| {"id": 1, "question": "Let f(x) be a continuously differentiable function on the interval (0, \u221e) such that f(1) = 2 and lim(t^10 f(x) - x^10 f(t) / t^9 - x^9) = 1 for each x > 0. Then, for all x > 0, f(x) is equal to", "response_choices": "(A) 31/11x^10 + 9/11*x^10, (B) 9/11x^10 + 13/11*x^10, (C) -9/11x^10 + 31/11*x^10, (D) 13/11x^10 - 9/11*x^10", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 2, "question": "A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question, he gives the correct answer. Assume that the probability of the student giving the correct answer for a question, given that he has guessed it, is 1/2. Also assume that the probability of the answer for a question being guessed, given that the student's answer is correct, is 1/6. Then the probability that the student knows the answer of a randomly chosen question is", "response_choices": "(A) 1/12, (B) 1/7, (C) 5/7, (D) 5/12", "answer": "C", "page_number": 1, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 3, "question": "Let \u03c0/2 < x < \u03c0 be such that cot x = -5/\u221a11. Then (sin(11x/2)(sin 6x - cos 6x) + cos(11x/2)(sin 6x + cos 6x)) is equal to", "response_choices": "(A) \u221a11-1/2\u221a3, (B) \u221a11+1/2\u221a3, (C) \u221a11+1/3\u221a2, (D) \u221a11-1/3\u221a2", "answer": "(B)", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 4, "question": "Consider the ellipse x^2/9 + y^2/4 = 1. Let S(p, q) be a point in the first quadrant such that p^2/9 + q^2/4 > 1. Two tangents are drawn from S to the ellipse, of which one meets the ellipse at one end point of the minor axis and the other meets the ellipse at a point T in the fourth quadrant. Let R be the vertex of the ellipse with positive x-coordinate and O be the center of the ellipse. If the area of the triangle \u0394ORT is 3/2, then which of the following options is correct?", "response_choices": "(A) q = 2, p = 3\u221a3, (B) q = 2, p = 4\u221a3, (C) q =1, p = 5\u221a3, (D) q =1, p = 6\u221a3", "answer": "(C)", "page_number": 2, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 5, "question": "Let S = {a + b\u221a2 : a, b \u2208 \u2124}, T1 = {(-1 + \u221a2)^n : n \u2208 \u2115}, and T2 = {(1 + \u221a2)^n : n \u2208 \u2115}. Then which of the following statements is (are) TRUE?", "response_choices": "(A) \u2124 \u22c3 T1 \u22c3 T2 \u2286 S, (B) T1 \u22c2 (0, 1/2024) = \u2205, where \u2205 denotes the empty set, (C) T2 \u22c2 (2024, \u221e) \u2260 \u2205, (D) For any given a, b \u2208 \u2124, cos(\u03c0(a + b\u221a2)) + i sin(\u03c0(a + b\u221a2)) \u2208 \u2124, if and only if b = 0, where i = \u221a-1.", "answer": "A,D", "page_number": 3, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 6, "question": "Let R^2 denote R\u00d7R. Let S = {(a,b,c) : a,b,c \u2208 R and ax^2 + 2bxy + cy^2 > 0 for all (x, y) \u2208 R^2 \u2212 {(0,0)}}. Then which of the following statements is (are) TRUE?", "response_choices": "(A) (2, -2, 6) \u2208 S\n\n(B) If (3,b, 1/12) \u2208 S, then | 2b | < 1.\n\n(C) For any given (a,b,c) \u2208 S, the system of linear equations\nax + by = 1\nbx + cy = \u22121\nhas a unique solution.\n\n(D) For any given (a,b,c) \u2208 S, the system of linear equations\n(a + 1)x + by = 0\nbx + (c + 1)y = 0\nhas a unique solution.", "answer": "No selected answer", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 7, "question": "Let R^3 denote the three-dimensional space. Take two points P = (1, 2, 3) and Q = (4, 2, 7). Let dist(X,Y) denote the distance between two points X and Y in R^3. Let S = {X \u2208 R^3 : (dist(X, P))^2 \u2212 (dist(X, Q))^2 = 50} and T = {Y \u2208 R^3 : (dist(Y, Q))^2 \u2212 (dist(Y, P))^2 = 50}. Then which of the following statements is (are) TRUE?", "response_choices": "(A) There is a triangle whose area is 1 and all of whose vertices are from S.\n(B) There are two distinct points L and M in T such that each point on the line segment LM is also in T.\n(C) There are infinitely many rectangles of perimeter 48, two of whose vertices are from S and the other two vertices are from T.