{"id": 1, "question": "A particle P starts from the point z\u2080 = 1 + 2i, where i = \u221a-1. It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z\u2081. From z\u2081 the particle moves \u221a2 units in the direction of the vector i + j and then it moves through an angle \u03c0/2 in anticlockwise direction on a circle with centre at origin, to reach a point z\u2082. The point z\u2082 is given by", "response_choices": "(A) 6 + 7i, (B) -7 + 6i, (C) 7 + 6i, (D) -6 + 7i", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "mathematics"}
{"id": 2, "question": "Let the function g : (-\u221e, \u221e) \u2192 (\u03c0/2, \u03c0/2) be given by g(u) = 2tan\u207b\u00b9(e\u1d58) - \u03c0/2. Then, g is", "response_choices": "(A) even and is strictly increasing in (0, \u221e), (B) odd and is strictly decreasing in (-\u221e, \u221e), (C) odd and is strictly increasing in (-\u221e, \u221e), (D) neither even nor odd, but is strictly increasing in (-\u221e, \u221e)", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "mathematics"}
{"id": 3, "question": "Consider a branch of the hyperbola x\u00b2 - 2y\u00b2 - 2\u221a2x - 4\u221a2y - 6 = 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is", "response_choices": "(A) 1 - 2/\u221a3, (B) \u221a(3/2) - 1, (C) 1 + 2/\u221a3, (D) 3/\u221a2 + 1", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "mathematics"}
{"id": 4, "question": "The area of the region between the curves y = \u221a(1+sinx/cosx) and y = \u221a(1-sinx/cosx) bounded by the lines x = 0 and x = \u03c0/4 is", "response_choices": "(A) \u222b\u2080^(\u03c0/2\u221a1+t\u00b2)dt/(1+t\u00b2\u221a1-t\u00b2), (B) \u222b\u2080^(\u03c0/2\u221a1-t\u00b2)4t/(1+t\u00b2\u221a1-t\u00b2) dt, (C) \u222b\u2080^(\u03c0/4\u221a1+t\u00b2)4t/(1+t\u00b2\u221a1-t\u00b2) dt, (D) \u222b\u2080^(\u03c0/1\u221a1-t\u00b2)t/(1+t\u00b2\u221a1-t\u00b2) dt", "answer": "B", "page_number": 1, "image_available": "yes", "question_subject": "mathematics"}
{"id": 5, "question": "Consider three points P = (- sin(\u03b2 - \u03b1), - cos \u03b2), Q = (cos(\u03b2 - \u03b1), sin \u03b2) and R = (cos(\u03b2 - \u03b1 + \u03b8), sin(\u03b2 - \u03b8)), where 0 < \u03b1 , \u03b2 , \u03b8 < \u03c0/4. Then,", "response_choices": "(A) P lies on the line segment RQ\n(B) Q lies on the line segment PR\n(C) R lies on the line segment QP\n(D) P, Q, R are non-collinear", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "mathematics"}
{"id": 6, "question": "An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is", "response_choices": "(A) 2, 4 or 8\t(B) 3, 6 or 9\t(C) 4 or 8\t(D) 5 or 10", "answer": "D", "page_number": 2, "image_available": "no", "question_subject": "mathematics"}
{"id": 7, "question": "Let two non-collinear unit vectors \u00e2 and b\u0302 form an acute angle. A point P moves so that at any time t the position vector OP\u20d7  (where O is the origin) is given by \u00e2 cost + b\u0302 sin t. When P is farthest from origin O , let M be the length of OP\u20d7  and \u00fb be the unit vector along OP\u20d7 . Then,", "response_choices": "(A) \u00fb = (\u00e2 + b\u0302) / |\u00e2 + b\u0302| and M = (1 + \u00e2 . b\u0302)^(1/2)\t(B) \u00fb = (\u00e2 - b\u0302) / |\u00e2 - b\u0302| and M = (1 + \u00e2 . b\u0302)^(1/2)\n(C) \u00fb = (\u00e2 + b\u0302) / |\u00e2 + b\u0302| and M = (1 + 2\u00e2 . b\u0302)^(1/2)\t(D) \u00fb = (\u00e2 - b\u0302) / |\u00e2 - b\u0302| and M = (1 + 2\u00e2 . b\u0302)^(1/2)", "answer": "A", "page_number": 2, "image_available": "no", "question_subject": "mathematics"}
