JEE_papers/JSON/JEE_2010_1.jsonl

{"id": 1, "question": "The correct structure of ethylenediaminetetraacetic acid (EDTA) is", "response_choices": "A) HOOC-CH2 | N-CH=CH-N | CH2-COOH, B) HOOC | N-CH2-CH2-N | COOH, C) HOOC-CH2 | N-CH2-CH2-N | CH2-COOH, D) HOOC-CH2 | CH2 | N-CH-CH-N | CH2-COOH", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"}
{"id": 2, "question": "The ionization isomer of [Cr(H2O)4Cl(NO2)]Cl is", "response_choices": "A) [Cr(H2O)4(O2N)]Cl2, B) [Cr(H2O)4Cl2](NO2), C) [Cr(H2O)4Cl(ONO)]Cl, D) [Cr(H2O)4Cl2(NO2)]\u00b7H2O", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"}
{"id": 3, "question": "The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are", "response_choices": "A) BrCH2CH2CH2CH2CH3 and CH3CH2C\u2261CH, B) BrCH2CH2CH3 and CH3CH2CH2C\u2261CH, C) BrCH2CH2CH2CH2CH3 and CH3C\u2261CH, D) BrCH2CH2CH2CH3 and CH3CH2C\u2261CH", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"}
{"id": 4, "question": "The correct statement about the following disaccharide is", "response_choices": "A) Ring (a) is pyranose with \u03b1-glycosidic link\nB) Ring (a) is furanose with \u03b1-glycosidic link\nC) Ring (b) is furanose with \u03b1-glycosidic link\nD) Ring (b) is pyranose with \u03b2-glycosidic link", "answer": "A", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"}
{"id": 5, "question": "In the reaction the products are", "response_choices": "A) Br-OCH3 and H2\nB) Br and CH3Br\nC) Br and CH3OH\nD) OH and CH3Br", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"}
{"id": 6, "question": "Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is", "response_choices": "A) K, B) k, C) k, D) k", "answer": "A", "page_number": 3, "image_available": "yes", "question_subject": "chemistry"}
{"id": 7, "question": "The species which by definition has ZERO standard molar enthalpy of formation at 298 K is", "response_choices": "A) Br2 (g), B) Cl2 (g), C) H2O (g), D) CH4 (g)", "answer": "B", "page_number": 3, "image_available": "no", "question_subject": "chemistry"}
{"id": 8, "question": "The bond energy (in kcal mol^-1) of a C-C single bond is approximately", "response_choices": "A) 1, B) 10, C) 100, D) 1000", "answer": "C", "page_number": 3, "image_available": "no", "question_subject": "chemistry"}
{"id": 9, "question": "The reagent(s) used for softening the temporary hardness of water is(are)", "response_choices": "A) Ca3(PO4)2   B) Ca(OH)2   C) Na2CO3   D) NaOCl", "answer": "B", "page_number": 4, "image_available": "no", "question_subject": "chemistry"}
{"id": 10, "question": "In the reaction the intermediate(s) is(are)", "response_choices": "A)   B)   C)   D)", "answer": "A and C", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"}
{"id": 11, "question": "In the Newman projection for 2,2-dimethylbutane X and Y can respectively be", "response_choices": "A) H and H   B) H and C2H5   C) C2H5 and H   D) CH3 and CH3", "answer": "B and D", "page_number": 4, "image_available": "yes", "question_subject": "chemistry"}
{"id": 12, "question": "Among the following, the intensive property is (properties are)", "response_choices": "A) molar conductivity   B) electromotive force   C) resistance   D) heat capacity", "answer": "A and B", "page_number": 4, "image_available": "no", "question_subject": "chemistry"}
{"id": 13, "question": "Aqueous solutions of HNO3, KOH, CH3COOH, and CH3COONa of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)", "response_choices": "A) HNO3 and CH3COOH, B) KOH and CH3COONa, C) HNO3 and CH3COONa, D) CH3COOH and CH3COONa", "answer": "C and D", "page_number": 5, "image_available": "no", "question_subject": "chemistry"}
{"id": 14, "question": "Partial roasting of chalcopyrite produces", "response_choices": "A) Cu2S and FeO, B) Cu2O and FeO, C) CuS and Fe2O3, D) Cu2O and Fe2O3", "answer": "A", "page_number": 5, "image_available": "no", "question_subject": "chemistry"}
{"id": 15, "question": "Iron is removed from chalcopyrite as", "response_choices": "A) FeO, B) FeS, C) Fe2O3, D) FeSiO3", "answer": "D", "page_number": 5, "image_available": "no", "question_subject": "chemistry"}
{"id": 16, "question": "In self-reduction, the reducing species is", "response_choices": "A) S, B) O\u00b2\u207b, C) S\u00b2\u207b, D) SO\u2082", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "chemistry"}
{"id": 17, "question": "For the above cell", "response_choices": "A) Ecell < 0; \u0394G > 0, B) Ecell > 0; \u0394G < 0, C) Ecell < 0; \u0394G\u00b2 > 0, D) Ecell > 0; \u0394G\u00b2 < 0", "answer": "B", "page_number": 6, "image_available": "no", "question_subject": "chemistry"}
{"id": 18, "question": "If the 0.05 molar solution of M+ is replaced by a 0.0025 molar M+ solution, then the magnitude of the cell potential would be", "response_choices": "A) 35 mV, B) 70 mV, C) 140 mV, D) 700 mV", "answer": "C", "page_number": 6, "image_available": "no", "question_subject": "chemistry"}
{"id": 19, "question": "The total number of basic groups in the following form of lysine is", "response_choices": "", "answer": "2", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"}
{"id": 20, "question": "The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C\u2087H\u2088 is", "response_choices": "", "answer": "5", "page_number": 7, "image_available": "no", "question_subject": "chemistry"}