\n(D) There is a square of perimeter 48, two of whose vertices are from S and the other two vertices are from T.", "answer": "No selected answer", "page_number": 4, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 8, "question": "Let a = 3\u221a2 and b = 5\u221a(6/6). If x, y \u2208 \u211d are such that 3x + 2y = log\u2082 (18)\u2075 and 2x \u2212 y = log\u2082 (\u221a1080), then 4x + 5y is equal to _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 9, "question": "Let f(x) = x\u2074 + \u03b1x\u00b3 + \u03b2x\u00b2 + c be a polynomial with real coefficients such that f(1) = \u22129. Suppose that t\u221a3 is a root of the equation 4x\u00b3 + 3\u03b1x\u00b2 + 2\u03b2x = 0, where i = \u221a\u22121. If \u03b1\u2081, \u03b1\u2082, \u03b1\u2083, and \u03b1\u2084 are all the roots of the equation f(x) = 0, then |\u03b1\u2081|\u00b2 + |\u03b1\u2082|\u00b2 + |\u03b1\u2083|\u00b2 + |\u03b1\u2084|\u00b2 is equal to _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 10, "question": "Let S = {A = (0 1 c) | 1 a d |: a, b, c, d, e \u2208 {0, 1} and |A| \u2208 {\u22121, 1}}, where |A| denotes the | 1 b e| determinant of A. Then the number of elements in S is _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 11, "question": "A group of 9 students, s\u2081, s\u2082, . . . , s\u2089, is to be divided to form three teams X, Y , and Z of sizes 2, 3, and 4, respectively. Suppose that s\u2081 cannot be selected for the team X, and s\u2082 cannot be selected for the team Y . Then the number of ways to form such teams, is _______.", "response_choices": "", "answer": "", "page_number": 5, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 12, "question": "Let OP = (\u03b1\u22121)i + j + k, OQ = i + (\u03b2\u22121)j + k and OR = i + j + (1/2)k be three vectors, where \u03b1, \u03b2 \u2208 R\u2212{0} and O denotes the origin. If (OP\u00d7OQ) \u00b7 OR = 0 and the point (\u03b1, \u03b2, 2) lies on the plane 3x + 3y - z + l = 0, then the value of l is _______.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 13, "question": "Let X be a random variable, and let P(X = x) denote the probability that X takes the value x. Suppose that the points (x, P(X = x)), x = 0,1,2,3,4, lie on a fixed straight line in the xy-plane, and P(X = x) = 0 for all x \u2208 R\u2212{0,1,2,3,4}. If the mean of X is 5/2, and the variance of X is \u03b1, then the value of 24\u03b1 is _______.", "response_choices": "", "answer": "", "page_number": 6, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 14, "question": "Let \u03b1 and \u03b2 be the distinct roots of the equation x^2 + x - 1 = 0. Consider the set T = {1, \u03b1, \u03b2}. For a 3\u00d73 matrix M = (aij)i\u22643,j\u22643, define Ri = ai1 + ai2 + ai3 and Cj = a1j + a2j + a3j for i = 1, 2, 3 and j = 1, 2, 3.", "response_choices": "(P) The number of matrices M = (aij)i\u22643,j\u22643 with all entries in T such that Ri = Cj = 0 for all i, j, is (1) / (Q) The number of symmetric matrices M = (aij)i\u22643,j\u22643 with all entries in T such that Cj = 0 for all j, is (2) 12 / (R) Let M = (aij)i\u22643,j\u22643 be a skew symmetric matrix such that aij \u2208 T for i > j. Then the number of elements in the set [[x], [y], [z]]: x, y, z \u2208 \u211d, M [y] = [0], [z] [-a23]] is (3) infinite / (S) Let M = (aij)i\u22643,j\u22643 be a matrix with all entries in T such that Ri = 0 for all i. Then the absolute value of the determinant of M is (4) 6", "answer": "(5) 0", "page_number": 7, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 15, "question": "Let the straight line y = 2x touch a circle with center (0, \u03b1), \u03b1 > 0, and radius r at a point A. Let B be the point on the circle such that the line segment AB is a diameter of the circle. Let \u03b1 + r = 5 + \u221a5. Match each entry in List-I to the correct entry in List-II.", "response_choices": "(P) \u03b1 equals, (Q) r equals, (R) A equals, (S) B equals", "answer": "(C) (P) \u2192 (4) (Q) \u2192 (2) (R) \u2192 (5) (S) \u2192 (3)", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 16, "question": "Let y \u2208 \u211d be such that the lines L\u2081: x + 11/1 = y + 21/2 = z + 29/3 and L\u2082: x + 16/3 = y + 11/2 = z + 4/y intersect. Let R\u2080 be the point of intersection of L\u2081 and L\u2082. Let O = (0, 0, 0), and \u1e45 denote a unit normal vector to the plane containing both the lines L\u2081 and L\u2082. Match each entry in