{"id": 8, "question": "Let I = \u222b(e^x / e^4x + e^2x + 1) dx, J = \u222b(e^-x / e^-4x + e^-2x + 1) dx. Then, for an arbitrary constant C, the value of J - I equals", "response_choices": "(A) (1/2) log[((e^4x - e^2x + 1) / (e^4x + e^2x + 1))] + C\t(B) (1/2) log[((e^2x + e^x + 1) / (e^2x - e^x + 1))] + C\n(C) (1/2) log[((e^2x - e^x + 1) / (e^2x + e^x + 1))] + C\t(D) (1/2) log[((e^4x + e^2x + 1) / (e^4x - e^2x + 1))] + C", "answer": "C", "page_number": 2, "image_available": "no", "question_subject": "mathematics"}
{"id": 9, "question": "Let g(x) = log f(x) where f(x) is a twice differentiable positive function on (0, \u221e) such that f(x + 1) = x f(x). Then, for N = 1, 2, 3,..., g'(N + 1/2) - g'(1/2) =", "response_choices": "(A) -4{1 + 1/9 + 1/25 + ... + 1/(2N - 1)^2}, (B) 4{1 + 1/9 + 1/25 + ... + 1/(2N - 1)^2}, (C) -4{1 + 1/9 + 1/25 + ... + 1/(2N + 1)^2}, (D) 4{1 + 1/9 + 1/25 + ... + 1/(2N + 1)^2}", "answer": "(A)", "page_number": 3, "image_available": "no", "question_subject": "mathematics"}
{"id": 10, "question": "Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let b1 = a1, b2 = b1 + a2, b3 = b2 + a3 and b4 = b3 + a4. STATEMENT-1 : The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P. and STATEMENT-2 : The numbers b1, b2, b3, b4 are in H.P.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "(C)", "page_number": 3, "image_available": "no", "question_subject": "mathematics"}
{"id": 11, "question": "Let a, b, c, p, q be real numbers. Suppose \u03b1, \u03b2 are the roots of the equation x^2 + 2px + q = 0 and \u03b1, 1/\u03b2 are the roots of the equation ax^2 + 2bx + c = 0, where \u03b2^2 \u2208 {-1, 0, 1}. STATEMENT-1 : (p^2 - q)(b^2 - ac) \u2265 0 and STATEMENT-2 : b \u2260 pa or c \u2260 qa", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "(B)", "page_number": 3, "image_available": "no", "question_subject": "mathematics"}
{"id": 12, "question": "Consider L1 : 2x + 3y + p - 3 = 0, L2 : 2x + 3y + p + 3 = 0, where p is a real number, and C : x^2 + y^2 + 6x - 10y + 30 = 0. STATEMENT-1 : If line L1 is a chord of circle C, then line L2 is not always a diameter of circle C. and STATEMENT-2 : If line L1 is a diameter of circle C, then line L2 is not a chord of circle C.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 4, "image_available": "no", "question_subject": "mathematics"}
{"id": 13, "question": "Let a solution y = y(x) of the differential equation x\u221a(x^2 - 1) dy - y\u221a(y^2 - 1) dx = 0 satisfy y(2) = 2/\u221a3. STATEMENT-1 : y(x) = sec(sec^-1 x - \u03c0/6) and STATEMENT-2 : y(x) is given by 1/(2\u221a3 - \u221a(1 - x^2))", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 4, "image_available": "no", "question_subject": "mathematics"}
{"id": 14, "question": "Which of the following is true?", "response_choices": "(A) (2 + a)^2 f''(1) + (2 - a)^2 f''(-1) = 0 (B) (2 - a)^2 f''(1) - (2 + a)^2 f''(-1) = 0 (C) f'(1) f'(-1) = (2 - a)^2 (D) f'(1) f'(-1) = -(2 + a)^2", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "mathematics"}
{"id": 15, "question": "Which of the following is true?", "response_choices": "(A) f(x) is decreasing on (-1, 1) and has a local minimum at x = 1 (B) f(x) is increasing on (-1, 1) and has a local maximum at x = 1 (C) f(x) is increasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1 (D) f(x) is decreasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "mathematics"}
{"id": 16, "question": "Let g(x) = \u222b(0 to x) f'(t) / (1 + t^2) dt. Which of the following is true?", "response_choices": "(A) g'(x) is positive on (- \u221e, 0) and negative on (0, \u221e) (B) g'(x) is negative on (- \u221e, 0) and positive on (0, \u221e) (C) g'(x) changes sign on both (- \u221e, 0) and (0, \u221e) (D) g'(x) does not change sign on (- \u221e, \u221e)", "answer": "B", "page_number": 5, "image_available": "no", "question_subject": "mathematics"}
