jsonl b/JEE_papers/JSON/JEE_2022_2_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..8e3b5fbba4c1b1853a21b65a405b04d48eadb5e4 --- /dev/null +++ b/JEE_papers/JSON/JEE_2022_2_English.jsonl @@ -0,0 +1,49 @@ +{"id": 1, "question": "Let \u03b1 and \u03b2 be real numbers such that \u03c0/4 < \u03b2 < 0 < \u03b1 < \u03c0/4. If sin(\u03b1 + \u03b2) = 1/3 and cos(\u03b1 - \u03b2) = 2/3, then the greatest integer less than or equal to ((sin \u03b1 / cos \u03b2 + cos \u03b1 / sin \u03b2 + sin \u03b2 / cos \u03b1)^2) is", "response_choices": "No response choices provided", "answer": "No answer provided, question requires numeric entry", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "If y(x) is the solution of the differential equation xdy - (y^2 - 4y)dx = 0 for x > 0, y(1) = 2, and the slope of the curve y = y(x) is never zero, then the value of 10 y(\u221a2) is", "response_choices": "No response choices provided", "answer": "No answer provided, question requires numeric entry", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "The greatest integer less than or equal to (\u222b(1 to 2) log2(x^3 + 1) dx + \u222b(1 to log2 9) (2^x - 1)^(-1) dx) is", "response_choices": "No response choices provided", "answer": "No answer provided, question requires numeric entry", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "The product of all positive real values of x satisfying the equation x(16(log5 x)^3 -68 log5 x) = 5^-16 is", "response_choices": "No response choices provided", "answer": "No answer provided, question requires numeric entry", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "If \u03b2 = lim(x\u21920) ((e^(x^4) - (1 - x^3)^(1/3) + ((1 - x^2)^(1/2) - 1) sin x) / (x sin^2 x)), then the value of 6\u03b2 is _______.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let \u03b2 be a real number. Consider the matrix A = (\u03b2 0 1, 2 1 -2, 3 1 -2). If A^7 - (\u03b2 - 1)A^6 - \u03b2A^5 is a singular matrix, then the value of 9\u03b2 is _______.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Consider the hyperbola (x^2/100) - (y^2/64) = 1 with foci at S and S1, where S lies on the positive x-axis. Let P be a point on the hyperbola, in the first quadrant. Let \u2220SPS1 = \u03b1, with \u03b1 < \u03c0/2. The straight line passing through the point S and having the same slope as that of the tangent at P to the hyperbola, intersects the straight line S1P at P1. Let \u03b4 be the distance of P from the straight line SP1, and \u03b2 = S1P. Then the greatest integer less than or equal to (\u03b2\u03b4/\u03b1) sin(\u03b1/2) is _______.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "yes", "question_subject": "mathematics"} +{"id": 8, "question": "Consider the functions f , g : \u211d \u2192 \u211d defined by f(x) = x^2 + (5/12) and g(x) = (2 (1 - (4|x|/3)), |x| \u2264 3/4; 0, |x| > 3/4). If \u03b1 is the area of the region {(x,y) \u03f5 \u211d x \u211d : |x| \u2264 3/4 , 0 \u2264 y \u2264 min(f(x),g(x))}, then the value of 9\u03b1 is _________.", "response_choices": "", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let PQRS be a quadrilateral in a plane, where QR = 1, \u2220PQR = \u2220QRS = 70\u00b0, \u2220PQS = 15\u00b0 and \u2220PRS = 40\u00b0. If \u2220RPS = 0\u00b0, PQ = \u03b1 and PS = \u03b2, then the interval(s) that contain(s) the value of 4 \u03b1 \u03b2 sin 0\u00b0 is/are", "response_choices": "(A) (0, \u221a2), (B) (1, 2), (C) (\u221a2, 3), (D) (2\u221a2, 3\u221a2)", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let g : [0, 1] \u2192 R be the function defined by g(x) = 2^(x*x) + 2^(a(1-x)) . Then, which of the following statements is/are TRUE ?", "response_choices": "(A) The minimum value of g(x) is 2e (B) The maximum value of g(x) is 1 + 2e (C) The function g(x) attains its maximum at more than one point (D) The function g(x) attains its minimum at more than one point", "answer": "", "page_number": 4, "image_available": "yes", "question_subject": "mathematics"} +{"id": 11, "question": "Let z denote the complex conjugate of a complex number z. If z is a non-zero complex number for which both real and imaginary parts of (z )^2 + 1/z^2 are integers, then which of the following is/are possible value(s) of |z| ?", "response_choices": "(A) (43+3\u221a(205))^(1/4) / 2 (B) (7+\u221a33)^(1/4) / 4 (C) (9+\u221a(65))^(1/4) / 4 (D) (7+\u221a33)^(1/4) / 6", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let G be a circle of radius R > 0. Let G1, G2, ..., Gn be n circles of equal radius r > 0. Suppose each of the n circles G1, G2, ..., Gn touches the circle G externally. Also, for i = 1, 2, ..., n \u2212 1, the circle Gi touches Gi+1 externally, and Gn touches G1 externally. Then, which of the following statements is/are TRUE ?", "response_choices": "(A) If n = 4, then (\u221a2 \u2212 1)r < R\n(B) If n = 5, then r < R\n(C) If n = 8, then (\u221a2 \u2212 1) r < R\n(D) If n = 12, then \u221a2 (\u221a3 + 1) r > R", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let i, j and k be the unit vectors along the three positive coordinate axes. Let\na = 3i + j \u2212 k,\nb = i + b2j + b3k, b2, b3 \u2208 \u211d,\nc = c1i + c2j + c3k, c1, c2, c3 \u2208 \u211d\nbe three vectors such that b2b3 > 0, a\u20d7 \u22c5 b\u20d7 = 0 and\n\u239b0 \u2212c3 c2\u239e \u239b1\u239e \u239b3 \u2212 c1\u239e\n\u239cc3 0 \u2212c1\u239f \u239cb2\u239f = \u239c1 \u2212 c2\u239f\n\u239d\u2212c2 c1 0 \u23a0 \u239db3\u23a0 \u239d\u22121 \u2212 c3\u23a0\nThen, which of the following is/are TRUE ?", "response_choices": "(A) a\u20d7 \u22c5 c\u20d7 = 0\n(B) b\u20d7 \u22c5 c\u20d7 = 0\n(C) |b\u20d7| > \u221a10\n(D) |c\u20d7| \u2264 \u221a11", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "For x \u2208 \u211d, let the function y(x) be the solution of the differential equation dy/dx + 12y = cos(\u03c0x/12), y(0) = 0. Then, which of the following statements is/are TRUE?", "response_choices": "(A) y(x) is an increasing function, (B) y(x) is a decreasing function, (C) There exists a real number \u03b2 such that the line y = \u03b2 intersects the curve y = y(x) at infinitely many points, (D) y(x) is a periodic function", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?", "response_choices": "(A) 21816\t(B) 85536\t(C) 12096\t(D) 156816", "answer": "(C) 12096", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "If M = \\begin{pmatrix} 5 & 3 \\\\ 2 & -2 \\\\ -3 & -1 \\\\ 2 & 2 \\end{pmatrix}, then which of the following matrices is equal to M^{2022} ?", "response_choices": "(A) \\begin{pmatrix} 3034 & 3033 \\\\ -3033 & -3032 \\end{pmatrix}\n\n(B) \\begin{pmatrix} 3034 & -3033 \\\\ 3033 & -3032 \\end{pmatrix}\n\n(C) \\begin{pmatrix} 3033 & 3032 \\\\ -3032 & -3031 \\end{pmatrix}\n\n(D) \\begin{pmatrix} 3032 & 3031 \\\\ -3031 & -3030 \\end{pmatrix}", "answer": "(D) \\begin{pmatrix} 3032 & 3031 \\\\ -3031 & -3030 \\end{pmatrix}", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III contains 1 blue, 12 green and 3 yellow balls, Box-IV contains 10 green, 16 orange and 6 white balls. A ball is chosen randomly from Box-I: call this ball b. If b is red then a ball is chosen randomly from Box-II, if b is blue then a ball is chosen randomly from Box-III, and if b is green then a ball is chosen randomly from Box-IV. The conditional probability of the event 'one of the chosen balls is white' given that the event 'at least one of the chosen balls is green' has happened, is equal to", "response_choices": "(A) 15/256, (B) 3/16, (C) 5/52, (D) 1/8", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 18, "question": "For positive integer n, define f(n) = n + 16 + 5n - 3n^2/(4n + 3n^2) + 32 + n - 3n^2/(8n + 3n^2) + 48 - 3n - 3n^2/(12n + 3n^2) + ... + 25n - 7n^2/7n^2 . Then, the value of lim f(n) is equal to", "response_choices": "(A) 3 + 4/3 log_e 7, (B) 4 - 3/4 log_e (2/3), (C) 4 - 4/3 log_e (2/7), (D) 3 + 2/3 log_e 7", "answer": "A", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "A particle of mass 1 kg is subjected to a force which depends on the position as F\u20d7 = \u2212k(x i\u20d7 + y j\u20d7) kg m s\u22122 with k = 1 kg s\u22122. At time t = 0, the particle's position r\u20d7 = (1\u20442 i\u20d7 + \u221a2 j\u20d7) m and its velocity v\u20d7 = (\u2212\u221a2 i\u20d7 + \u221a2 j\u20d7 + 2\u20d7k) m s\u22121. Let vx and vy denote the x and the y components of the particle's velocity, respectively. Ignore gravity. When z = 0.5 m, the value of (x vx \u2212 y vy) is ____ m2s\u22121.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "In a radioactive decay chain reaction, 230\u204490Th nucleus decays into 214\u204484Po nucleus. The ratio of the number of \u03b1 to number of \u03b2\u2212 particles emitted in this process is ____.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Two resistances R1 = X \u03a9 and R2 = 1 \u03a9 are connected to a wire AB of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from 0.2 mm at A to 1 mm at B. A galvanometer (G) connected to the center of the wire, 50 cm from each end along its axis, shows zero deflection when A and B are connected to a battery. The value of X is ____.", "response_choices": "", "answer": "", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "In a particular system of units, a physical quantity can be expressed in terms of the electric charge e, electron mass me, Planck's constant h, and Coulomb's constant k = 1/4\u03c0\u03b50, where \u03b50 is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is [B] = [e]^\u03b1 [me]^\u03b2 [h]^\u03b3 [k]^\u03b4. The value of \u03b1 + \u03b2 + \u03b3 + \u03b4 is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "Consider a configuration of n identical units, each consisting of three layers. The first layer is a column of air of height h = 1\u20442 cm, and the second and third layers are of equal thickness d = \u221a3\u20131\u20442 cm, and refractive indices \u03bc1 = \u221a2 and \u03bc2 = \u221a3, respectively. A light source O is placed on the top of the first unit, as shown in the figure. A ray of light from O is incident on the second layer of the first unit at an angle of \u03b8 = 60\u00b0 to the normal. For a specific value of n, the ray of light emerges from the bottom of the configuration at a distance l = \u221a3\u20442 cm, as shown in the figure. The value of n is ___.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A charge q is surrounded by a closed surface consisting of an inverted cone of height h and base radius R, and a hemisphere of radius R as shown in the figure. The electric flux through the conical surface is \u03c0 q/\u03b50 (in SI units). The value of n is _______.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "On a frictionless horizontal plane, a bob of mass m = 0.1 kg is attached to a spring with natural length l0 = 0.1 m. The spring constant is k2 = 0.009 N/m^-1 when the length of the spring l > l0 and is k2 = 0.016 N/m^-1 when l < l0. Initially the bob is released from l = 0.15 m. Assume that Hooke's law remains valid throughout the motion. If the time period of the full oscillation is T = (\u03c0 \u03c0) s, then the integer closest to \u03c0 is __.", "response_choices": "", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "An object and a concave mirror of focal length f = 10 cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V0 = 15 cm s^-1 towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u. When u = 30 cm, the speed of the mirror Vm is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of Vm is ____ cm s^-1.", "response_choices": "", "answer": "", "page_number": 11, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "In the figure, the inner (shaded) region A represents a sphere of radius rA = 1, within which the electrostatic charge density varies with the radial distance r from the center as \u03c1A = kr, where k is positive. In the spherical shell B of outer radius rB, the electrostatic charge density varies as \u03c1B = c/r^2. Assume that dimensions are taken care of. All physical quantities are in their SI units. Which of the following statement(s) is(are) correct?", "response_choices": "(A) If rB = \u221a5/\u221a2, then the electric field is zero everywhere outside B. (B) If rB = 3, then the electric potential just outside B is k/rB. (C) If rB = 2, then the total charge of the configuration is 15\u03c0k. (D) If rB = 2, then the magnitude of the electric field just outside B is 13\u03c0k/rB.", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "In Circuit-1 and Circuit-2 shown in the figures, R1 = 1 \u03a9, R2 = 2 \u03a9 and R3 = 3 \u03a9. P1 and P2 are the power dissipations in Circuit-1 and Circuit-2 when the switches S1 and S2 are in open conditions, respectively. Q1and Q2 are the power dissipations in Circuit-1 and Circuit-2 when the switches S1 and S2 are in closed conditions, respectively. Which of the following statement(s) is(are) correct? (A) When a voltage source of 6 V is connected across A and B in both circuits, P1 < P2. (B) When a constant current source of 2 Amp is connected across A and B in both circuits, P1 > P2. (C) When a voltage source of 6 V is connected across A and B in Circuit-1, Q1 > P1. (D) When a constant current source of 2 Amp is connected across A and B in both circuits, Q2 < Q1.", "response_choices": "A, B, C, D", "answer": "B, C", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 11, "question": "A bubble has surface tension S. The ideal gas inside the bubble has ratio of specific heats \u03b3 = 5/3. