{"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<f1. (D) If the wind blows from the source to the observer, f2<f1.", "answer": "AB", "page_number": 7, "image_available": "no", "question_subject": "physics"}
{"id": 9, "question": "The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is", "response_choices": "(A) BR/4, (B) BR/2, (C) BR, (D) 2BR", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "physics"}
{"id": 10, "question": "The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is", "response_choices": "(A) - \u03b3 BOR^2, (B) - \u03b3 BOR^2/2, (C) \u03b3 BOR^2/2, (D) \u03b3 BOR^2", "answer": "B", "page_number": 8, "image_available": "no", "question_subject": "physics"}
{"id": 11, "question": "The correct statement is", "response_choices": "(A) The nucleus 6Li can emit an alpha particle. (B) The nucleus 210Po can emit a proton. (C) Deuteron and alpha particle can undergo complete fusion. (D) The nuclei 70Zn and 34Se can undergo complete fusion.", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "physics"}
{"id": 12, "question": "The kinetic energy (in keV) of the alpha particle, when the nucleus 210Po at rest undergoes alpha decay, is", "response_choices": "(A) 5319 (B) 5422 (C) 5707 (D) 5818", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "physics"}
{"id": 13, "question": "The speed of the block when it reaches the point Q is", "response_choices": "A) 5 ms^-1, B) 10 ms^-1, C) 10\u221a3ms^-1, D) 20 ms^-1", "answer": "B", "page_number": 10, "image_available": "yes", "question_subject": "physics"}
{"id": 14, "question": "The magnitude of the normal reaction that acts on the block at the point Q is", "response_choices": "A) 7.5 N, B) 8.6 N, C) 11.5 N, D) 22.5 N", "answer": "A", "page_number": 10, "image_available": "yes", "question_subject": "physics"}
{"id": 15, "question": "If the direct transmission method with a cable of resistance 0.4 \u03a9 km\u207b\u00b9 is used, the power dissipation (in %) during transmission is", "response_choices": "(A) 20 (B) 30 (C) 40 (D) 50", "answer": "B", "page_number": 11, "image_available": "no", "question_subject": "physics"}
{"id": 16, "question": "In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is 1 : 10. If the power to the consumers has to be supplied at 200 V, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is", "response_choices": "(A) 200 : 1 (B) 150 : 1 (C) 100 : 1 (D) 50 : 1", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "physics"}
{"id": 17, "question": "Match List I with List II and select the correct answer using the codes given below the lists:", "response_choices": "List I: P. Boltzmann constant, Q. Coefficient of viscosity, R. Planck constant, S. Thermal conductivity\nList II: 1. [ML^2T^-1], 2. [ML^-1T^-1], 3. [MLT^-3K^-1], 4. [ML^2T^-2K^-1]\nCodes: (A) P-3, Q-1, R-2, S-4\n(B) P-3, Q-2, R-1, S-4\n(C) P-4, Q-2, R-1, S-3\n(D) P-4, Q-1, R-2, S-3", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "physics"}
{"id": 18, "question": "A right angled prism of refractive index \u03bc1 is placed in a rectangular block of refractive index \u03bc2, which is surrounded by a medium of refractive index \u03bc3, as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between \u03bc1, \u03bc2 and \u03bc3, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.", "response_choices": "List I / \u0938\u0942\u091a\u0940 I: P. e\u2192f, Q. e\u2192g, R. e\u2192h, S. e\u2192i\n\nList II / \u0938\u0942\u091a\u0940 II:\n1. \u03bc1 > \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"}