{"id": 17, "question": "The unit vector perpendicular to both L1 and L2 is", "response_choices": "A) -i + 7j + 7k/\u221a99, B) -i - 7j + 5k/5\u221a3, C) -i + 7j + 5k/5\u221a3, D) 7i - 7j - k/\u221a99", "answer": "B", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"}
{"id": 18, "question": "The shortest distance between L1 and L2 is", "response_choices": "A) 0, B) 17/\u221a3, C) 41/5\u221a3, D) 17/5\u221a3", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"}
{"id": 19, "question": "The distance of the point (1, 1, 1) from the plane passing through the point (-1, -2, -1) and whose normal is perpendicular to both the lines L1 and L2 is", "response_choices": "A) 2/\u221a75, B) 7/\u221a75, C) 13/\u221a75, D) 23/\u221a75", "answer": "C", "page_number": 6, "image_available": "yes", "question_subject": "mathematics"}
{"id": 20, "question": "Consider the lines given by L1 : x + 3y - 5 = 0 L2 : 3x - ky - 1 = 0 L3 : 5x + 2y - 12 = 0 Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) L1, L2, L3 are concurrent, if (B) One of L1, L2, L3 is parallel to at least one of the other two, if (C) L1, L2, L3 form a triangle, if (D) L1, L2, L3 do not form a triangle, if (p) k = -9 (q) k = - 6/5 (r) k = 5/6 (s) k = 5", "answer": "p:O, q:O, r:O, s:*, A:O, B:*, C:O, D:*", "page_number": 7, "image_available": "yes", "question_subject": "mathematics"}
{"id": 21, "question": "Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.", "response_choices": "(A) The minimum value of x^2 + 2x + 4/x + 2 is (B) Let A and B be 3 x 3 matrices of real numbers, where A is symmetric, B is skew-symmetric, and (A + B) (A - B) = (A - B) (A + B). If (AB)' = (-1)^k AB, where (AB)' is the transpose of the matrix AB, then the possible values of k are (C) Let a = log\u2083 2, log\u2082 2. An integer k satisfying 1 < 2^(-k + 3 - a) < 2, must be less than (D) If sin \u03b8 = cos \u03c6, then the possible values of 1/\u03c0 (\u03b8 + \u03c6 - \u03c0/2) are (p) 0 (q) 1 (r) 2 (s) 3", "answer": "p:O, q:*, r:*, s:O, A:O, B:O, C:*, D:*", "page_number": 7, "image_available": "yes", "question_subject": "mathematics"}
{"id": 22, "question": "Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the 4 \u00d7 4 matrix given in the ORS.", "response_choices": "Column I: (A) The number of permutations containing the word ENDEA is, (B) The number of permutations in which the letter E occurs in the first and the last positions is, (C) The number of permutations in which none of the letters D, L, N occurs in the last five positions is, (D) The number of permutations in which the letters A, E, O occur only in odd positions is\nColumn II: (p) 5!, (q) 2 \u00d7 5!, (r) 7 \u00d7 5!, (s) 21 \u00d7 5!", "answer": "A: p, B: s, C: r, D: q", "page_number": 8, "image_available": "no", "question_subject": "mathematics"}
{"id": 23, "question": "Consider a system of three charges q, q and 2q/3 placed at points A, B and C, respectively, as shown in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60\u00b0\n\nFigure:\n\n(A) The electric field at point O is q/8\u03c0\u03b5\u2080R\u00b2 directed along the negative x-axis\n(B) The potential energy of the system is zero\n(C) The magnitude of the force between the charges at C and B is q\u00b2/54\u03c0\u03b5\u2080R\u00b2\n(D) The potential at point O is q/12\u03c0\u03b5\u2080R", "response_choices": "(A), (B), (C), (D)", "answer": "(C)", "page_number": 8, "image_available": "yes", "question_subject": "physics"}
{"id": 24, "question": "A radioactive sample S1 having an activity of 5 \u03bcCi has twice the number of nuclei as another sample S2 which has an activity of 10 \u03bcCi. The half lives of S1 and S2 can be", "response_choices": "(A) 20 years and 5 years, respectively\n(B) 20 years and 10 years, respectively\n(C) 10 years each\n(D) 5 years each", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "physics"}