List-I to the correct entry in List-II.", "response_choices": "(P) y equals (Q) A possible choice for \u1e45 is (R) OR\u2080 equals (S) A possible value of OR\u2080 \u00b7 \u1e45 is", "answer": "(P) \u2192 (3), (Q) \u2192 (4), (R) \u2192 (1), (S) \u2192 (2)", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 17, "question": "Let f : R \u2192 R and g : R \u2192 R be the functions defined by f(x) = {x | x | sin(1/x), x \u2260 0, 0, x = 0} and g(x) = {1\u22122x, 0 \u2264 x \u2264 1/2, 0, otherwise}. Let a, b, c, d \u2208 R. Define the function h : R \u2192 R by h(x) = a f(x) + b [g(x) + g(1/2 - x)] + c (x - g(x)) + d g(x), x \u2208 R. Match each entry in List-I to the correct entry in List-II.", "response_choices": "List-I \n(P) If a = 0, b = 1, c = 0, and d = 0, then \n(Q) If a = 1, b = 0, c = 0, and d = 0, then \n(R) If a = 0, b = 0, c = 1, and d = 0, then \n(S) If a = 0, b = 0, c = 0, and d = 1, then\n\nList-II\n(1) h is one-one.\n(2) h is onto.\n(3) h is differentiable on R.\n(4) the range of h is [0,1].\n(5) the range of h is {0,1}.", "answer": "(A) (P) \u2192 (4) (Q) \u2192 (3) (R) \u2192 (1) (S) \u2192 (2)", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 1, "question": "A dimensionless quantity is constructed in terms of electronic charge e, permittivity of free space \u03b50, Planck's constant h, and speed of light c. If the dimensionless quantity is written as e\u1d45\u03b50\u1d47h\u1d9cc\u1d48 and n is a non-zero integer, then (\u03b1, \u03b2, \u03b3, \u03b4) is given by", "response_choices": "(A) (2n, \u2212n, \u2212n, \u2212n), (B) (n, \u2212n, \u22122n, \u2212n), (C) (n, \u2212n, \u2212n, \u22122n), (D) (2n, \u2212n, \u22122n, \u22122n)", "answer": "(C) (n, \u2212n, \u2212n, \u22122n)", "page_number": 11, "image_available": "no", "question_subject": "physics"} | |
| {"id": 2, "question": "An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field B. The magnitude of the line integral \u222b B\u20d7 \u22c5d\u2113\u20d7 along a straight line from the point (\u2212\u221a3a, a, 0) to (a, a, 0) is given by [\u03bc0 is the magnetic permeability of free space.]", "response_choices": "(A) 7\u03bc0I/24, (B) 7\u03bc0I/12, (C) \u03bc0I/8, (D) \u03bc0I/6", "answer": "(C) \u03bc0I/8", "page_number": 11, "image_available": "no", "question_subject": "physics"} | |
| {"id": 3, "question": "Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [\u03b50 is the permittivity of free space.]", "response_choices": "(A) q\u00b2/(4\u03c0\u03b50R\u00b3m), (B) q\u00b2/(32\u03c0\u03b50R\u00b3m), (C) q\u00b2/(8\u03c0\u03b50R\u00b3m), (D) q\u00b2/(16\u03c0\u03b50R\u00b3m)", "answer": "(C) q\u00b2/(8\u03c0\u03b50R\u00b3m)", "page_number": 11, "image_available": "no", "question_subject": "physics"} | |
| {"id": 4, "question": "A block of mass 5 kg moves along the x-direction subject to the force F = (\u221220x + 10) N, with the value of x in metre. At time t = 0 s, it is at rest at position x = 1 m. The position and momentum of the block at t = (\u03c0/4) s are", "response_choices": "(A) \u22120.5 m, 5 kg m/s, (B) 0.5 m, 0 kg m/s, (C) 0.5 m, \u22125 kg m/s, (D) \u22121 m, 5 kg m/s", "answer": "(A) \u22120.5 m, 5 kg m/s", "page_number": 11, "image_available": "no", "question_subject": "physics"} | |
| {"id": 5, "question": "A particle of mass m is moving in a circular orbit under the influence of the central force F(r) = -kr, corresponding to the potential energy V(r) = kr^2/2, where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L = nh, where h = h/(2\u03c0), h is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?", "response_choices": "(A) r^2 = nh \u221a(k/mk) (B) v^2 = nh (k/m) (C) L = (k/mr^2) \u221a(m) (D) E = nh (k/2\u221am)", "answer": "D", "page_number": 12, "image_available": "no", "question_subject": "physics"} | |