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is Pat1, the radius of the bubble is found to be r1 and the temperature of the enclosed gas is T1. When the atmospheric pressure is Pat2, the radius of the bubble and the temperature of the enclosed gas are r2 and T2, respectively. Which of the following statement(s) is(are) correct? (A) If the surface of the bubble is a perfect heat insulator, then (r1/r2)^5 = Pat2*r2^5/Pat1*r1^5. (B) If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including its surface energy does not change with the external atmospheric pressure. (C) If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then (T1/T2)^3 = Pat2*r2^5/Pat1*r1^5. (D) If the surface of the bubble is a perfect heat insulator, then (T2/T1)^5 = Pat2*r2^4/Pat1*r1^4.", "response_choices": "A, B, C, D", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "A disk of radius R with uniform positive charge density \u03c3 is placed on the xy plane with its center at the origin. The Coulomb potential along the z-axis is V(z) = (\u03c3/2\u03b50)\u221a(R^2+z^2-z). A particle of positive charge q is placed initially at rest at a point on the z axis with z=z0 and z0>0. In addition to the Coulomb force, the particle experiences a vertical force F=-ck with c>0. Let \u03b2 = 2c\u03b50/q\u03c3. Which of the following statement(s) is(are) correct?", "response_choices": "(A) For \u03b2=1/3 and z0=2/3R, the particle reaches the origin. \n(B) For \u03b2=1/3 and z0=3/4R, the particle reaches the origin.\n(C) For \u03b2=1/3 and z0=R/5, the particle returns back to z=z0.\n(D) For \u03b2>1 and z0>0, the particle always reaches the origin.", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index n2. The other slit is at the interface of this medium with another medium 1 of refractive index n1 (\u2260 n2). The line joining the slits is perpendicular to the interface and the distance between the slits is d. The slit widths are much smaller than d. A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle \u03b8 from the line joining them, so that \u03b8 equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.", "response_choices": "(A) The phase difference between the two rays is independent of d.\n(B) The two rays interfere constructively at the detector. \n(C) The phase difference between the two rays depends on n1 but is independent of n2.\n(D) The phase difference between the two rays vanishes only for certain values of d and the angle of incidence of the beam, with \u03b8 being the corresponding angle of refraction.", "answer": "D", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "In the given P-V diagram, a monoatomic gas (\u03b3 = 5/3) is first compressed adiabatically from state A to state B. Then it expands isothermally from state B to state C. [Given: (\u03b3) 0/\u03b3 \u2248 0.5, ln 2 \u2248 0.7 ]. Which of the following statement(s) is(are) correct?", "response_choices": "(A) The magnitude of the total work done in the process A \u2192 B \u2192 C is 144 kJ. (B) The magnitude of the work done in the process B \u2192 C is 84 kJ. (C) The magnitude of the work done in the process A \u2192 B is 60 kJ. (D) The magnitude of the work done in the process C \u2192 A is zero.", "answer": "", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed \u03c9 about the vertical axis passing through the center of A. The angular momentum of B is nM\u03c9R^2 with respect to the center of A. Which of the following is the value of n?", "response_choices": "A) 2, B) 5, C) 7/2, D) 9/2", "answer": "C) 7/2", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is 6.0 V. This potential drops to 0.6 V if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take hc/e = 1.24 \u00d7 10^-6 J m C^-1]", "response_choices": "A) 1.72 x 10^7 m, 1.20 eV, B) 1.72 x 10^7 m, 5.60 eV, C) 3.78 x 10^7 m, 5.60 eV, D) 3.78 x 10^7 m, 1.20 eV", "answer": "D) 3.78 x 10^7 m, 1.20 eV", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "Concentration of H2SO4 and Na2SO4 in a solution is 1 M and 1.8 \u00d7 10^-2 M, respectively. Molar solubility of PbSO4 in the same solution is X \u00d7 10^-8 M (expressed in scientific notation). The value of Y is _________.", "response_choices": "There are no multiple choice options provided.", "answer": "The question requires a numerical response.", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "An aqueous solution is prepared by dissolving 0.1 mol of an ionic salt in 1.8 kg of water at 35 \u00b0C. The salt remains 90% dissociated in the solution. The vapour pressure of the solution is 59.724 mm of Hg. Vapor pressure of water at 35 \u00b0C is 60.000 mm of Hg. The number of ions present per formula unit of the ionic salt is _______.", "response_choices": "There are no multiple choice options provided.", "answer": "The question requires a numerical response.", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Consider the strong electrolytes Z, X-, U, Y- and V, X-. Limiting molar conductivity (\u039b0) of Um-Yn and Vm-Xn are 250 and 440 S cm2 mol\u22121, respectively. The value of (m + n + p) is ________.", "response_choices": "No multiple choice options given", "answer": "The question requires a numerical response to fill in the blank.", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The reaction of Xe and O2F2 gives a Xe compound P. The number of moles of HF produced by the complete hydrolysis of 1 mol of P is _______.", "response_choices": "No multiple choice options given", "answer": "The question requires a numerical response to fill in the blank.", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "Thermal decomposition of AgNO3 produces two paramagnetic gases. The total number of electrons present in the antibonding molecular orbitals of the gas that has the higher number of unpaired electrons is _______.", "response_choices": "No multiple choice options given", "answer": "The question requires a numerical response to fill in the blank.", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "The number of isomeric tetracnes (NOT containing sp-hybridized carbon atoms) that can be formed from the following reaction sequence is _______.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The number of -CH2- (methylene) groups in the product formed from the following reaction sequence is _______.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "The total number of chiral molecules formed from one molecule of P on complete ozonolysis (O3/Zn/H2O) is _______.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "To check the principle of multiple proportions, a series of pure binary compounds (P_xQ_y) were analyzed and their composition is tabulated below. The correct option(s) is(are)", "response_choices": "(A) If empirical formula of compound 3 is P_xQ_y, then the empirical formula of compound 2 is P_xQ_2y. (B) If empirical formula of compound 3 is P_xQ_y and atomic weight of element P is 20, then the atomic weight of Q is 45. (C) If empirical formula of compound 2 is PQ, then the empirical formula of the compound 1 is P_2Q. (D) If atomic weight of P and Q are 70 and 35, respectively, then the empirical formula of compound 1 is P_2Q.", "answer": "", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "Considering the following reaction sequence, the correct statement(s) is(are)", "response_choices": "(A) Compounds P and Q are carboxylic acids. (B) Compound S decolorizes bromine water. (C) Compounds P and S react with hydroxylamine to give the corresponding oximes. (D) Compound R reacts with dialkylcadmium to give the corresponding tertiary alcohol.", "answer": "", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "Among the following, the correct statement(s) about polymers is(are)", "response_choices": "(A) The polymerization of chloroprene gives natural rubber. (B) Teflon is prepared from tetrafluoroethene by heating it with persulphate catalyst at high pressures. (C) PVC are thermoplastic polymers. (D) Ethene at 350-570 K temperature and 1000-2000 atm pressure in the presence of a peroxide initiator yields high density polythene.", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The packing efficiency (in %) of the resultant solid is closest to", "response_choices": "(A) 25 (B) 35 (C) 55 (D) 75", "answer": "(B) 35", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "The reaction of HClO3 with HCl gives a paramagnetic gas, which upon reaction with O2 produces", "response_choices": "(A) Cl2O (B) ClO2 (C) Cl2O6 (D) Cl2O7", "answer": "(B) ClO2", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The reaction of Pb(NO3)2 and NaCl in water produces a precipitate that dissolves upon the addition of HCl of appropriate concentration. The dissolution of the precipitate is due to the formation of", "response_choices": "(A) PbCl2 (B) PbCl4 (C) [PbCl4]2- (D) [PbCl6]2-", "answer": "(C) [PbCl4]2-", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 18, "question": "Treatment of D-glucose with aqueous NaOH results in a mixture of monosaccharides, which are", "response_choices": "(A), (B), (C), (D)", "answer": "(A), (B), (C), (D)", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} diff --git a/JEE_papers/JSON/JEE_2023_1_English.jsonl b/JEE_papers/JSON/JEE_2023_1_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..3c6a80faa0901f7b5c31aa916433aaa31ccf5bb1 --- /dev/null +++ b/JEE_papers/JSON/JEE_2023_1_English.jsonl @@ -0,0 +1,47 @@ +{"id": 1, "question": "Let S = (0,1) \u222a (1,2) \u222a (3,4) and T = {0,1,2,3}. Then which of the following statements is(are) true?", "response_choices": "(A) There are infinitely many functions from S to T\n(B) There are infinitely many strictly increasing functions from S to T\n(C) The number of continuous functions from S to T is at most 120\n(D) Every continuous function from S to T is differentiable", "answer": "", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let f : (0,1) -> R be the function defined as f(x) = sqrt(n) if x = (1/n + 1/n) where n \u2208 N . Let g : (0,1) -> R be a function such that (\u222b(x to 1) (1-t/sqrt(t)) dt <= g(x) <= 2sqrt(x) for all x \u2208 (0,1). Then lim f(x)g(x)x->0+", "response_choices": "(A) does NOT exist\n(B) is equal to 1\n(C) is equal to 2\n(D) is equal to 3", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let Q be the cube with the set of vertices {(x1,x2,x3) \u2208 R^3 : x1,x2,x3 \u2208 {0,1}}. Let F be the set of all twelve lines containing the diagonals of the six faces of the cube Q. Let S be the set of all four lines containing the main diagonals of the cube Q; for instance, the line passing through the vertices (0,0,0) and (1,1,1) is in S . For lines \u21131 and \u21132 , let d(\u21131,\u21132) denote the shortest distance between them. Then the maximum value of d(\u21131,\u21132), as \u21131 varies over F and \u21132 varies over S , is", "response_choices": "(A) 1/sqrt(6)\t(B) 1/sqrt(8)\t(C) 1/sqrt(3)\t(D) 1/sqrt(12)", "answer": "B", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let X = {(x, y) \u2208 Z\u00d7Z : x^2/8 + y^2/20 < 1 and y^2 <= 5x}. Three distinct points P, Q and R are randomly chosen from X . Then the probability that P, Q and R form a triangle whose area is a positive integer, is", "response_choices": "(A) 71/220\t(B) 73/220\t(C) 79/220\t(D) 83/220", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let P be a point on the parabola y^2 = 4ax , where a > 0 . The normal to the parabola at P meets the x-axis at a point Q. The area of the triangle PFQ , where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a,m) is", "response_choices": "(A) (2,3)\t(B) (1,3)\t(C) (2,4)\t(D) (3,4)", "answer": "(D) (3,4)", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let tan^(-1)(x) \u2208 (-\u03c0/2, \u03c0/2), for x \u2208 \u211d. Then the number of real solutions of the equation \u221a(1+cos(2x)) = \u221a2 tan^(-1)(tan x) in the set (-3\u03c0/2, -\u03c0/2) \u222a (-\u03c0/2, \u03c0/2) \u222a (\u03c0/2, 3\u03c0/2) is equal to", "response_choices": "No response choices provided.", "answer": "2", "page_number": 5, "image_available": "yes", "question_subject": "mathematics"} +{"id": 9, "question": "Let n \u2265 2 be a natural number and f :[0,1] \u2192 \u211d be the function defined by f(x) = n(1-2nx) if 0 \u2264 x \u2264 1/2n, 2n(2nx-1) if 1/2n \u2264 x \u2264 3/4n, 4n(1-nx) if 3/4n \u2264 x \u2264 1/n, n/(n-1) (nx-1) if 1/n \u2264 x \u2264 1. If n is such that the area of the region bounded by the curves x = 0 , x = 1 , y = 0 and y = f (x) is 4 , then the maximum value of the function f is", "response_choices": "No response choices provided.", "answer": "2", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let 75\u22ef57 denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5. Consider the sum S = 77 + 757 + 7557 + \u22ef + 75\u22ef57. If S = 75\u22ef57 + m/n , where m and n are natural numbers less than 3000, then the value of m + n is", "response_choices": "No response choices provided.", "answer": "1567", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let A = {1967 + 1686i sin \u03b8 / 7 - 365cos \u03b8 : \u03b8 \u2208 R}. If A contains exactly one positive integer n , then the value of n is", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let P be the plane \u221a3x + 2y + 3z = 16 and let S = {\u03b1i + \u03b2j + \u03b3k : \u03b1\u00b2 + \u03b2\u00b2 + \u03b3\u00b2 = 1 and the distance of (\u03b1, \u03b2, \u03b3) from the plane P is 7/2}. Let u, v and w be three distinct vectors in S such that |u - v| = |v - w| = |w - u|. Let V be the volume of the parallelepiped determined by vectors u, v and w. Then the value of 80\u221a3/V is", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let a and b be two nonzero real numbers. If the coefficient of x\u2075 in the expansion of (ax\u00b2 + 70/27bx)^4 is equal to the coefficient of x^5 in the expansion of (ax - 1/bx^4)^5, then the value of 2b is", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Let \u03b1, \u03b2 and \u03b3 be real numbers. Consider the following system of linear equations \nx + 2y + z = 7\nx + \u03b1z = 11\n2x - 3y + \u03b2z = \u03b3\n\nMatch each entry in List-I to the correct entries in List-II.", "response_choices": "(P) If \u03b2 = 1/2 (7\u03b1 - 3) and \u03b3 = 28, then the system has \n(Q) If \u03b2 = 1/2 (7\u03b1 - 3) and \u03b3 \u2260 28, then the system has\n(R) If \u03b2 \u2260 1/2 (7\u03b1 - 3) where \u03b1 = 1 and \u03b3 \u2260 28, then the system has\n(S) If \u03b2 \u2260 1/2 (7\u03b1 - 3) where \u03b1 = 1 and \u03b3 = 28, then the system has", "answer": "(A) (P) \u2192 (3) \t(Q) \u2192 (2) \t(R) \u2192 (1) \t(S) \u2192 (4)", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Consider the given data with frequency distribution xi 3 8 11 10 5 4 fi 5 2 3 2 4 4 Match each entry in List-I to the correct entries in List-II. List-I (P) The mean of the above data is (Q) The median of the above data is (R) The mean deviation about the mean of the above data is (S) The mean deviation about the median of the above data is List-II (1) 2.5 (2) 5 (3) 6 (4) 2.7 (5) 2.4 The correct option is: (A) (P) \u2192 (3) (Q) \u2192 (2) (R) \u2192 (4) (S) \u2192 (5) (B) (P) \u2192 (3) (Q) \u2192 (2) (R) \u2192 (1) (S) \u2192 (5) (C) (P) \u2192 (2) (Q) \u2192 (3) (R) \u2192 (4) (S) \u2192 (1) (D) (P) \u2192 (3) (Q) \u2192 (3) (R) \u2192 (5) (S) \u2192 (5)", "response_choices": "(A) (P) \u2192 (3) (Q) \u2192 (2) (R) \u2192 (4) (S) \u2192 (5), (B) (P) \u2192 (3) (Q) \u2192 (2) (R) \u2192 (1) (S) \u2192 (5), (C) (P) \u2192 (2) (Q) \u2192 (3) (R) \u2192 (4) (S) \u2192 (1), (D) (P) \u2192 (3) (Q) \u2192 (3) (R) \u2192 (5) (S) \u2192 (5)", "answer": "(D) (P) \u2192 (3) (Q) \u2192 (3) (R) \u2192 (5) (S) \u2192 (5)", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let \u21131 and \u21132 be the lines \u1fbdr = \u03bb(i\u02c6 + j\u02c6 + k\u02c6) and \u1fbdr = (j\u02c6 - k\u02c6) + \u03bc(i\u02c6 + k\u02c6), respectively. Let X be the set of all the planes H that contain the line \u21131. For a plane H, let d(H) denote the smallest possible distance between the points of \u21132 and H. Let H0 be a plane in X for which d(H0) is the maximum value of d(H) as H varies over all planes in X.", "response_choices": "Match each entry in List-I to the correct entries in List-II. \n\nList-I\n(P) The value of d(H0) is\n(Q) The distance of the point (0,1,2) from H0 is\n\n(R) The distance of origin from H0 is\n(S) The distance of origin from the point of intersection of planes y = z, x = 1 and H0 is \n\nList-II\n(1) \u221a3\n(2) 1/\u221a3\n(3) 0\n(4) \u221a2\n\n(5) 1/\u221a2", "answer": "(A) (P) \u2192 (2) (Q) \u2192 (4) (R) \u2192 (5) (S) \u2192 (1)", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Let z be a complex number satisfying | z |\u00b3 + 2z\u00b2 + 4z\u0304 - 8 = 0 , where z\u0304 denotes the complex conjugate of z . Let the imaginary part of z be nonzero.", "response_choices": "Match each entry in List-I to the correct entries in List-II.\n\nList-I\n(P) | z |\u00b2 is equal to\n(Q) | z - z\u0304 |\u00b2 is equal to\n(R) | z |\u2074 + | z + z\u0304 |\u00b2 is equal to\n(S) | z + 1|\u00b2 is equal to\n\nList-II\n(1) 12\n(2) 4\n(3) 8\n(4) 10\n(5) 7", "answer": "(A) (P) \u2192 (1) (Q) \u2192 (3) (R) \u2192 (5) (S) \u2192 (4)", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "A slide with a frictionless curved surface, which becomes horizontal at its lower end, is fixed on the terrace of a building of height 3h from the ground, as shown in the figure. A spherical ball of mass m is released on the slide from rest at a height h from the top of the terrace. The ball leaves the slide with a velocity \u01690 = u0x\u0302 and falls on the ground at a distance d from the building making an angle \u03b8 with the horizontal. It bounces off with a velocity \u1e7d and reaches a maximum height h1. The acceleration due to gravity is g and the coefficient of restitution of the ground is 1/\u221a3. Which of the following statement(s) is(are) correct?", "response_choices": "A) \u01690 = \u221a(2gh)x\u0302\nB) \u1e7d = \u221a(2gh(x\u0302 - \u03bb))\nC) \u03b8 = 60\u00b0\nD) d/h1 = 2\u221a3", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is \u03b4 = 60\u00b0 (see Figure-1). The angle of minimum deviation for red light from the same prism is \u03b4min = 30\u00b0 (see Figure-2). The refractive index of the prism material for blue light is \u221a3. Which of the following statement(s) is(are) correct?", "response_choices": "(A) The blue light is polarized in the plane of incidence.\n(B) The angle of the prism is 45\u00b0.\n(C) The refractive index of the material of the prism for red light is \u221a2.\n(D) The angle of refraction for blue light in air at the exit plane of the prism is 60\u00b0.", "answer": "", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "In a circuit shown in the figure, the capacitor C is initially uncharged and the key K is open. In this condition, a current of 1 A flows through the 1 \u03a9 resistor. The key is closed at time t = t0. Which of the following statement(s) is(are) correct?", "response_choices": "(A) The value of the resistance R is 3 \u03a9.\n(B) For t < t0, the value of current I1 is 2 A.\n(C) At t = t0 + 7.2 \u03bcs, the current in the capacitor is 0.6 A.\n(D) For t \u2192 \u221e, the charge on the capacitor is 12 \u03bcC.", "answer": "", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 4, "question": "A bar of mass M = 1.00 kg and length L = 0.20 m is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass m = 0.10 kg is moving on the same horizontal surface with 5.00 m s\u22121 speed on a path perpendicular to the bar. It hits the bar at a distance L/2 from the pivoted end and returns back on the same path with speed v. After this elastic collision, the bar rotates with an angular velocity \u03c9. Which of the following statement is correct?", "response_choices": "(A) \u03c9 = 6.98 rad s\u22121 and v = 4.30 m s\u22121 \n(C) \u03c9 = 3.75 rad s\u22121 and v = 10.0 m s\u22121", "answer": "B", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A container has a base of 50 cm \u00d7 5 cm and height 50 cm, as shown in the figure. It has two parallel electrically conducting walls each of area 50 cm \u00d7 50 cm. The remaining walls of the container are thin and non-conducting. The container is being filled with a liquid of dielectric constant 3 at a uniform rate of 250 cm3 s\u22121. What is the value of the capacitance of the container after 10 seconds?", "response_choices": "(A) 27 pF \n(C) 81 pF \n(D) 135 pF", "answer": "D", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "One mole of an ideal gas expands adiabatically from an initial state (Ti, Vi) to final state (Tf, 5Vi). Another mole of the same gas expands isothermally from a different initial state (TB, VB) to the same final state (Tf, 5Vi). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is \u03b3. What is the ratio TB/Ti?", "response_choices": "(A) 5\u03b3\u22121, (B) 51\u2212\u03b3, (C) 5\u03b3, (D) 51+\u03b3", "answer": "(B) 51\u2212\u03b3", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "Two satellites P and Q are moving in different circular orbits around the Earth (radius R). The heights of P and Q from the Earth surface are hP and hQ, respectively, where hP = R/3. The accelerations of P and Q due to Earth's gravity are gP and gQ, respectively. If gP/gQ = 36/25, what is the value of hQ?", "response_choices": "(A) 3R/5, (B) R/6, (C) 6R/5, (D) 5R/6", "answer": "(B) R/6", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A Hydrogen-like atom has atomic number Z. Photons emitted in the electronic transitions from level n = 4 to level n = 3 in these atoms are used to perform photoelectric effect experiment on a target metal. The maximum kinetic energy of the photoelectrons generated is 1.95 eV. If the photoelectric threshold wavelength for the target metal is 310 nm, the value of Z is _______.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "An optical arrangement consists of two concave mirrors M1 and M2, and a convex lens L with a common principal axis, as shown in the figure. The focal length of L is 10 cm. The radii of curvature of M1 and M2 are 20 cm and 24 cm, respectively. The distance between L and M2 is 20 cm. A point object S is placed at the mid-point between L and M2 on the axis. When the distance between L and M1 is n/7 cm, one of the images coincides with S. The value of n is _______.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "In an experiment for determination of the focal length of a thin convex lens, the distance of the object from the lens is 10 \u00b1 0.1 cm and the distance of its real image from the lens is 20 \u00b1 0.2 cm. The error in the determination of focal length of the lens is n %. The value of n is _______.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas (\u03b3 = 5/3) and one mole of an ideal diatomic gas (\u03b3 = 7/5). Here, \u03b3 is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of 66 Joule when heated at constant pressure. The change in its internal energy is _______ Joule.", "response_choices": "Multiple choice options not provided", "answer": "No answer provided", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is 60 cm s^-1, the speed of the tip of the person's shadow on the ground with respect to the person is ______ cm s^-1.", "response_choices": "Multiple choice options not provided", "answer": "No answer provided", "page_number": 17, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm. This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1.2 \u00d7 10^-8 N m rad^-1. The angular frequency of the oscillations in n \u00d7 10^-3 rad s^-1. The value of n is _____.", "response_choices": "Multiple choice options not provided", "answer": "No answer provided", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.", "response_choices": "(A) P \u2192 4, Q \u2192 3, R \u2192 2, S \u2192 1 (C) P \u2192 5, Q \u2192 3, R \u2192 1, S \u2192 4 (B) P \u2192 4, Q \u2192 1, R \u2192 2, S \u2192 5 (D) P \u2192 5, Q \u2192 1, R \u2192 3, S \u2192 2", "answer": "(B) P \u2192 4, Q \u2192 1, R \u2192 2, S \u2192 5", "page_number": 18, "image_available": "no", "question_subject": "physics"} +{"id": 15, "question": "Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as 2.9 \u00d7 10^-3 m-K and hc/e = 1.24 \u00d7 10^-6 V-m]", "response_choices": "(A) P \u2192 3, Q \u2192 5, R \u2192 2, S \u2192 3 (C) P \u2192 3, Q \u2192 4, R \u2192 2, S \u2192 1 (B) P \u2192 3, Q \u2192 2, R \u2192 4, S \u2192 1 (D) P \u2192 1, Q \u2192 2, R \u2192 5, S \u2192 3", "answer": "(B) P \u2192 3, Q \u2192 2, R \u2192 4, S \u2192 1", "page_number": 18, "image_available": "no", "question_subject": "physics"} +{"id": 16, "question": "A series LCR circuit is connected to a 45 sin(\u03c9t) Volt source. The resonant angular frequency of the circuit is 10^5 rad s^-1 and current amplitude at resonance is I0. When the angular frequency of the source is \u03c9 = \u03b2 \u00d7 10^4 rad s^-1, the current amplitude in the circuit is 0.05 I0. If \u03b2 = 50 mH, match each entry in List-I with an appropriate value from List-II and choose the correct option.", "response_choices": "(P) I0 in mA, (Q) The quality factor of the circuit, (R) The bandwidth of the circuit in rad s^-1, (S) The peak power dissipated at resonance in Watt; (A) P \u2192 2, Q \u2192 3, R \u2192 5, S \u2192 1, (C) P \u2192 4, Q \u2192 5, R \u2192 3, S \u2192 1, (B) P \u2192 3, Q \u2192 1, R \u2192 4, S \u2192 2, (D) P \u2192 4, Q \u2192 2, R \u2192 1, S \u2192 5", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "physics"} +{"id": 17, "question": "A thin conducting rod MN of mass 20 gm, length 25 cm and resistance 1.0 \u03a9 is held on frictionless, long, perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field B0 = 4 T directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time t = 0 and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-I with an appropriate value from List-II, and choose the correct option. [Given: The acceleration due to gravity g = 10 m s^-2 and e^-1 = 0.4]", "response_choices": "(P) At t = 0.2 s, the magnitude of the induced emf in Volt, (Q) At t = 0.2 s, the magnitude of the magnetic force in Newton, (R) At t = 0.2 s, the power dissipated as heat in Watt, (S) The magnitude of terminal velocity of the rod in m s^-1; (A) P \u2192 5, Q \u2192 2, R \u2192 3, S \u2192 1, (C) P \u2192 4, Q \u2192 3, R \u2192 1, S \u2192 2, (B) P \u2192 3, Q \u2192 1, R \u2192 4, S \u2192 5, (D) P \u2192 3, Q \u2192 4, R \u2192 2, S \u2192 5", "answer": "B", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "The correct statement(s) related to processes involved in the extraction of metals is(are)", "response_choices": "(A) Roasting of Malachite produces Cuprite, (B) Calcination of Calamine produces Zincite, (C) Copper pyrites is heated with silica in a reverberatory furnace to remove iron, (D) Impure silver is treated with aqueous KCN in the presence of oxygen followed by reduction with zinc metal", "answer": "A,B,D", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "The correct statement(s) about P, Q, R, and S is(are)", "response_choices": "(A) Both P and Q have asymmetric carbon(s).\n(B) Both Q and R have asymmetric carbon(s).\n(C) Both P and R have asymmetric carbon(s).