{"id": 25, "question": "A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is", "response_choices": "(A) \u221a(3\u03c0\u00f750) m/s\n(B) -\u221a(3\u03c0\u00f750) m/s\n(C) \u221a(3\u03c0\u00f750) m/s\n(D) -\u221a(3\u03c0\u00f750) m/s", "answer": "A", "page_number": 9, "image_available": "yes", "question_subject": "physics"}
{"id": 26, "question": "A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4 k, respectively (see figure 1). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is", "response_choices": "A) 4, B) 2, C) 1/2, D) 1/4", "answer": "C", "page_number": 10, "image_available": "yes", "question_subject": "physics"}
{"id": 27, "question": "A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle \u03b8 at which the speed of the bob is half of that at A, satisfies", "response_choices": "A) \u03b8 = \u03c0/4, B) \u03c0/4 < \u03b8 < \u03c0/2, C) \u03c0/2 < \u03b8 < 3\u03c0/4, D) 3\u03c0/4 < \u03b8 < \u03c0", "answer": "D", "page_number": 10, "image_available": "yes", "question_subject": "physics"}
{"id": 28, "question": "A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve,", "response_choices": "(A) air from end 1 flows towards end 2. No change in the volume of the soap bubbles\n(B) air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases\n(C) no change occurs\n(D) air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases", "answer": "B", "page_number": 11, "image_available": "yes", "question_subject": "physics"}
{"id": 29, "question": "A vibrating string of certain length \u2113 under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in Hz is", "response_choices": "(A) 344\t(B) 336\t(C) 117.3\t(D) 109.3", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "physics"}
{"id": 30, "question": "A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K = 2. The level of liquid is d/3 initially. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is", "response_choices": "(A) 6\u03b5oR / 5d+3Vt, (B) (15d+9Vt)\u03b5oR / 2d^2-3dVt-9V^2t^2, (C) 6\u03b5oR / 5d-3Vt, (D) (15d-9Vt)\u03b5oR / 2d^2+3dVt-9V^2t^2", "answer": "A", "page_number": 12, "image_available": "yes", "question_subject": "physics"}
{"id": 31, "question": "A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are no, no/2, no/6 and no/8, respectively. The angle of incidence \u03b8 for which the beam just misses entering Region IV is", "response_choices": "(A) sin^-1(3/4), (B) sin^-1(1/5), (C) sin^-1(1/4), (D) sin^-1(1/3)", "answer": "B", "page_number": 12, "image_available": "yes", "question_subject": "physics"}
{"id": 32, "question": "STATEMENT-1\nFor an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.\nand\nSTATEMENT-2\nIf the observer and the object are moving at velocities V1 and V2 respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is V2 - V1.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "physics"}
{"id": 33, "question": "STATEMENT-1\nIt is easier to pull a heavy object than to push it on a level ground.\nand\nSTATEMENT-2\nThe magnitude of frictional force depends on the nature of the two surfaces in contact.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 13, "image_available": "no", "question_subject": "physics"}
{"id": 34, "question": "STATEMENT-1\n\nFor practical purposes, the earth is used as a reference at zero potential in electrical circuits.\n\nand\n\nSTATEMENT-2\n\nThe electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by Q/4\u03c0\u03b50R.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 14, "image_available": "no", "question_subject": "physics"}
