{"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"}