\n(D) P has asymmetric carbon(s), S does not have any asymmetric carbon.", "answer": "", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"} +{"id": 3, "question": "Consider the following reaction scheme and choose the correct option(s) for the major products Q, R and S.", "response_choices": "(A) Q, R, S (B) Q, R, S (C) Q, R, S (D) Q, R, S", "answer": "(D)", "page_number": 22, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "In the scheme given below, X and Y, respectively, are", "response_choices": "(A) CrO4^2- and Br2 \n(B) MnO4^2- and Cl2 \n(C) MnO4- and Cl2 \n(D) MnSO4 and HOCl", "answer": "B", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "Plotting 1/\u039bm against c\u221am for aqueous solutions of a monobasic weak acid (HX) resulted in a straight line with y-axis intercept of P and slope of S. The ratio P/S is", "response_choices": "(A) Ka \u039b^0_m \n(B) Ka \u039b^0_m/2 \n(C) 2 Ka \u039b^0_m \n(D) 1 / (Ka \u039b^0_m)", "answer": "D", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "On decreasing the pH from 7 to 2, the solubility of a sparingly soluble salt (MX) of a weak acid (HX) increased from 10^-4 mol L^-1 to 10^-3 mol L^-1. The pKa of HX is", "response_choices": "(A) 3, (B) 4, (C) 5, (D) 2", "answer": "(D) 2", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 7, "question": "In the given reaction scheme, P is a phenyl alkyl ether, Q is an aromatic compound; R and S are the major products. The correct statement about S is", "response_choices": "(A) It primarily inhibits noradrenaline degrading enzymes. (B) It inhibits the synthesis of prostaglandin. (C) It is a narcotic drug. (D) It is ortho-acetylbenzoic acid.", "answer": "(D) It is ortho-acetylbenzoic acid.", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "The stoichiometric reaction of 516 g of dimethyldichlorosilane with water results in a tetrameric cyclic product X in 75% yield. The weight (in g) of X obtained is __.", "response_choices": "Integer response", "answer": "Integer value to be entered", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "A gas has a compressibility factor of 0.5 and a molar volume of 0.4 dm3 mol\u22121 at a temperature of 800 K and pressure x atm. If it shows ideal gas behaviour at the same temperature and pressure, the molar volume will be y dm3 mol\u22121. The value of x/y is ___.", "response_choices": "Integer response", "answer": "Integer value to be entered", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "The plot of log kf versus 1/T for a reversible reaction A (g) \u21cc P (g) is shown.", "response_choices": "", "answer": "", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} +{"id": 11, "question": "One mole of an ideal monoatomic gas undergoes two reversible processes (A \u2192 B and B \u2192 C) as shown in the given figure:", "response_choices": "", "answer": "", "page_number": 26, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "In a one-litre flask, 6 moles of A undergoes the reaction A (g) \u21cc P (g). The progress of product formation at two temperatures (in Kelvin), T1 and T2, is shown in the figure:", "response_choices": "", "answer": "If T1 = 2T2 and (\u0394G\u1dbb\u2081 - \u0394G\u1dbb\u2082) = RT2 ln x, then the value of x is ___.", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "The total number of sp\u00b2 hybridised carbon atoms in the major product P (a non-heterocyclic compound) of the following reaction is ___:", "response_choices": "", "answer": "", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"} +{"id": 14, "question": "Match the reactions (in the given stoichiometry of the reactants) in List-I with one of their products given in List-II and choose the correct option.", "response_choices": "(A) P \u2192 2; Q \u2192 3; R \u2192 1; S \u2192 5\n(B) P \u2192 3; Q \u2192 5; R \u2192 4; S \u2192 2\n(C) P \u2192 5; Q \u2192 2; R \u2192 1; S \u2192 3\n(D) P \u2192 2; Q \u2192 3; R \u2192 4; S \u2192 5", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The major products obtained from the reactions in List-II are the reactants for the named reactions mentioned in List-I. Match List-I with List-II and choose the correct option.", "response_choices": "(A) P -> 2; Q -> 4; R -> 1; S -> 3, (B) P -> 1; Q -> 3; R -> 5; S -> 2, (C) P -> 3; Q -> 2; R -> 1; S -> 4, (D) P -> 3; Q -> 4; R -> 5; S -> 2", "answer": "(B) P -> 1; Q -> 3; R -> 5; S -> 2", "page_number": 30, "image_available": "yes", "question_subject": "chemistry"} diff --git a/JEE_papers/JSON/JEE_2023_2_English.jsonl b/JEE_papers/JSON/JEE_2023_2_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..8f29c279d74a7e4e4e3041a97742f7f1171d457e --- /dev/null +++ b/JEE_papers/JSON/JEE_2023_2_English.jsonl @@ -0,0 +1,50 @@ +{"id": 1, "question": "Let f :[1,\u221e) \u2192 \u211d be a differentiable function such that f(1) = 3 and 3 \u222b1x f(t)dt = x f (x) - x3, x \u2208 [1, \u221e). Let e denote the base of the natural logarithm. Then the value of f(e) is", "response_choices": "(A) e2 + 4/3, (B) log e 4 + e/3, (C) 4e2/3, (D) e2 - 4/3", "answer": "(B) log e 4 + e/3", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is 1/3, then the probability that the experiment stops with head is", "response_choices": "(A) 1/3, (B) 5/21, (C) 4/21, (D) 2/7", "answer": "(C) 4/21", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "For any y \u2208 \u211d, let cot\u22121(y) \u2208 (0, \u03c0) and tan\u22121(y) \u2208 (- \u03c0/2, \u03c0/2). Then the sum of all the solutions of the equation tan\u22121(6y/9 - y5) + cot\u22121(9 - y2/6y) = 2\u03c0/3 for 0 \u2264| y| \u2264 3, is equal to", "response_choices": "(A) 2\u221a3 - 3, (B) 3 - 2\u221a3, (C) 4\u221a3 - 6, (D) 6 - 4\u221a3", "answer": "(C) 4\u221a3 - 6", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let the position vectors of the points P, Q, R and S be \u20d7a = i\u20d7 + 2j\u20d7 - 5k\u20d7, \u20d7b = 3i\u20d7 + 6j\u20d7 + 3k\u20d7, \u20d7c = (17/5)i\u20d7 + (16/5)j\u20d7 + 7k\u20d7 and \u20d7d = 2i\u20d7 + j\u20d7 + k\u20d7, respectively. Then which of the following statements is true?", "response_choices": "A) The points P, Q, R and S are NOT coplanar\nB) (\u20d7b + 2\u20d7d)/3 is the position vector of a point which divides PR internally in the ratio 5:4\nC) (\u20d7b + 2\u20d7d)/3 is the position vector of a point which divides PR externally in the ratio 5:4\nD) The square of the magnitude of the vector \u20d7b \u00d7 \u20d7d is 95", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let M = (aij), i, j \u2208 {1, 2, 3}, be the 3\u00d73 matrix such that aij = 1 if j + 1 is divisible by i, otherwise aij = 0 . Then which of the following statements is(are) true?", "response_choices": "(A) M is invertible\n(B) There exists a nonzero column matrix \u23a1a1\u23a4 \u23a2a2\u23a5 such that M \u23a2a3\u23a5 = \u23a2\u23a1a1\u23a4\u23a2-a2\u23a5\u23a2a3\u23a5\u23a5\n(C) The set {X \u2208 R3 : MX = 0} \u2260 {0}, where 0 = \u23a20\u23a5\n(D) The matrix (M - 2I) is invertible, where I is the 3\u00d73 identity matrix", "answer": "B,C", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let f : (0,1) -> R be the function defined as f(x) = [4x]( x - 1/4 ) ( x - 1/2 ), where [x] denotes the greatest integer less than or equal to x. Then which of the following statements is(are) true?", "response_choices": "(A) The function f is discontinuous exactly at one point in (0,1) \n\n(B) There is exactly one point in (0,1) at which the function f is continuous but NOT differentiable \n\n(C) The function f is NOT differentiable at more than three points in (0,1) \n\n(D) The minimum value of the function f is -1/512", "answer": "D", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let S be the set of all twice differentiable functions f from R to R such that d^2f/dx^2 (x) > 0 for all x \u2208 (-1,1). For f \u2208 S , let X_f be the number of points x \u2208 (-1,1) for which f'(x) = x. Then which of the following statements is(are) true?", "response_choices": "(A) There exists a function f \u2208 S such that X_f = 0 \n\n(B) For every function f \u2208 S , we have X_f \u2264 2 \n\n(C) There exists a function f \u2208 S such that X_f = 2 \n\n(D) There does NOT exist any function f in S such that X_f = 1", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "For x \u2208 \u211d, let tan^(-1)(x) \u2208 (-\u03c0/2, \u03c0/2). Then the minimum value of the function f : \u211d \u2192 \u211d defined by f(x) = \u222b(x tan^(-1)x) / (e^((x-cos(x))) / (1 + t^2/25)) dt is", "response_choices": "No response choices provided", "answer": "Numeric response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "For x \u2208 \u211d, let y(x) be a solution of the differential equation (x^2 - 5) dy/dx - 2x y = -2x(x^2 - 5)^2 such that y(2) = 7. Then the maximum value of the function y(x) is", "response_choices": "No response choices provided", "answer": "Numeric response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let X be the set of all five digit numbers formed using 1,2,2,2,4,4,0. For example, 22240 is in X while 02244 and 44422 are not in X. Suppose that each element of X has an equal chance of being chosen. Let p be the conditional probability that an element chosen at random is a multiple of 20 given that it is a multiple of 5. Then the value of 38p is equal to", "response_choices": "No response choices provided", "answer": "Numeric response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let A1, A2, A3, ..., A8 be the vertices of a regular octagon that lie on a circle of radius 2. Let P be a point on the circle and let PAi denote the distance between the points P and Ai for i = 1, 2, ..., 8. If P varies over the circle, then the maximum value of the product PA1 \u00b7 PA2 \u00b7 ... \u00b7 PA8 , is", "response_choices": "No response choices provided", "answer": "Numeric response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let R = { [a 3 b], [c 2 d], [0 5 0] : a,b,c,d \u2208 {0,3,5,7,11,13,17,19} }. Then the number of invertible matrices in R is", "response_choices": "No response choices provided", "answer": "Numeric response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let C1 be the circle of radius 1 with center at the origin. Let C2 be the circle of radius r with center at the point A = (4, 1), where 1 < r < 3. Two distinct common tangents PQ and ST of C1 and C2 are drawn. The tangent PQ touches C1 at P and C2 at Q. The tangent ST touches C1 at S and C2 at T. Mid points of the line segments PQ and ST are joined to form a line which meets the x-axis at a point B. If AB = \u221a5 , then the value of r2 is", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"} +{"id": 14, "question": "Let a be the area of the triangle ABC. Then the value of (64\u2044a)^2 is", "response_choices": "", "answer": "", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Then the inradius of the triangle ABC is", "response_choices": "", "answer": "", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let pi be the probability that a randomly chosen point has i many friends, i = 0,1,2,3,4 . Let X be a random variable such that for i = 0,1,2,3,4 , the probability P(X = i) = pi . Then the value of 7E(X) is", "response_choices": "", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "mathematics"} +{"id": 17, "question": "Two distinct points are chosen randomly out of the points A1,A2,...,A49 . Let p be the probability that they are friends. Then the value of 7p is", "response_choices": "", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "mathematics"} +{"id": 1, "question": "An electric dipole is formed by two charges +q and \u2212q located in xy-plane at (0,2) mm and (0,\u22122) mm, respectively, as shown in the figure. The electric potential at point P (100,100) mm due to the dipole is V0. The charges +q and \u2212q are then moved to the points (\u22121,2) mm and (1,\u22122) mm, respectively. What is the value of electric potential at P due to the new dipole?", "response_choices": "(A) V0/4, (B) V0/2, (C) V0/\u221a2, (D) 3V0/4", "answer": "(C) V0/\u221a2", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "Young's modulus of elasticity Y is expressed in terms of three derived quantities, namely, the gravitational constant G, Planck's constant \u0127 and the speed of light c, as Y = c^\u03b1 \u0127^\u03b2 G^\u03b3. Which of the following is the correct option?", "response_choices": "(A) \u03b1 = 7, \u03b2 = \u22121, \u03b3 = \u22122, (B) \u03b1 = \u22127, \u03b2 = \u22121, \u03b3 = \u22122, (C) \u03b1 = 7, \u03b2 = \u22121, \u03b3 = 2, (D) \u03b1 = \u22127, \u03b2 = 1, \u03b3 = \u22122", "answer": "(C) \u03b1 = 7, \u03b2 = \u22121, \u03b3 = 2", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A particle of mass m is moving in the xy-plane such that its velocity at a point (x, y) is given as \u20d7v = \u03b1(yx\u0302 + 2x\u0177), where \u03b1 is a non-zero constant. What is the force F\u20d7 acting on the particle?", "response_choices": "(A) F\u20d7 = 2m\u03b12(xx\u0302 + y\u0177), (B) F\u20d7 = m\u03b12(yx\u0302 + 2x\u0177), (C) F\u20d7 = 2m\u03b12(yx\u0302 + x\u0177), (D) F\u20d7 = m\u03b12(xx\u0302 + 2y\u0177)", "answer": "(B) F\u20d7 = m\u03b12(yx\u0302 + 2x\u0177)", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is U\u2080 and the speed of sound in the gas is v\u2080. At a fixed temperature and pressure, which of the following is the correct option?", "response_choices": "(A) v\u2083 < v\u2086 and U\u2083 > U\u2086, (B) v\u2085 > v\u2083 and U\u2083 > U\u2085, (C) v\u2085 > v\u2087 and U\u2085 < U\u2087, (D) v\u2086 < v\u2087 and U\u2086 < U\u2087", "answer": "", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from n1 to n2 over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?", "response_choices": "(A) It will deflect up by an angle tan^-1 [(n2^2-n1^2)/2h], (B) It will deflect up by an angle tan^-1 [(n2-n1)/d], (C) It will not deflect, (D) The deflection angle depends only on (n2 - n1) and not on the individual values of n1 and n2.", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "An annular disk of mass M, inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction \u03bc, as shown in the figure. At some time, an impulse J0 is applied at a height h above the center of the disk. If h = hcrit then the disk rolls