{"id": 35, "question": "STATEMENT-1\n\nThe sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.\n\nand\n\nSTATEMENT-2\n\nSoft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\n(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\n(C) STATEMENT-1 is True, STATEMENT-2 is False\n(D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "C", "page_number": 14, "image_available": "no", "question_subject": "physics"}
{"id": 36, "question": "The electric field at r = R is", "response_choices": "(A) independent of a, (B) directly proportional to a, (C) directly proportional to a^2, (D) inversely proportional to a", "answer": "A", "page_number": 15, "image_available": "yes", "question_subject": "physics"}
{"id": 37, "question": "For a = 0, the value of d (maximum value of \u03c1 as shown in the figure) is", "response_choices": "(A) 3Ze/(4\u03c0R^3), (B) 3Ze/(\u03c0R^3), (C) 4Ze/(3\u03c0R^3), (D) Ze/(3\u03c0R^3)", "answer": "B", "page_number": 15, "image_available": "yes", "question_subject": "physics"}
{"id": 38, "question": "The electric field within the nucleus is generally observed to be linearly dependent on r. This implies", "response_choices": "(A) a = 0, (B) a = R/2, (C) a = R, (D) a = 2R/3", "answer": "C", "page_number": 15, "image_available": "yes", "question_subject": "physics"}
{"id": 39, "question": "The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is", "response_choices": "(A) -kx, (B) -2kx, (C) -2kx/3, (D) 4kx/3", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"}
{"id": 40, "question": "The centre of mass of the disk undergoes simple harmonic motion with angular frequency \u03c9 equal to", "response_choices": "(A) \u221a(k/M), (B) \u221a(2k/M), (C) \u221a(2k/3M), (D) \u221a(4k/3M)", "answer": "D", "page_number": 16, "image_available": "yes", "question_subject": "physics"}
{"id": 41, "question": "The maximum value of V0 for which the disk will roll without slipping is", "response_choices": "(A) \u03bcg\u221a(k/M), (B) \u03bcg\u221a(2k/M), (C) \u03bcg\u221a(3M/k), (D) \u03bcg\u221a(5M/2k)", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"}
{"id": 42, "question": "Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4x4 matrix given in the ORS.", "response_choices": "A) Potential energy of a simple pendulum (y axis) as a function of displacement (x axis), B) Displacement (y axis) as a function of time (x axis) for a one dimensional motion at zero or constant acceleration when the body is moving along the positive x-direction, C) Range of a projectile (y axis) as a function of its velocity (x axis) when projected at a fixed angle, D) The square of the time period (y axis) of a simple pendulum as a function of its length (x axis)", "answer": "B, C, D", "page_number": 17, "image_available": "yes", "question_subject": "physics"}
{"id": 43, "question": "An optical component and an object S placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "A, B, C, D. Matrix response with options p, q, r, s", "answer": "p, q, r, s", "page_number": 18, "image_available": "yes", "question_subject": "physics"}
{"id": 44, "question": "Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "A) ... B) ... C) ... D) ...", "answer": "A: q, B: r and q, C: p and s, D: s", "page_number": 19, "image_available": "yes", "question_subject": "physics"}
{"id": 45, "question": "The correct stability order for the following species is", "response_choices": "(A) (II) > (IV) > (I) > (III), (B) (I) > (II) > (III) > (IV), (C) (II) > (I) > (IV) > (III), (D) (I) > (III) > (II) > (IV)", "answer": "D", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"}