| {"id": 6, "question": "Two uniform strings of mass per unit length \u03bc and 4\u03bc, and length L and 2L, respectively, are joined at point O, and tied at two fixed ends P and Q, as shown in the figure. The strings are under a uniform tension T. If we define the frequency v0 = 1/(2L) \u221a(T/\u03bc), which of the following statement(s) is(are) correct?", "response_choices": "(A) With a node at O, the minimum frequency of vibration of the composite string is v0. (B) With an antinode at O, the minimum frequency of vibration of the composite string is 2v0. (C) When the composite string vibrates at the minimum frequency with a node at O, it has 6 nodes, including the end nodes. (D) No vibrational mode with an antinode at O is possible for the composite string.", "answer": "", "page_number": 13, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 7, "question": "A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of h (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?", "response_choices": "(A) For n = 1.42, h = 50 cm. (B) For n = 1.35, h = 36 cm. (C) For n = 1.45, h = 65 cm. (D) For n = 1.48, h = 85 cm.", "answer": "", "page_number": 13, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 8, "question": "The specific heat capacity of a substance is temperature dependent and is given by the formula C = kT, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from \u221273 \u00b0C to 27 \u00b0C is nk, the value of n is", "response_choices": "No response choices provided.", "answer": "To be entered as a non-negative integer", "page_number": 14, "image_available": "no", "question_subject": "physics"} | |
| {"id": 9, "question": "A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass M and radius R/2 is fixed to the motor's thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \u03c9. If the angular speed at which the large disc rotates is \u03c9/n, then the value of n is", "response_choices": "No response choices provided.", "answer": "To be entered as a non-negative integer", "page_number": 14, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 10, "question": "A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio r = IA/IB of the intensities of light is 2. If a set of two polaroids having 45\u00b0 angle between their pass-axes is placed just before point B, then the new value of r will be", "response_choices": "No response choices provided.", "answer": "To be entered as a non-negative integer", "page_number": 14, "image_available": "no", "question_subject": "physics"} | |
| {"id": 1, "question": "A source (S) of sound has frequency 240 Hz. When the observer (O) and the source move towards each other at a speed v with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be 288 Hz. However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be n Hz. The value of n is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 2, "question": "Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height h in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If H = (49/4) h, then the ratio t1/t2 is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "no", "question_subject": "physics"} | |
| {"id": 3, "question": "A thin uniform rod of length l, and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.", "response_choices": "No response choices provided", "answer": "No answer provided", "page_number": 15, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 14, "question": "One mole of a monatomic ideal gas undergoes the cyclic process J\u2192 K\u2192 L\u2192 M\u2192 J, as shown in the P-T diagram.", "response_choices": "(A) P \u2192 1; Q \u2192 3; R \u2192 5; S \u2192 4\n(C) P \u2192 4; Q \u2192 1; R \u2192 2; S \u2192 2\n(B) P \u2192 4; Q \u2192 3; R \u2192 5; S \u2192 2\n(D) P \u2192 2; Q \u2192 5; R \u2192 3; S \u2192 4", "answer": "None", "page_number": 16, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 15, "question": "Four identical thin, square metal sheets, S1, S2, S3 and S4, each of side a are kept parallel to each other with equal distance d (\u226a a) between them, as shown in the figure. Let C0 = \u03b50a^2/d, where \u03b50 is the permittivity of free space. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.", "response_choices": "List-I: (P) The capacitance between S1 and S4, with S2 and S3 not connected, is; (Q) The capacitance between S1 and S4, with S2 shorted to S3, is; (R) The capacitance between S1 and S4, with S2 shorted to S3, is; (S) The capacitance between S1 and S2, with S3 shorted to S1, and S2 shorted to S4, is. List-II: (1) 3C0; (2) C0/2; (3) C0/3; (4) 2C0/3; (5) 2C0. (A) P \u2192 3; Q \u2192 2; R \u2192 4; S \u2192 5, (B) P \u2192 2; Q \u2192 3; R \u2192 2; S \u2192 1, (C) P \u2192 3; Q \u2192 2; R \u2192 4; S \u2192 1, (D) P \u2192 3; Q \u2192 2; R \u2192 2; S \u2192 5", "answer": "(B) P -> 2; Q -> 3; R -> 2; S -> 1", "page_number": 17, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 16, "question": "A light ray is incident on the surface of a sphere of refractive index n at an angle of incidence \u03b80. The ray partially refracts into the sphere with angle of refraction \u03d50 and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is \u03b1. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.", "response_choices": "List-I: (P) If n = 2 and \u03b1 = 180\u00b0, then all the possible values of \u03b80 will be; (Q) If n = \u221a3 and \u03b1 = 180\u00b0, then all the possible values of \u03b80 will be; (R) If n = \u221a3 and \u03b1 = 180\u00b0, then all the possible values of \u03d50 will be; (S) If n = \u221a2 and \u03b80 = 45\u00b0, then all the possible values of \u03b1 will be. List-II: (1) 30\u00b0 and 0\u00b0; (2) 60\u00b0 and 0\u00b0; (3) 45\u00b0 and 0\u00b0; (4) 150\u00b0; (5) 0\u00b0. (A) P \u2192 5; Q \u2192 2; R\u2192 1; S\u2192 4, (B) P \u2192 5; Q \u2192 1; R\u2192 2; S\u2192 4, (C) P \u2192 3; Q \u2192 2; R\u2192 1; S\u2192 4, (D) P \u2192 3; Q \u2192 1; R\u2192 2; S\u2192 5", "answer": "(B) P -> 5; Q -> 1; R-> 2; S-> 4", "page_number": 17, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 17, "question": "The circuit shown in the figure contains an inductor L, a capacitor C0, a resistor R0 and an ideal battery. The circuit also contains two keys K1 and K2. Initially, both the keys are open and there is no charge on the capacitor. At an instant, key K1 is closed and immediately after this the current in R0 is found to be I1. After a long time, the current attains a steady state value I2. Thereafter, K2 is closed and simultaneously K1 is opened and the voltage across C0 oscillates with amplitude V0 and angular frequency \u03c90. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.", "response_choices": "(A) P \u2192 1; Q \u2192 3; R \u2192 2; S \u2192 5 (B) P \u2192 1; Q \u2192 2; R \u2192 3; S \u2192 5 (C) P \u2192 1; Q \u2192 3; R \u2192 2; S \u2192 4 (D) P \u2192 2; Q \u2192 5; R \u2192 3; S \u2192 4", "answer": "(B) P \u2192 1; Q \u2192 2; R \u2192 3; S \u2192 5", "page_number": 18, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 1, "question": "A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is", "response_choices": "(A) 2\u221a2 : \u221a3, (B) 2\u221a2 : 1, (C) 1 : 2, (D) 2 : 1", "answer": "C", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 2, "question": "At room temperature, disproportionation of an aqueous solution of in situ generated nitrous acid (HNO2) gives the species", "response_choices": "(A) H3O+, NO3- and NO, (B) H3O+, NO3- and NO2, (C) H3O+, NO- and NO2, (D) H3O+, NO3- and N2O", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 3, "question": "Aspartame, an artificial sweetener, is a dipeptide aspartyl phenylalanine methyl ester. The structure of aspartame is", "response_choices": "(A), (B), (C), (D)", "answer": "(B)", "page_number": 20, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 4, "question": "Among the following options, select the option in which each complex in Set-I shows geometrical isomerism and the two complexes in Set-II are ionization isomers of each other. [en = H2NCH2CH2NH2]", "response_choices": "(A) Set-I: [Ni(CO)3] and [PdCl4(PPh3)2] Set-II: [Co(NH3)5Cl]SO4 and [Co(NH3)4(SO4)]Cl, (B) Set-I: [Co(en)(NH3)2Cl2] and [PdCl4(PPh3)2] Set-II: [Co(NH3)6][Cr(CN)6] and [Cr(NH3)6][Co(CN)6], (C) Set-I: [Co(NH3)4(NO2)2] and [Co(en)2Cl2] Set-II: [Co(NH3)5Cl]SO4 and [Co(NH3)4(SO4)]Cl, (D) Set-I: [Cr(NH3)5Cl]Cl2 and [Co(en)(NH3)2Cl2] Set-II: [Cr(H2O)6]Cl3 and [Cr(H2O)4Cl]Cl2\u00b7H2O", "answer": "(B)", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 5, "question": "Among the following, the correct statement(s) for electrons in an atom is(are)", "response_choices": "(A) Uncertainty principle rules out the existence of definite paths for electrons. (B) The energy of an electron in 2s orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus. (C) According to Bohr's model, the most negative energy value for an electron is given by n = 1, which corresponds to the most stable orbit. (D) According to Bohr's model, the magnitude of velocity of electrons increases with increase in values of n.", "answer": "", "page_number": 21, "image_available": "no", "question_subject": "physics"} | |