without slipping along the x-axis. Which of the following statement(s) is(are) correct?", "response_choices": "(A) For \u03bc \u2260 0 and a \u2192 0, hcrit = b/2, (B) For \u03bc \u2260 0 and a \u2192 b, hcrit = b, (C) For h = hcrit, the initial angular velocity does not depend on the inner radius a, (D) For \u03bc = 0 and h = 0, the wheel always slides without rolling.", "answer": "D", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by E = 30(2x + y)sin [2\u03c0 (5 \u00d7 10^14 t - 10^7/3)] V m^-1. Which of the following option(s) is(are) correct?", "response_choices": "(A) Bx = -2 \u00d7 10^-7 sin [2\u03c0 (5 \u00d7 10^14 t - 10^7/3)] Wb m^-2, (B) By = 2 \u00d7 10^-7 sin [2\u03c0 (5 \u00d7 10^14 t - 10^7/3)] Wb m^-2, (C) The wave is polarized in the xy-plane with polarization angle 30\u00b0 with respect to the x-axis, (D) The refractive index of the medium is 2.", "answer": "", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "A thin circular coin of mass 5 gm and radius 4/3 cm is initially in a horizontal xy-plane. The coin is tossed vertically up (+z direction) by applying an impulse of \u221a6 x 10^-2 N-s at a distance 2/3 cm from its center. The coin spins about its diameter and moves along the +z direction. By the time the coin reaches back to its initial position, it completes n rotations. The value of n is _____.", "response_choices": "n/a (Non-Multiple Choice)", "answer": "4", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 9, "question": "A rectangular conducting loop of length 4 cm and width 2 cm is in the xy-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction 2/3 x + y with a constant speed v. The wire is carrying a steady current I = 10 A in the positive x-direction. A current of 10 \u03bcA flows through the loop when it is at a distance d = 4 cm from the wire. If the resistance of the loop is 0.1 \u03a9, then the value of v is _____ m s^-1.", "response_choices": "n/a (Non-Multiple Choice)", "answer": "-10^-6", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "A string of length 1 m and mass 2 \u00d7 10^-5 kg is under tension T. When the string vibrates, two successive harmonics are found to occur at frequencies 750 Hz and 1000 Hz. The value of tension T is _____ Newton.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 11, "question": "An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius 0.1 mm is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume V0 to 100/101 V0 with the movable piston. Considering air as an ideal gas, the height (h) of the liquid column in the capillary above the liquid level in cm is_______.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 12, "question": "In a radioactive decay process, the activity is defined as A = - dN/dt, where N(t) is the number of radioactive nuclei at time t. Two radioactive sources, S1 and S2 have same activity at time t = 0. At a later time, the activities of S1 and S2 are A1 and A2, respectively. When S1 and S2 have just completed their 3rd and 7th half-lives, respectively, the ratio A1/A2 is __________.", "response_choices": "", "answer": "", "page_number": 16, "image_available": "no", "question_subject": "physics"} +{"id": 13, "question": "One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the P-V diagrams below. In cycle I, processes a, b, c and d are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes a', b', c' and d' are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is WI and that during cycle II is WII. The ratio WI/WII is _______.", "response_choices": "No multiple choice options provided", "answer": "No answer provided", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "When only S2 is emitting sound and it is at Q, the frequency of sound measured by the detector in Hz is _________.", "response_choices": "Numerical Response", "answer": "656", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "Consider both sources emitting sound. When S\u2082 is at R and S\u2081 approaches the detector with a speed 4 m s\u207b\u00b9, the beat frequency measured by the detector is _______Hz.", "response_choices": "", "answer": "", "page_number": 19, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "Considering the air flow to be streamline, the steady mass flow rate of air exiting the chimney is ___ g m s^-1.", "response_choices": "No response choices provided", "answer": "", "page_number": 20, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "When the chimney is closed using a cap at the top, a pressure difference \u0394P develops between the top and the bottom surfaces of the cap. If the changes in the temperature and density of the hot air, due to the stoppage of air flow, are negligible then the value of \u0394P is ______ N m^-2.", "response_choices": "", "answer": "", "page_number": 21, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "The correct molecular orbital diagram for F2 molecule in the ground state is", "response_choices": "A, B, C, D", "answer": "B", "page_number": 22, "image_available": "yes", "question_subject": "chemistry"} +{"id": 2, "question": "Consider the following statements related to colloids. \n\n(I) Lyophobic colloids are not formed by simple mixing of dispersed phase and dispersion medium. \n(II) For emulsions, both the dispersed phase and the dispersion medium are liquid. \n(III) Micelles are produced by dissolving a surfactant in any solvent at any temperature. \n(IV) Tyndall effect can be observed from a colloidal solution with dispersed phase having the same refractive index as that of the dispersion medium.", "response_choices": "(A) (I) and (II)\n\n(B) (II) and (III)\n\n(C) (III) and (IV)\n\n(D) (II) and (IV)", "answer": "(B) (II) and (III)", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "In the following reactions, P, Q, R, and S are the major products.\n\n(i) Mg, dry ether\n(ii) H2O P\n\n(i) Mg, dry ether\n(ii) CO2, dry ether\n(iii) H3O+ Q\n(iv) NaOH\n\n(i) Mg, dry ether\n(ii) CH3CHO, then H2O\n(iii) CrO3 R\n\n(i) ethanolic NaCN\n(ii) H2/ Ni\n(iii) CHCI3/KOH, \u0394 S\n(iv) LiAIH4, then H2O", "response_choices": "(A) P is a primary alcohol with four carbons.\n(B) Q undergoes Kolbe's electrolysis to give an eight-carbon product.\n(C) R has six carbons and it undergoes Cannizzaro reaction.\n(D) S is a primary amine with six carbons.", "answer": "(B) Q undergoes Kolbe's electrolysis to give an eight-carbon product.", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "A disaccharide X cannot be oxidised by bromine water. The acid hydrolysis of X leads to a laevorotatory solution. The disaccharide X is", "response_choices": "A, B, C, D", "answer": "B", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"} +{"id": 5, "question": "The complex(es), which can exhibit the type of isomerism shown by [Pt(NH3)3Br3], is(are) [en = H2NCH2CH2NH2]", "response_choices": "(A) [Pt(en)(SCN)2] (B) [Zn(NH3)4Cl2] (C) [Pt(NH3)2Cl4] (D) [Cr(en)3(H2O)(SO4)]", "answer": "C", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "Atoms of metals x, y, and z form face-centred cubic (fcc) unit cell of edge length Lx, body-centred cubic (bcc) unit cell of edge length Ly, and simple cubic unit cell of edge length Lz, respectively. If rx = (\u221a3)/2 ry : ry = 8/(\u221a3) rx : Mz = 3/2 My and Mz = 3Mx, then the correct statement(s) is(are)", "response_choices": "(A) Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of unit cell of z (B) Lx > Lz (C) Lx > Ly (D) Density of x > Density of y", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "In the following reactions, P, Q, R, and S are the major products.", "response_choices": "(A) P and Q are monomers of polymers dacron and glyptal, respectively. (B) P, Q, and R are dicarboxylic acids. (C) Compounds Q and R are the same. (D) R does not undergo aldol condensation and S does not undergo Cannizzaro reaction.", "answer": "", "page_number": 26, "image_available": "yes", "question_subject": "chemistry"} +{"id": 8, "question": "H2S (5 moles) reacts completely with acidified aqueous potassium permanganate solution. In this reaction, the number of moles of water produced is x, and the number of moles of electrons involved is y. The value of (x + y) is ____.", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "Among [I3]-, [SiO3]4-, SO3Cl-, XeF5, SF6, ClF3, Ni(CO)4, XeOF4, [PtCl6]2-, XeF6, and SOCl2, the total number of species having sp3 hybridised central atom is ____.", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Consider the following molecules: Br2O6, F2O, H2S3O6, H2S2O8, and C2O2. Count the number of atoms existing in their zero oxidation state in each molecule. Their sum is____.", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "For He+, a transition takes place from the orbit of radius 105.8 pm to the orbit of radius 26.45 pm. The wavelength (in nm) of the emitted photon during the transition is ___.", "response_choices": "", "answer": "", "page_number": 27, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "50 mL of 0.2 molal urea solution (density = 1.012 g mL^-1 at 300 K) is mixed with 250 mL of a solution containing 0.06 g of urea. Both the solutions were prepared in the same solvent. The osmotic pressure (in Torr) of the resulting solution at 300 K is ___.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 28, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "The reaction of 4-methyloct-1-ene (P, 2.52 g) with HBr in the presence of (C2H5CO)2O2 gives two isomeric bromides in a 9 : 1 ratio, with a combined yield of 50%. Of these, the entire amount of the primary alkyl bromide was reacted with an appropriate amount of diethylamine followed by treatment with aq. K2CO3 to give a non-ionic product S in 100% yield. The mass (in mg) of S obtained is ___.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 28, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "The value of enthalpy change, H\u03b2 \u2013 H\u03b1 (in J mol\u22121), at 300 K is ___.", "response_choices": "", "answer": "", "page_number": 30, "image_available": "yes", "question_subject": "chemistry"} +{"id": 16, "question": "The number of heteroatoms present in one molecule of R is _______.", "response_choices": "", "answer": "", "page_number": 30, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The total number of carbon atoms and heteroatoms present in one molecule of S is _______.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 31, "image_available": "no", "question_subject": "chemistry"} diff --git a/JEE_papers/JSON/JEE_2024_1_English.jsonl b/JEE_papers/JSON/JEE_2024_1_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..7a9b5c236fdb539cec91f9dc49b64953a690b27c --- /dev/null +++ b/JEE_papers/JSON/JEE_2024_1_English.jsonl @@ -0,0 +1,48 @@ +{"id": 1, "question": "Let f(x) be a continuously differentiable function on the interval (0, \u221e) such that f(1) = 2 and lim(t^10 f(x) - x^10 f(t) / t^9 - x^9) = 1 for each x > 0. Then, for all x > 0, f(x) is equal to", "response_choices": "(A) 31/11x^10 + 9/11*x^10, (B) 9/11x^10 + 13/11*x^10, (C) -9/11x^10 + 31/11*x^10, (D) 13/11x^10 - 9/11*x^10", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 1/2. Also assume that the probability of the answer for a question being guessed, given that the student's answer is correct, is 1/6. Then the probability that the student knows the answer of a randomly chosen question is", "response_choices": "(A) 1/12, (B) 1/7, (C) 5/7, (D) 5/12", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let \u03c0/2 < x < \u03c0 be such that cot x = -5/\u221a11. Then (sin(11x/2)(sin 6x - cos 6x) + cos(11x/2)(sin 6x + cos 6x)) is equal to", "response_choices": "(A) \u221a11-1/2\u221a3, (B) \u221a11+1/2\u221a3, (C) \u221a11+1/3\u221a2, (D) \u221a11-1/3\u221a2", "answer": "(B)", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Consider the ellipse x^2/9 + y^2/4 = 1. Let S(p, q) be a point in the first quadrant such that p^2/9 + q^2/4 > 1. Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let R be the vertex of the ellipse with positive x-coordinate and O be the center of the ellipse. If the area of the triangle \u0394ORT is 3/2, then which of the following options is correct?", "response_choices": "(A) q = 2, p = 3\u221a3, (B) q = 2, p = 4\u221a3, (C) q =1, p = 5\u221a3, (D) q =1, p = 6\u221a3", "answer": "(C)", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let S = {a + b\u221a2 : a, b \u2208 \u2124}, T1 = {(-1 + \u221a2)^n : n \u2208 \u2115}, and T2 = {(1 + \u221a2)^n : n \u2208 \u2115}. Then which of the following statements is (are) TRUE?", "response_choices": "(A) \u2124 \u22c3 T1 \u22c3 T2 \u2286 S, (B) T1 \u22c2 (0, 1/2024) = \u2205, where \u2205 denotes the empty set, (C) T2 \u22c2 (2024, \u221e) \u2260 \u2205, (D) For any given a, b \u2208 \u2124, cos(\u03c0(a + b\u221a2)) + i sin(\u03c0(a + b\u221a2)) \u2208 \u2124, if and only if b = 0, where i = \u221a-1.", "answer": "A,D", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "Let R^2 denote R\u00d7R. Let S = {(a,b,c) : a,b,c \u2208 R and ax^2 + 2bxy + cy^2 > 0 for all (x, y) \u2208 R^2 \u2212 {(0,0)}}. Then which of the following statements is (are) TRUE?", "response_choices": "(A) (2, -2, 6) \u2208 S\n\n(B) If (3,b, 1/12) \u2208 S, then | 2b | < 1.\n\n(C) For any given (a,b,c) \u2208 S, the system of linear equations\nax + by = 1\nbx + cy = \u22121\nhas a unique solution.\n\n(D) For any given (a,b,c) \u2208 S, the system of linear equations\n(a + 1)x + by = 0\nbx + (c + 1)y = 0\nhas a unique solution.", "answer": "No selected answer", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let R^3 denote the three-dimensional space. Take two points P = (1, 2, 3) and Q = (4, 2, 7). Let dist(X,Y) denote the distance between two points X and Y in R^3. Let S = {X \u2208 R^3 : (dist(X, P))^2 \u2212 (dist(X, Q))^2 = 50} and T = {Y \u2208 R^3 : (dist(Y, Q))^2 \u2212 (dist(Y, P))^2 = 50}. Then which of the following statements is (are) TRUE?", "response_choices": "(A) There is a triangle whose area is 1 and all of whose vertices are from S.