{"id": 46, "question": "Cellulose upon acetylation with excess acetic anhydride/H\u2082SO\u2084 (catalytic) gives cellulose triacetate whose structure is", "response_choices": "Options shown as molecular structure diagrams (A), (B), (C), and (D)", "answer": "A", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"}
{"id": 47, "question": "In the following reaction sequence, the correct structures of E, F and G are", "response_choices": "(A) E = Ph* CH3, F = Ph* O Na, G = CH3; (B) E = Ph* CH3, F = Ph* ONa, G = CH3; (C) E = Ph* CH3, F = Ph* O Na, G = CH3; (D) E = Ph* CH3, F = Ph* ONa, G = CH3I", "answer": "C", "page_number": 21, "image_available": "yes", "question_subject": "chemistry"}
{"id": 48, "question": "Among the following, the coloured compound is", "response_choices": "(A) CuCl; (B) K3 [Cu(CN)4]; (C) CuF2; (D) [Cu(CH3CN)4]BF4", "answer": "C", "page_number": 21, "image_available": "no", "question_subject": "chemistry"}
{"id": 49, "question": "Both [Ni(CO)4] and [Ni(CN)4]2- are diamagnetic. The hybridisations of nickel in these complexes, respectively, are", "response_choices": "(A) sp3, sp3; (B) sp3, dsp2; (C) dsp2, sp3; (D) dsp2, dsp2", "answer": "B", "page_number": 21, "image_available": "no", "question_subject": "chemistry"}
{"id": 50, "question": "The IUPAC name of [Ni(NH3)4] [NiCl4] is", "response_choices": "(A) Tetrachloronickel (II) - tetraammineniickel (II), (B) Tetraammineniickel (II) - tetrachloronickel (II), (C) Tetraammineniickel (II) - tetrachloronickelate (II), (D) Tetrachloronickel (II) - tetraammineniickelate (I)", "answer": "C", "page_number": 22, "image_available": "no", "question_subject": "chemistry"}
{"id": 51, "question": "Electrolysis of dilute aqueous NaCl solution was carried out by passing 10 milli ampere current. The time required to liberate 0.01 mol of H2 gas at the cathode is (1 Faraday = 96500 C mol^-1)", "response_choices": "(A) 9.65 \u00d7 10^4 sec, (B) 19.3 \u00d7 10^4 sec, (C) 28.95 \u00d7 10^4 sec, (D) 38.6 \u00d7 10^4 sec", "answer": "B", "page_number": 22, "image_available": "no", "question_subject": "chemistry"}
{"id": 52, "question": "Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is", "response_choices": "(A) CH3(CH2)15 N^+(CH3)3 Br^-, (B) CH3(CH2)11 OSO3^- Na^+, (C) CH3(CH2)9 COO^- Na^+, (D) CH3(CH2)11 N^+(CH3)3 Br^-", "answer": "A", "page_number": 22, "image_available": "no", "question_subject": "chemistry"}
{"id": 53, "question": "Solubility product constants (Ksp) of salts of types MX, MX2 and M3X at temperature 'T' are 4.0 x 10^-8, 3.2 x 10^-14 and 2.7 x 10^-16, respectively. Solubilities (mol dm^-3) of the salts at temperature 'T' are in the order", "response_choices": "(A) MX > MX2 > M3X, (B) M3X > MX2 > MX, (C) MX2 > M3X > MX, (D) MX > M3X > MX2", "answer": "D", "page_number": 22, "image_available": "no", "question_subject": "chemistry"}
{"id": 54, "question": "STATEMENT-1 : Aniline on reaction with NaNO2/HCl at 0 \u00b0C followed by coupling with \u03b2-napththol gives a dark blue coloured precipitate. and STATEMENT-2 : The colour of the compound formed in the reaction of aniline with NaNO2/HCl at 0 \u00b0C followed by coupling with \u03b2-napththol is due to the extended conjugation.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "D", "page_number": 23, "image_available": "no", "question_subject": "chemistry"}
{"id": 55, "question": "STATEMENT-1 : [Fe(H2O)6NO]SO4 is paramagnetic. and STATEMENT-2 : The Fe in [Fe(H2O)6 NO]SO4 has three unpaired electrons.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "A", "page_number": 23, "image_available": "no", "question_subject": "chemistry"}
{"id": 56, "question": "STATEMENT-1 : The geometrical isomers of the complex [M(NH3)4Cl2] are optically inactive. and STATEMENT-2 : Both geometrical isomers of the complex [M(NH3)4Cl2] possess axis of symmetry.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "B", "page_number": 23, "image_available": "no", "question_subject": "chemistry"}