| {"id": 8, "question": "Consider the following volume-temperature (V-T) diagram for the expansion of 5 moles of an ideal monoatomic gas. Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X->Y->Z is _____.", "response_choices": "The question does not have explicit multiple choice options listed.", "answer": "The answer field requires entering a numerical value.", "page_number": 23, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 9, "question": "Consider the following reaction, 2H2(g) + 2NO(g) \u2192 N2(g) + 2H2O(g) which follows the mechanism given below: 2NO(g) \u21cc_k1 N2O2(g) (fast equilibrium) N2O2(g) + H2(g) \u21d2_k2 N2O(g) + H2O(g) (slow reaction) N2O(g) + H2(g) \u21d2_k3 N2(g) + H2O(g) (fast reaction) The order of the reaction is _______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 10, "question": "Complete reaction of acetaldehyde with excess formaldehyde, upon heating with conc. NaOH solution, gives P and Q. Compound P does not give Tollens' test, whereas Q on acidification gives positive Tollens' test. Treatment of P with excess cyclohexanone in the presence of catalytic amount of p-toluenesulfonic acid (PTSA) gives product R. Sum of the number of methylene groups (-CH2-) and oxygen atoms in R is ______.", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 11, "question": "Among V(CO)6, Cr(CO)5, Cu(CO)3, Mn(CO)5, Fe(CO)5, [Co(CO)3]3-, [Cr(CO)4]4-, and Ir(CO)3, the total number of species isoelectronic with Ni(CO)4 is ______. [Given, atomic number: V = 23, Cr = 24, Mn = 25, Fe = 26, Co = 27, Ni = 28, Cu = 29, Ir = 77]", "response_choices": "", "answer": "", "page_number": 24, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 12, "question": "In the following reaction sequence, the major product P is formed. \n\n i) Hg2+, H3O+ \n ii) Zn-Hg/HCl \n iii) H3O+, \u0394 \n\n Glycerol reacts completely with excess P in the presence of an acid catalyst to form Q. Reaction of Q with excess NaOH followed by the treatment with CaCl2 yields Ca-soap R, quantitatively. \n\nStarting with one mole of Q, the amount of R produced in gram is _____.", "response_choices": "", "answer": "", "page_number": 25, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 13, "question": "Among the following complexes, the total number of diamagnetic species is _____. \n\n [Mn(NH3)6]3+, [MnCl6]3-, [FeFe4]2-, [CoF6]3-, [Fe(NH3)6]3+, and [Co(en)3]3+\n\n[Given, atomic number: Mn = 25, Fe = 26, Co = 27; \n\nen = H2NCH2CH2NH2]", "response_choices": "", "answer": "", "page_number": 25, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 14, "question": "In a conductometric titration, small volume of titrant of higher concentration is added stepwise to a larger volume of titrate of much lower concentration, and the conductance is measured after each addition. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.", "response_choices": "A) P-4, Q-3, R-2, S-5\nB) P-2, Q-4, R-3, S-1\nC) P-3, Q-4, R-2, S-5\nD) P-4, Q-3, R-2, S-1", "answer": "", "page_number": 27, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 15, "question": "Based on VSEPR model, match the xenon compounds given in List-I with the corresponding geometries and the number of lone pairs on xenon given in List-II and choose the correct option.", "response_choices": "(A) P-5, Q-2, R-3, S-1\n(B) P-5, Q-3, R-2, S-4\n(C) P-4, Q-3, R-2, S-1\n(D) P-4, Q-2, R-5, S-3", "answer": "", "page_number": 28, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 16, "question": "List-I contains various reaction sequences and List-II contains the possible products. Match each entry in List-I with the appropriate entry in List-II and choose the correct option.", "response_choices": "A) P-3, Q-5, R-4, S-1\nB) P-3, Q-2, R-4, S-1\nC) P-3, Q-5, R-1, S-4\nD) P-5, Q-2, R-4, S-1", "answer": "(A) P-3, Q-5, R-4, S-1", "page_number": 29, "image_available": "yes", "question_subject": "chemistry"} | |