| {"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"} | |