{"id": 57, "question": "STATEMENT-1 : There is a natural asymmetry between converting work to heat and converting heat to work. and STATEMENT-2 : No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.", "response_choices": "(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1, (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1, (C) STATEMENT-1 is True, STATEMENT-2 is False, (D) STATEMENT-1 is False, STATEMENT-2 is True", "answer": "(A)", "page_number": 24, "image_available": "no", "question_subject": "physics"}
{"id": 58, "question": "Compound H is formed by the reaction of", "response_choices": "(A) Ph CH3 + PhMgBr, (B) Ph CH3 + PhCH2 MgBr, (C) Ph H + PhCH2MgBr, (D) Ph H + Ph MgBr", "answer": "(B)", "page_number": 24, "image_available": "yes", "question_subject": "chemistry"}
{"id": 59, "question": "The structure of compound I is", "response_choices": "(A) Ph CH3, (B) H3C Ph, (C) Ph CH3, (D) H3C CH3", "answer": "A", "page_number": 25, "image_available": "yes", "question_subject": "chemistry"}
{"id": 60, "question": "The structures of compounds J, K and L, respectively, are", "response_choices": "(A) PhCOCH3, PhCH2COCH3 and PhCH2COO-K+, (B) PhCHO, PhCH2CHO and PhCOO-K+, (C) PhCOCH3, PhCH2CHO and CH3COO-K+, (D) PhCHO, PhCOCH3 and PhCOO-K+", "answer": "D", "page_number": 25, "image_available": "no", "question_subject": "chemistry"}
{"id": 61, "question": "The number of atoms in this HCP unit cell is", "response_choices": "(A) 4, (B) 6, (C) 12, (D) 17", "answer": "B", "page_number": 26, "image_available": "no", "question_subject": "chemistry"}
{"id": 62, "question": "The volume of this HCP unit cell is", "response_choices": "(A) 24\u221a2 r^3, (B) 16\u221a2 r^3, (C) 12\u221a2 r^3, (D) (64)/(3\u221a3) r^3", "answer": "A", "page_number": 26, "image_available": "no", "question_subject": "chemistry"}
{"id": 63, "question": "The empty space in this HCP unit cell is", "response_choices": "(A) 74%, (B) 47.6%, (C) 32%, (D) 26%", "answer": "D", "page_number": 26, "image_available": "no", "question_subject": "chemistry"}
{"id": 64, "question": "Match the compounds in Column I with their characteristic test(s)/reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.", "response_choices": "A, B, C, D - Matrix Response", "answer": "B: C, D; C: A, B, C; D: A, B, D OR A: B, C; B: A, B; C: A, B, C; D: A", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"}
{"id": 65, "question": "Match the conversions in Column I with the type(s) of reaction(s) given in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS", "response_choices": "(A) PbS -> PbO, (B) CaCO3 -> CaO, (C) ZnS -> Zn, (D) Cu2S -> Cu, (p) roasting, (q) calcination, (r) carbon reduction, (s) self reduction", "answer": "A:p, B:q, C:r,s, D:s", "page_number": 28, "image_available": "yes", "question_subject": "chemistry"}
{"id": 66, "question": "Match the entries in Column I with the correctly related quantum number(s) in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS", "response_choices": "(A) Orbital angular momentum of the electron in a hydrogen-like atomic orbital, (B) A hydrogen-like one-electron wave function obeying Pauli principle, (C) Shape, size and orientation of hydrogen-like atomic orbitals, (D) Probability density of electron at the nucleus in hydrogen-like atom, (p) Principal quantum number, (q) Azimuthal quantum number, (r) Magnetic quantum number, (s) Electron spin quantum number", "answer": "A:q,r, B:p,q,r,s, C:p,q,r, D:p,s", "page_number": 28, "image_available": "yes", "question_subject": "physics"}