\n(B) There are two distinct points L and M in T such that each point on the line segment LM is also in T.\n(C) There are infinitely many rectangles of perimeter 48, two of whose vertices are from S and the other two vertices are from T.\n(D) There is a square of perimeter 48, two of whose vertices are from S and the other two vertices are from T.", "answer": "No selected answer", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let a = 3\u221a2 and b = 5\u221a(6/6). If x, y \u2208 \u211d are such that 3x + 2y = log\u2082 (18)\u2075 and 2x \u2212 y = log\u2082 (\u221a1080), then 4x + 5y is equal to _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "Let f(x) = x\u2074 + \u03b1x\u00b3 + \u03b2x\u00b2 + c be a polynomial with real coefficients such that f(1) = \u22129. Suppose that t\u221a3 is a root of the equation 4x\u00b3 + 3\u03b1x\u00b2 + 2\u03b2x = 0, where i = \u221a\u22121. If \u03b1\u2081, \u03b1\u2082, \u03b1\u2083, and \u03b1\u2084 are all the roots of the equation f(x) = 0, then |\u03b1\u2081|\u00b2 + |\u03b1\u2082|\u00b2 + |\u03b1\u2083|\u00b2 + |\u03b1\u2084|\u00b2 is equal to _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let S = {A = (0 1 c) | 1 a d |: a, b, c, d, e \u2208 {0, 1} and |A| \u2208 {\u22121, 1}}, where |A| denotes the | 1 b e| determinant of A. Then the number of elements in S is _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "A group of 9 students, s\u2081, s\u2082, . . . , s\u2089, is to be divided to form three teams X, Y , and Z of sizes 2, 3, and 4, respectively. Suppose that s\u2081 cannot be selected for the team X, and s\u2082 cannot be selected for the team Y . Then the number of ways to form such teams, is _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "Let OP = (\u03b1\u22121)i + j + k, OQ = i + (\u03b2\u22121)j + k and OR = i + j + (1/2)k be three vectors, where \u03b1, \u03b2 \u2208 R\u2212{0} and O denotes the origin. If (OP\u00d7OQ) \u00b7 OR = 0 and the point (\u03b1, \u03b2, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that the points (x, P(X = x)), x = 0,1,2,3,4, lie on a fixed straight line in the xy-plane, and P(X = x) = 0 for all x \u2208 R\u2212{0,1,2,3,4}. If the mean of X is 5/2, and the variance of X is \u03b1, then the value of 24\u03b1 is _______.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "Let \u03b1 and \u03b2 be the distinct roots of the equation x^2 + x - 1 = 0. Consider the set T = {1, \u03b1, \u03b2}. For a 3\u00d73 matrix M = (aij)i\u22643,j\u22643, define Ri = ai1 + ai2 + ai3 and Cj = a1j + a2j + a3j for i = 1, 2, 3 and j = 1, 2, 3.", "response_choices": "(P) The number of matrices M = (aij)i\u22643,j\u22643 with all entries in T such that Ri = Cj = 0 for all i, j, is (1) / (Q) The number of symmetric matrices M = (aij)i\u22643,j\u22643 with all entries in T such that Cj = 0 for all j, is (2) 12 / (R) Let M = (aij)i\u22643,j\u22643 be a skew symmetric matrix such that aij \u2208 T for i > j. Then the number of elements in the set [[x], [y], [z]]: x, y, z \u2208 \u211d, M [y] = [0], [z] [-a23]] is (3) infinite / (S) Let M = (aij)i\u22643,j\u22643 be a matrix with all entries in T such that Ri = 0 for all i. Then the absolute value of the determinant of M is (4) 6", "answer": "(5) 0", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "Let the straight line y = 2x touch a circle with center (0, \u03b1), \u03b1 > 0, and radius r at a point A. Let B be the point on the circle such that the line segment AB is a diameter of the circle. Let \u03b1 + r = 5 + \u221a5. Match each entry in List-I to the correct entry in List-II.", "response_choices": "(P) \u03b1 equals, (Q) r equals, (R) A equals, (S) B equals", "answer": "(C) (P) \u2192 (4) (Q) \u2192 (2) (R) \u2192 (5) (S) \u2192 (3)", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "Let y \u2208 \u211d be such that the lines L\u2081: x + 11/1 = y + 21/2 = z + 29/3 and L\u2082: x + 16/3 = y + 11/2 = z + 4/y intersect. Let R\u2080 be the point of intersection of L\u2081 and L\u2082. Let O = (0, 0, 0), and \u1e45 denote a unit normal vector to the plane containing both the lines L\u2081 and L\u2082. Match each entry in List-I to the correct entry in List-II.", "response_choices": "(P) y equals (Q) A possible choice for \u1e45 is (R) OR\u2080 equals (S) A possible value of OR\u2080 \u00b7 \u1e45 is", "answer": "(P) \u2192 (3), (Q) \u2192 (4), (R) \u2192 (1), (S) \u2192 (2)", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} +{"id": 17, "question": "Let f : R \u2192 R and g : R \u2192 R be the functions defined by f(x) = {x | x | sin(1/x), x \u2260 0, 0, x = 0} and g(x) = {1\u22122x, 0 \u2264 x \u2264 1/2, 0, otherwise}. Let a, b, c, d \u2208 R. Define the function h : R \u2192 R by h(x) = a f(x) + b [g(x) + g(1/2 - x)] + c (x - g(x)) + d g(x), x \u2208 R. Match each entry in List-I to the correct entry in List-II.", "response_choices": "List-I \n(P) If a = 0, b = 1, c = 0, and d = 0, then \n(Q) If a = 1, b = 0, c = 0, and d = 0, then \n(R) If a = 0, b = 0, c = 1, and d = 0, then \n(S) If a = 0, b = 0, c = 0, and d = 1, then\n\nList-II\n(1) h is one-one.\n(2) h is onto.\n(3) h is differentiable on R.\n(4) the range of h is [0,1].\n(5) the range of h is {0,1}.", "answer": "(A) (P) \u2192 (4) (Q) \u2192 (3) (R) \u2192 (1) (S) \u2192 (2)", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} +{"id": 1, "question": "A dimensionless quantity is constructed in terms of electronic charge e, permittivity of free space \u03b50, Planck's constant h, and speed of light c. If the dimensionless quantity is written as e\u1d45\u03b50\u1d47h\u1d9cc\u1d48 and n is a non-zero integer, then (\u03b1, \u03b2, \u03b3, \u03b4) is given by", "response_choices": "(A) (2n, \u2212n, \u2212n, \u2212n), (B) (n, \u2212n, \u22122n, \u2212n), (C) (n, \u2212n, \u2212n, \u22122n), (D) (2n, \u2212n, \u22122n, \u22122n)", "answer": "(C) (n, \u2212n, \u2212n, \u22122n)", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 2, "question": "An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field B. The magnitude of the line integral \u222b B\u20d7 \u22c5d\u2113\u20d7 along a straight line from the point (\u2212\u221a3a, a, 0) to (a, a, 0) is given by [\u03bc0 is the magnetic permeability of free space.]", "response_choices": "(A) 7\u03bc0I/24, (B) 7\u03bc0I/12, (C) \u03bc0I/8, (D) \u03bc0I/6", "answer": "(C) \u03bc0I/8", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [\u03b50 is the permittivity of free space.]", "response_choices": "(A) q\u00b2/(4\u03c0\u03b50R\u00b3m), (B) q\u00b2/(32\u03c0\u03b50R\u00b3m), (C) q\u00b2/(8\u03c0\u03b50R\u00b3m), (D) q\u00b2/(16\u03c0\u03b50R\u00b3m)", "answer": "(C) q\u00b2/(8\u03c0\u03b50R\u00b3m)", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "A block of mass 5 kg moves along the x-direction subject to the force F = (\u221220x + 10) N, with the value of x in metre. At time t = 0 s, it is at rest at position x = 1 m. The position and momentum of the block at t = (\u03c0/4) s are", "response_choices": "(A) \u22120.5 m, 5 kg m/s, (B) 0.5 m, 0 kg m/s, (C) 0.5 m, \u22125 kg m/s, (D) \u22121 m, 5 kg m/s", "answer": "(A) \u22120.5 m, 5 kg m/s", "page_number": 11, "image_available": "no", "question_subject": "physics"} +{"id": 5, "question": "A particle of mass m is moving in a circular orbit under the influence of the central force F(r) = -kr, corresponding to the potential energy V(r) = kr^2/2, where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L = nh, where h = h/(2\u03c0), h is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?", "response_choices": "(A) r^2 = nh \u221a(k/mk) (B) v^2 = nh (k/m) (C) L = (k/mr^2) \u221a(m) (D) E = nh (k/2\u221am)", "answer": "D", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 6, "question": "Two uniform strings of mass per unit length \u03bc and 4\u03bc, and length L and 2L, respectively, are joined at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension T. If we define the frequency v0 = 1/(2L) \u221a(T/\u03bc), which of the following statement(s) is(are) correct?", "response_choices": "(A) With a node at O, the minimum frequency of vibration of the composite string is v0. (B) With an antinode at O, the minimum frequency of vibration of the composite string is 2v0. (C) When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes. (D) No vibrational mode with an antinode at O is possible for the composite string.", "answer": "", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 7, "question": "A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of h (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?", "response_choices": "(A) For n = 1.42, h = 50 cm. (B) For n = 1.35, h = 36 cm. (C) For n = 1.45, h = 65 cm. (D) For n = 1.48, h = 85 cm.", "answer": "", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "The specific heat capacity of a substance is temperature dependent and is given by the formula C = kT, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from \u221273 \u00b0C to 27 \u00b0C is nk, the value of n is", "response_choices": "No response choices provided.", "answer": "To be entered as a non-negative integer", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 9, "question": "A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius R/2 is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \u03c9. If the angular speed at which the large disc rotates is \u03c9/n, then the value of n is", "response_choices": "No response choices provided.", "answer": "To be entered as a non-negative integer", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 10, "question": "A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio r = IA/IB of the intensities of light is 2. If a set of two polaroids having 45\u00b0 angle between their pass-axes is placed just before point B, then the new value of r will be", "response_choices": "No response choices provided.", "answer": "To be entered as a non-negative integer", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 1, "question": "A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed v with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be n Hz. The value of n is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height h in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If H = (49/4) h, then the ratio t1/t2 is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A thin uniform rod of length l, and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 14, "question": "One mole of a monatomic ideal gas undergoes the cyclic process J\u2192 K\u2192 L\u2192 M\u2192 J, as shown in the P-T diagram.", "response_choices": "(A) P \u2192 1; Q \u2192 3; R \u2192 5; S \u2192 4\n(C) P \u2192 4; Q \u2192 1; R \u2192 2; S \u2192 2\n(B) P \u2192 4; Q \u2192 3; R \u2192 5; S \u2192 2\n(D) P \u2192 2; Q \u2192 5; R \u2192 3; S \u2192 4", "answer": "None", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance d (\u226a a) between them, as shown in the figure. Let C0 = \u03b50a^2/d, where \u03b50 is the permittivity of free space. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.", "response_choices": "List-I: (P) The capacitance between S1 and S4, with S2 and S3 not connected, is; (Q) The capacitance between S1 and S4, with S2 shorted to S3, is; (R) The capacitance between S1 and S4, with S2 shorted to S3, is; (S) The capacitance between S1 and S2, with S3 shorted to S1, and S2 shorted to S4, is. List-II: (1) 3C0; (2) C0/2; (3) C0/3; (4) 2C0/3; (5) 2C0. (A) P \u2192 3; Q \u2192 2; R \u2192 4; S \u2192 5, (B) P \u2192 2; Q \u2192 3; R \u2192 2; S \u2192 1, (C) P \u2192 3; Q \u2192 2; R \u2192 4; S \u2192 1, (D) P \u2192 3; Q \u2192 2; R \u2192 2; S \u2192 5", "answer": "(B) P -> 2; Q -> 3; R -> 2; S -> 1", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence \u03b80. The ray partially refracts into the sphere with angle of refraction \u03d50 and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is \u03b1. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.", "response_choices": "List-I: (P) If n = 2 and \u03b1 = 180\u00b0, then all the possible values of \u03b80 will be; (Q) If n = \u221a3 and \u03b1 = 180\u00b0, then all the possible values of \u03b80 will be; (R) If n = \u221a3 and \u03b1 = 180\u00b0, then all the possible values of \u03d50 will be; (S) If n = \u221a2 and \u03b80 = 45\u00b0, then all the possible values of \u03b1 will be. List-II: (1) 30\u00b0 and 0\u00b0; (2) 60\u00b0 and 0\u00b0; (3) 45\u00b0 and 0\u00b0; (4) 150\u00b0; (5) 0\u00b0. (A) P \u2192 5; Q \u2192 2; R\u2192 1; S\u2192 4, (B) P \u2192 5; Q \u2192 1; R\u2192 2; S\u2192 4, (C) P \u2192 3; Q \u2192 2; R\u2192 1; S\u2192 4, (D) P \u2192 3; Q \u2192 1; R\u2192 2; S\u2192 5", "answer": "(B) P -> 5; Q -> 1; R-> 2; S-> 4", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "The circuit shown in the figure contains an inductor L, a capacitor C0, a resistor R0 and an ideal battery. The circuit also contains two keys K1 and K2. Initially, both the keys are open and there is no charge on the capacitor. At an instant, key K1 is closed and immediately after this the current in R0 is found to be I1. After a long time, the current attains a steady state value I2. Thereafter, K2 is closed and simultaneously K1 is opened and the voltage across C0 oscillates with amplitude V0 and angular frequency \u03c90. