{"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"}