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.", "response_choices": "(A) P \u2192 1; Q \u2192 3; R \u2192 2; S \u2192 5 (B) P \u2192 1; Q \u2192 2; R \u2192 3; S \u2192 5 (C) P \u2192 1; Q \u2192 3; R \u2192 2; S \u2192 4 (D) P \u2192 2; Q \u2192 5; R \u2192 3; S \u2192 4", "answer": "(B) P \u2192 1; Q \u2192 2; R \u2192 3; S \u2192 5", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is", "response_choices": "(A) 2\u221a2 : \u221a3, (B) 2\u221a2 : 1, (C) 1 : 2, (D) 2 : 1", "answer": "C", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid (HNO2) gives the species", "response_choices": "(A) H3O+, NO3- and NO, (B) H3O+, NO3- and NO2, (C) H3O+, NO- and NO2, (D) H3O+, NO3- and N2O", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is", "response_choices": "(A), (B), (C), (D)", "answer": "(B)", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other. [en = H2NCH2CH2NH2]", "response_choices": "(A) Set-I: [Ni(CO)3] and [PdCl4(PPh3)2] Set-II: [Co(NH3)5Cl]SO4 and [Co(NH3)4(SO4)]Cl, (B) Set-I: [Co(en)(NH3)2Cl2] and [PdCl4(PPh3)2] Set-II: [Co(NH3)6][Cr(CN)6] and [Cr(NH3)6][Co(CN)6], (C) Set-I: [Co(NH3)4(NO2)2] and [Co(en)2Cl2] Set-II: [Co(NH3)5Cl]SO4 and [Co(NH3)4(SO4)]Cl, (D) Set-I: [Cr(NH3)5Cl]Cl2 and [Co(en)(NH3)2Cl2] Set-II: [Cr(H2O)6]Cl3 and [Cr(H2O)4Cl]Cl2\u00b7H2O", "answer": "(B)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "Among the following, the correct statement(s) for electrons in an atom is(are)", "response_choices": "(A) Uncertainty principle rules out the existence of definite paths for electrons. (B) The energy of an electron in 2s orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus. (C) According to Bohr's model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit. (D) According to Bohr's model, the magnitude of velocity of electrons increases with increase in values of n.", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "physics"} +{"id": 8, "question": "Consider the following volume-temperature (V-T) diagram for the expansion of 5 moles of an ideal monoatomic gas. Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X->Y->Z is _____.", "response_choices": "The question does not have explicit multiple choice options listed.", "answer": "The answer field requires entering a numerical value.", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} +{"id": 9, "question": "Consider the following reaction, 2H2(g) + 2NO(g) \u2192 N2(g) + 2H2O(g) which follows the mechanism given below: 2NO(g) \u21cc_k1 N2O2(g) (fast equilibrium) N2O2(g) + H2(g) \u21d2_k2 N2O(g) + H2O(g) (slow reaction) N2O(g) + H2(g) \u21d2_k3 N2(g) + H2O(g) (fast reaction) The order of the reaction is _______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH solution, gives P and Q. Compound P does not give Tollens' test, whereas Q on acidification gives positive Tollens' test. Treatment of P with excess cyclohexanone in the presence of catalytic amount of p-toluenesulfonic acid (PTSA) gives product R. Sum of the number of methylene groups (-CH2-) and oxygen atoms in R is ______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "Among V(CO)6, Cr(CO)5, Cu(CO)3, Mn(CO)5, Fe(CO)5, [Co(CO)3]3-, [Cr(CO)4]4-, and Ir(CO)3, the total number of species isoelectronic with Ni(CO)4 is ______. [Given, atomic number: V = 23, Cr = 24, Mn = 25, Fe = 26, Co = 27, Ni = 28, Cu = 29, Ir = 77]", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 12, "question": "In the following reaction sequence, the major product P is formed. \n\n i) Hg2+, H3O+ \n ii) Zn-Hg/HCl \n iii) H3O+, \u0394 \n\n Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of Q with excess NaOH followed by the treatment with CaCl2 yields Ca-soap R, quantitatively. \n\nStarting with one mole of Q, the amount of R produced in gram is _____.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "yes", "question_subject": "chemistry"} +{"id": 13, "question": "Among the following complexes, the total number of diamagnetic species is _____. \n\n [Mn(NH3)6]3+, [MnCl6]3-, [FeFe4]2-, [CoF6]3-, [Fe(NH3)6]3+, and [Co(en)3]3+\n\n[Given, atomic number: Mn = 25, Fe = 26, Co = 27; \n\nen = H2NCH2CH2NH2]", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.", "response_choices": "A) P-4, Q-3, R-2, S-5\nB) P-2, Q-4, R-3, S-1\nC) P-3, Q-4, R-2, S-5\nD) P-4, Q-3, R-2, S-1", "answer": "", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"} +{"id": 15, "question": "Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.", "response_choices": "(A) P-5, Q-2, R-3, S-1\n(B) P-5, Q-3, R-2, S-4\n(C) P-4, Q-3, R-2, S-1\n(D) P-4, Q-2, R-5, S-3", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.", "response_choices": "A) P-3, Q-5, R-4, S-1\nB) P-3, Q-2, R-4, S-1\nC) P-3, Q-5, R-1, S-4\nD) P-5, Q-2, R-4, S-1", "answer": "(A) P-3, Q-5, R-4, S-1", "page_number": 29, "image_available": "yes", "question_subject": "chemistry"} diff --git a/JEE_papers/JSON/JEE_2024_2_English.jsonl b/JEE_papers/JSON/JEE_2024_2_English.jsonl new file mode 100644 index 0000000000000000000000000000000000000000..8ef454ad697ca7d9b58016bd22b737056a6536c0 --- /dev/null +++ b/JEE_papers/JSON/JEE_2024_2_English.jsonl @@ -0,0 +1,51 @@ +{"id": 1, "question": "Considering only the principal values of the inverse trigonometric functions, the value of tan(sin^-1(3/5) - 2cos^-1(2/sqrt(5))) is", "response_choices": "(A) 7/24, (B) -7/24, (C) -5/24, (D) 5/24", "answer": "(B) -7/24", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 2, "question": "Let S = {(x, y) in R x R: x \u2265 0, y \u2265 0, y^2 \u2264 4x, y^2 \u2264 12 - 2x and 3y + sqrt(8) x \u2264 5sqrt(8)}. If the area of the region S is \u03b1 sqrt(2), then \u03b1 is equal to", "response_choices": "(A) 17/2, (B) 17/3, (C) 17/4, (D) 17/5", "answer": "(B) 17/3", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 3, "question": "Let k \u2208 \u211d. If lim (sin(sin kx) + cos x + x)^2 = e^x, then the value of k is", "response_choices": "(A) 1, (B) 2, (C) 3, (D) 4", "answer": "(C) 3", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} +{"id": 4, "question": "Let f : \u211d \u2192 \u211d be a function defined by f(x) = (x^2 sin(\u03c0/x^2), if x \u2260 0, 0, if x = 0). Then which of the following statements is TRUE?", "response_choices": "(A) f(x) = 0 has infinitely many solutions in the interval (1/10^10, \u221e), (B) f(x) = 0 has no solutions in the interval (1/\u03c0, \u221e), (C) The set of solutions of f(x) = 0 in the interval (0, 1/10^10) is finite, (D) f(x) = 0 has more than 25 solutions in the interval (1/\u03c0^2, 1/\u03c0)", "answer": "", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} +{"id": 5, "question": "Let S be the set of all (\u03b1, \u03b2) \u2208 \u211d \u00d7 \u211d such that lim[x\u2192\u221e] (sin(x^2)(log_e x)^\u03b1 sin(1/x^2))/(x^(\u03b2/\u03b1)(log_e (1+x))^\u03b2) = 0. Then which of the following is (are) correct?", "response_choices": "(A) (\u22121, 3) \u2208 S, (B) (\u22121, 1) \u2208 S, (C) (1, \u22121) \u2208 S, (D) (1, \u22122) \u2208 S", "answer": "", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} +{"id": 6, "question": "A straight line drawn from the point P(1, 3, 2), parallel to the line x - 2 = y - 4 = z - 6 / 1 = 2 = 1, intersects the plane L1 : x - y + 3z = 6 at the point Q. Another straight line which passes through Q and is perpendicular to the plane L1 intersects the plane L2 : 2x - y + z = -4 at the point R. Then which of the following statements is (are) TRUE?", "response_choices": "(A) The length of the line segment PQ is \u221a6\n(B) The coordinates of R are (1, 6, 3)\n(C) The centroid of the triangle PQR is (4 14 5 / 3 3 3)\n(D) The perimeter of the triangle PQR is \u221a2 + \u221a6 + \u221a11", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 7, "question": "Let A, B, C be three points in the xy-plane. Suppose that the lines AC and BC are tangents to the curve y\u00b2 = 8x at A and B, respectively. If O = (0, 0) and C1 = (-4, 0), then which of the following statements is (are) TRUE?", "response_choices": "(A) The length of the line segment OA1 is 4\u221a5\n(B) The length of the line segment A1B1 is 16\n(C) The orthocenter of the triangle A1B1C1 is (0, 0)\n(D) The orthocenter of the triangle A1B1C1 is (1, 0)", "answer": "", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} +{"id": 8, "question": "Let f : R \u2192 R be a function such that f (x + y) = f (x) + f (y) for all x, y \u2208 R, and g : R \u2192 (0, \u221e) be a function such that g (x + y) = g (x) g (y) for all x, y \u2208 R. If f (-3/5) = 12 and g (-1/3) = 2, then the value of f (1/4) + g (-2) - 8 g (0) is _______.", "response_choices": "No response choices provided", "answer": "No answer provided, response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "A bag contains N balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For i = 1, 2, 3, let Wi, Gi, and Bi denote the events that the ball drawn in the ith draw is a white ball, green ball, and blue ball, respectively. If the probability P(W1 \u2229 G2 \u2229 B3) = 2/5N and the conditional probability P(B3 | W1 \u2229 G2) = 2/9, then N equals _______.", "response_choices": "No response choices provided", "answer": "No answer provided, response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 10, "question": "Let the function f : R \u2192 R be defined by f (x) = (sin x (x^2023 + 2024x + 2025) / e^x) + 2 (x^2023 + 2024x + 2025) / (x^2 - x + 3) e^x. Then the number of solutions of f (x) = 0 in R is ______.", "response_choices": "No response choices provided", "answer": "No answer provided, response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 11, "question": "Let p = 2i + j + 3k and q = i - j + k. If for some real numbers \u03b1, \u03b2, and \u03b3, we have 15i + 10 j + 6k = \u03b1 (2p + q) + \u03b2 (p - 2q) + \u03b3 (p \u00d7 q), then the value of \u03b3 is _______.", "response_choices": "No response choices provided", "answer": "No answer provided, response required", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} +{"id": 12, "question": "A normal with slope 1/sqrt(6) is drawn from the point (0, -\u03b1) to the parabola x^2 = -4\u03b1y, where \u03b1 > 0. Let L be the line passing through (0, -\u03b1) and parallel to the directrix of the parabola. Suppose that L intersects the parabola at two points A and B. Let r denote the length of the latus rectum and s denote the square of the length of the line segment AB. If r : s = 1 : 16, then the value of 24\u03b1 is _____.", "response_choices": "No multiple choice options given", "answer": "No selected answer given", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 13, "question": "Let the function f : [1, \u221e) \u2192 \u211d be defined by\n\nf(t) = { (-1)^(t+1) 2, if t = 2n - 1, n \u2208 \u2115,\n (2n + 1 - t) {t - (2n - 1)} \n ---------------- + -----------------------, if 2n - 1 < t < 2n + 1, n \u2208 \u2115.\n 2 2 \n\nDefine g(x) = \u222b f(t) dt, x \u2208 (1, \u221e). Let \u03b1 denote the number of solutions of the equation\n\ng(x) = 0 in the interval (1, 8] and \u03b2 = lim g(x). Then the value of \u03b1 + \u03b2 is equal to _____.", "response_choices": "No multiple choice options given", "answer": "No selected answer given", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} +{"id": 14, "question": "If n(X) = n C6, then the value of m is __________.", "response_choices": "", "answer": "", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} +{"id": 15, "question": "If the value of n(Y) + n(Z) is k^2, then |k | is _____________.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} +{"id": 16, "question": "The value of \u222b[0 to \u03c0/2] f(x)g(x)dx - \u222b[0 to \u03c0/2] g(x)dx is ___________.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "mathematics"} +{"id": 17, "question": "The value of (16/\u03c0^3) \u222b[0 to \u03c0/2] f(x)g(x)dx is ___________.", "response_choices": "", "answer": "", "page_number": 8, "image_available": "yes", "question_subject": "mathematics"} +{"id": 1, "question": "A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field B pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height L, is placed in the x-y plane with its vertex P at x = 0 in the orientation shown in the figure. At t = 0, the loop starts entering the region of the magnetic field with a uniform velocity v along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion. Which of the following graph best depicts the variation of the induced emf (E) in the loop as a function of the distance (x) starting from x = 0?", "response_choices": "(A) (B) (C) (D)", "answer": "(B)", "page_number": 9, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "A particle of mass m is under the influence of the gravitational field of a body of mass M (>> m). The particle is moving in a circular orbit of radius r0 with time period T0 around the mass M. Then, the particle is subjected to an additional central force, corresponding to the potential energy Vc(r) = m\u03b1/r3, where \u03b1 is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius r0 in the combined gravitational potential due to M and Vc(r), but with a new time period T1, then (T1^2 - T0^2)/T1^2 is given by", "response_choices": "(A) 3\u03b1/6Mr0^2 (B) \u03b1/26Mr0^2 (C) \u03b1/6Mr0^2 (D) 2\u03b1/6Mr0^2", "answer": "C", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 3, "question": "A metal target with atomic number Z = 46 is bombarded with a high energy electron beam. The emission of X-rays from the target is analyzed. The ratio r of the wavelengths of the K\u03b1-line and the cut-off is found to be r = 2. If the same electron beam bombards another metal target with Z = 41, the value of r will be", "response_choices": "(A) 2.53 (B) 1.27 (C) 2.24 (D) 1.58", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "physics"} +{"id": 4, "question": "A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass m and radius r and it is in a uniform vertical magnetic field B0, as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity g, on two conducting supports at P and Q. When a current I is passed through the loop, the loop turns about the line PQ by an angle \u03b8 given by", "response_choices": "(A) tan \u03b8 = \u03c0r1B0/(mg) (B) tan \u03b8 = 2\u03c0r1B0/(mg) (C) tan \u03b8 = \u03c0r1B0/(2mg) (D) tan \u03b8 = mg/(\u03c0r1B0)", "answer": "B", "page_number": 10, "image_available": "yes", "question_subject": "physics"} +{"id": 5, "question": "A small electric dipole p0, having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R. The surface charge density \u03c3 is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle \u03b8 as shown in the figure. While staying at a distance r, the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct?", "response_choices": "[\u03b50 is the permittivity of free space.] (A) The dipole will undergo small oscillations at any finite value of r. (B) The dipole will undergo small oscillations at any finite value of r > R. (C) The dipole will undergo small oscillations with an angular frequency of \u221a(2\u03c3p0/\u03b5oI) at r = 2R. (D) The dipole will undergo small oscillations with an angular frequency of \u221a(\u03c3p0/100\u03b5oI) at r = 10R.", "answer": "", "page_number": 12, "image_available": "yes", "question_subject": "physics"} +{"id": 6, "question": "A table tennis ball has radius (3/2) \u00d7 10^\u22122 m and mass (22/7) \u00d7 10^\u22123 kg. It is slowly pushed down into a swimming pool to a depth of d = 0.7 m below the water surface and then released from rest. It emerges from the water surface at speed v, without getting wet, and rises up to a height H. Which of the following option(s) is(are) correct? [Given: \u03c0 = 22/7, g = 10 m s^-2, density of water = 1 \u00d7 10\u00b3 kg m^-3, viscosity of water = 1 \u00d7 10^\u22123 Pa.s.]", "response_choices": "(A) The work done in pushing the ball to the depth d is 0.077 J. (B) If we neglect the viscous force in water, then the speed v = 7 m/s. (C) If we neglect the viscous force in water, then the height H = 1.4 m. (D) The ratio of the magnitudes of the net force excluding the viscous force to the maximum viscous force in water is 500/9.", "answer": "", "page_number": 12, "image_available": "no", "question_subject": "physics"} +{"id": 7, "question": "A positive, singly ionized atom of mass number AM is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width w with magnetic field B0 = 0.1T Tesla, as shown in the figure. The ion finally hits a detector at the distance x below its starting trajectory.", "response_choices": "(A) The value of x for H+ ion is 4 cm.\n(B) The value of x for an ion with AM = 144 is 48 cm.\n(C) For detecting ions with 1 \u2264 AM \u2264 196, the minimum height (x1 \u2013 x0) of the detector is 55 cm.\n(D) The minimum width w of the region of the magnetic field for detecting ions with AM = 196 is 56 cm.", "answer": "C", "page_number": 13, "image_available": "yes", "question_subject": "physics"} +{"id": 8, "question": "The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in the determination of the volume is _______.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} +{"id": 9, "question": "A ball is thrown from the location (x0, y0) = (0,0) of a horizontal playground with an initial speed v0 at an angle \u03b80 from the +x-direction. The ball is to be hit by a stone, which is thrown at the same time from the location (x1, y1) = (I, 0). The stone is thrown at an angle (180 \u2212 \u03b81) from the +x-direction with a suitable initial speed. For a fixed v0, when (\u03b80, \u03b81) = (45\u00b0, 45\u00b0), the stone hits the ball after time T1, and when (\u03b80, \u03b81) = (60\u00b0, 30\u00b0), it hits the ball after time T2. In such a case, (T1/T2)\u00b2 is _______.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "no", "question_subject": "physics"} +{"id": 10, "question": "A charge is kept at the central point P of a cylindrical region. The two edges subtend a half-angle \u03b8 at P, as shown in the figure. When \u03b8 = 30\u00b0, then the electric flux through the curved surface of the cylinder is \u03a6. If \u03b8 = 60\u00b0, then the electric flux through the curved surface becomes \u03a6/\u221an, where the value of n is_______.", "response_choices": "", "answer": "", "page_number": 14, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "Two equilateral-triangular prisms P1 and P2 are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism P1 at an angle of incidence \u03b8 such that the outgoing ray undergoes minimum deviation in prism P2. If the respective refractive indices of P1 and P2 are \u221a2 and \u221a3, then \u03b8 = sin^-1[\u03b2/\u221a2 sin(\u03c0/\u03b2)], where the value of \u03b2 is _______.", "response_choices": "No response choices provided for this question.", "answer": "No answer provided for this question.", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 2, "question": "An infinitely long thin wire, having a uniform charge density per unit length of 5 nC/m, is passing through a spherical shell of radius 1 m, as shown in the figure. A 10 nC charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is ______.", "response_choices": "No response choices provided for this question.", "answer": "No answer provided for this question.", "page_number": 15, "image_available": "yes", "question_subject": "physics"} +{"id": 3, "question": "A spherical soap bubble inside an air chamber at pressure P0 = 10^5 Pa has a certain radius so that the excess pressure inside the bubble is \u0394P = 144 Pa. Now, the chamber pressure is reduced to 8P0/27 so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure \u0394P in both the cases to be much smaller than the chamber pressure. The new excess pressure \u0394P' in Pa is _______.", "response_choices": "No response choices provided for this question.", "answer": "No answer provided for this question.", "page_number": 15, "image_available": "no", "question_subject": "physics"} +{"id": 14, "question": "The 8th bright fringe above the point O oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer (\u03bcm), is _______.", "response_choices": "Numerical Response Question", "answer": "0.8", "page_number": 16, "image_available": "yes", "question_subject": "physics"} +{"id": 15, "question": "The maximum speed in \u03bcm/s at which the 8th bright fringe will move is __________.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 16, "question": "If the collision occurs at time t0 = 0, the value of vcm/(a\u03c9) will be __________.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 17, "image_available": "yes", "question_subject": "physics"} +{"id": 17, "question": "If the collision occurs at time t0 = \u03c0/(2\u03c9), then the value of 4b2/a2 will be _________.", "response_choices": "", "answer": "", "page_number": 18, "image_available": "yes", "question_subject": "physics"} +{"id": 1, "question": "According to Bohr's model, the highest kinetic energy is associated with the electron in the", "response_choices": "(A) first orbit of H atom\n(B) first orbit of He+\n(C) second orbit of He+\n(D) second orbit of Li2+", "answer": "A", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 2, "question": "In a metal deficient oxide sample, MxY2O4 (M and Y are metals), M is present in both +2 and +3 oxidation states and Y is in +3 oxidation state. If the fraction of M2+ ions present in M is 1/3, the value of X is _____.", "response_choices": "(A) 0.25\t(B) 0.33\t(C) 0.67\t(D) 0.75", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} +{"id": 3, "question": "In the following reaction sequence, the major product Q is", "response_choices": "(A)\n\nCl\nCl\nCl\nCl\n\n(B)\n\nCl\nCl\n\nCl\n\n(C)\n\nCl\n\nCl\n\n(D)\n\nCl\nCl\n\nCl\nCl\nCl", "answer": "B", "page_number": 19, "image_available": "yes", "question_subject": "chemistry"} +{"id": 4, "question": "The species formed on fluorination of phosphorus pentachloride in a polar organic solvent are", "response_choices": "(A) [PF4]+[PF6]- and [PCl4]+[PF6]- (B) [PCl4]+[PCl3F2]- and [PCl2]+[PF6]- (C) PF5 and PCl5 (D) PF5 and PCl3", "answer": "B", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} +{"id": 5, "question": "An aqueous solution of hydrazine (N\u2082H\u2084) is electrochemically oxidized by O\u2082, thereby releasing chemical energy in the form of electrical energy. One of the products generated from the electrochemical reaction is N\u2082(g). Choose the correct statement(s) about the above process", "response_choices": "(A) OH\u207b ions react with N\u2082H\u2084 at the anode to form N\u2082(g) and water, releasing 4 electrons to the anode. (B) At the cathode, N\u2082H\u2084 breaks to N\u2082(g) and nascent hydrogen released at the electrode reacts with oxygen to form water. (C) At the cathode, molecular oxygen gets converted to OH\u207b. (D) Oxides of nitrogen are major by-products of the electrochemical process.", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "chemistry"} +{"id": 6, "question": "The option(s) with correct sequence of reagents for the conversion of P to Q is(are)", "response_choices": "(A) i) Lindlar's catalyst, H\u2082; ii) SnCl\u2082/HCl; iii) NaBH\u2084; iv) H\u2082O\u207b, (B) i) Lindlar's catalyst, H\u2082; ii) H\u2082O\u207b; iii) SnCl\u2082/HCl; iv) NaBH\u2084, (C) i) NaBH\u2084; ii) SnCl\u2082/HCl; iii) H\u2082O\u207b; iv) Lindlar's catalyst, H\u2082, (D) i) Lindlar's catalyst, H\u2082; ii) NaBH\u2084; iii) SnCl\u2082/HCl; iv) H\u2082O\u207b", "answer": "", "page_number": 22, "image_available": "yes", "question_subject": "chemistry"} +{"id": 7, "question": "The compound(s) having peroxide linkage is(are)", "response_choices": "(A) H\u2082S\u2082O\u2087, (B) H\u2082S\u2082O\u2088, (C) H\u2082S\u2082O\u2085, (D) H\u2082SO\u2085", "answer": "", "page_number": 22, "image_available": "no", "question_subject": "chemistry"} +{"id": 8, "question": "To form a complete monolayer of acetic acid on 1g of charcoal, 100 mL of 0.5 M acetic acid was used. Some of the acetic acid remained unadsrobed. To neutralize the unadsrobed acetic acid, 40 mL of 1 M NaOH solution was required. If each molecule of acetic acid occupies P \u00d7 10^-23 m^2 surface area on charcoal, the value of P is _____.", "response_choices": "No response choices provided for this type of question.", "answer": "Numerical response expected.", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 9, "question": "Vessel-1 contains w2 g of a non-volatile solute X dissolved in w1 g of water. Vessel-2 contains w2 g of another non-volatile solute Y dissolved in w1 g of water. Both the vessels are at the same temperature and pressure. The molar mass of X is 80% of that of Y. The van't Hoff factor for X is 1.2 times of that of Y for their respective concentrations. The elevation of boiling point for solution in Vessel-1 is _____ % of the solution in Vessel-2.", "response_choices": "No response choices provided for this type of question.", "answer": "Numerical response expected.", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 10, "question": "For a double strand DNA, one strand is given below: 5' A G T C A C G T A A G T C 3' The amount of energy required to split the double strand DNA into two single strands is _____ kcal mol^-1. [Given: Average energy per H-bond for A-T base pair = 1.0 kcal mol^-1, G-C base pair = 1.5 kcal mol^-1, and A-U base pair = 1.25 kcal mol^-1. Ignore electrostatic repulsion between the phosphate groups.]", "response_choices": "No response choices provided for this type of question.", "answer": "Numerical response expected.", "page_number": 23, "image_available": "no", "question_subject": "chemistry"} +{"id": 11, "question": "A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into Pb-206 while the rest of it remains undisintegrated. When the age of the sample is P x10^8 years, the ratio of mass of Pb-206 to that of U-238 in the sample is found to be 7. The value of P is _____. [Given: Half-life of U-238 is 4.5 x10^9 years; log\u20822 = 0.693]", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "physics"} +{"id": 12, "question": "Among [Co(CN)\u2086]\u2074\u207b, [Co(CO)\u2083(NO)], XeF\u2084, [PtCl\u2084]\u00b2\u207b, [PdCl\u2084]\u00b2\u207b, [IrCl\u2086]\u00b3\u207b, [Cu(CN)\u2084]\u00b3\u207b and P\u2084 the total number of species with tetrahedral geometry is _____.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 13, "question": "An organic compound P having molecular formula C\u2088H\u2088O\u2083 gives ferric chloride test and does not have intramolecular hydrogen bond. The compound P reacts with 3 equivalents of NH\u2082OH to produce oxime Q. Treatment of P with excess methyl iodide in the presence of KOH produces compound R as the major product. Reaction of R with excess iso-butylmagnesium bromide followed by treatment with H\u2083O\u207a gives compound S as the major product. The total number of methyl (\u2013CH\u2083) group(s) in compound S is _____.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} +{"id": 14, "question": "Sum of number of oxygen atoms in S and T is _____.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 15, "question": "The molecular weight of U is _____.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} +{"id": 16, "question": "The number of moles of potassium iodide required to produce two moles of P is _____.", "response_choices": "", "answer": "", "page_number": 26, "image_available": "no", "question_subject": "chemistry"} +{"id": 17, "question": "The number of zinc ions present in the molecular formula of Q is _____.", "response_choices": "", "answer": "", "page_number": 26, "image_available": "no", "question_subject": 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