{"id": 21, "question": "In the product given, the stoichiometric ratio for the molecular aldol condensation reaction is", "response_choices": "", "answer": "1", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"}
{"id": 22, "question": "Amongst the following, the total number of compounds soluble in aqueous NaOH is", "response_choices": "", "answer": "4", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"}
{"id": 23, "question": "Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is", "response_choices": "KCN, K\u2082SO\u2084, (NH\u2084)\u2082C\u2082O\u2084, NaCl, Zn(NO\u2083)\u2082, FeCl\u2083, K\u2082CO\u2083, NH\u2084NO\u2083, LiCN", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "chemistry"}
{"id": 24, "question": "Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF\u2085 is", "response_choices": "", "answer": "either 0 or 8", "page_number": 8, "image_available": "no", "question_subject": "chemistry"}
{"id": 25, "question": "The value of n in the molecular formula Be\u2084Al\u2082Si\u2085O\u2081\u2088 is", "response_choices": "", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "chemistry"}
{"id": 26, "question": "A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is", "response_choices": "", "answer": "3", "page_number": 8, "image_available": "no", "question_subject": "chemistry"}
{"id": 27, "question": "The concentration of R in the reaction R \u2192 P was measured as a function of time and the following data is obtained:", "response_choices": "", "answer": "[R] (molar): 1.0, 0.75, 0.40, 0.10; t(min.): 0.0, 0.05, 0.12, 0.18", "page_number": 8, "image_available": "yes", "question_subject": "chemistry"}
{"id": 28, "question": "The number of neutrons emitted when \u00b2\u00b3\u2075\u2089\u2082U undergoes controlled nuclear fission to \u00b9\u2074\u00b2\u2085\u2084Xe and \u2079\u2070\u2083\u2088Sr is", "response_choices": "", "answer": "4", "page_number": 8, "image_available": "no", "question_subject": "physics"}
{"id": 29, "question": "If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression (a sin 2C + c sin 2A) / c is", "response_choices": "A) 1/2, B) \u221a3/2, C) 1, D) \u221a3", "answer": "D", "page_number": 9, "image_available": "no", "question_subject": "mathematics"}
{"id": 30, "question": "Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is", "response_choices": "A) x + 2y - 2z = 0, B) 3x + 2y - 2z = 0, C) x - 2y + z = 0, D) 5x + 2y - 4z = 0", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "mathematics"}
{"id": 31, "question": "Let \u03c9 be a complex cube root of unity with \u03c9\u22601. A fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that \u03c9\u00b9\u02e1 +\u03c9\u00b9\u00b2+\u03c9\u00b9\u00b3=0 is", "response_choices": "A) 1/18, B) 1/9, C) 2/9, D) 1/36", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "mathematics"}
{"id": 32, "question": "Let P, Q, R and S be the points on the plane with position vectors \u22122i\u2212j, 4i, 3i+3j and \u22123i+2j respectively. The quadrilateral PQRS must be a", "response_choices": "A) parallelogram, which is neither a rhombus nor a rectangle, B) square, C) rectangle, but not a square, D) rhombus, but not a square", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "mathematics"}
{"id": 33, "question": "The number of 3x3 matrices A whose entries are either 0 or 1 and for which the system A[x y z]^T = [1 0 0]^T has exactly two distinct solutions, is", "response_choices": "A) 0, B) 2^9 - 1, C) 168, D) 2", "answer": "A", "page_number": 10, "image_available": "no", "question_subject": "mathematics"}
{"id": 34, "question": "The value of lim [x->0] (1/x^3) \u222b(0 to 1) (x t \u03b8n (1+t))/(t^4 + 4) dt is", "response_choices": "A) 0, B) 1/12, C) 1/24, D) 1/64", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "mathematics"}
{"id": 35, "question": "Let p and q be real numbers such that p \u2260 0, p^3 \u2260 q and p^3 \u2260 -q . If \u03b1 and \u03b2 are nonzero complex numbers satisfying \u03b1 + \u03b2 = - p and \u03b1^2 + \u03b2^2 = q , then a quadratic equation having (\u03b1/\u03b2) and (\u03b1/\u03b1) as its roots is", "response_choices": "A) (p^3 + q) x^2 - (p^3 + 2q)x + (p^3 + q) = 0, B) (p^3 + q) x^2 - (p^3 - 2q)x + (p^3 + q) = 0, C) (p^3 - q) x^2 - (5p^3 - 2q) x + (p^3 - q) = 0, D) (p^3 - q) x^2 - (5p^3 + 2q) x + (p^3 - q) = 0", "answer": "B", "page_number": 10, "image_available": "no", "question_subject": "mathematics"}
{"id": 36, "question": "Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^x + e^-x, g(x) = xe^x + e^-x and h(x) = x^2 e^x + e^-x. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then", "response_choices": "A) a = b and c \u2260 b, B) a = c and a \u2260 b, C) a \u2260 b and c \u2260 b, D) a = b = c", "answer": "D", "page_number": 10, "image_available": "no", "question_subject": "mathematics"}
{"id": 37, "question": "Let A and B be two distinct points on the parabola y^2 = 4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be", "response_choices": "A) -1/r, B) 1/r, C) 2/r, D) -2/r", "answer": "C and D", "page_number": 11, "image_available": "no", "question_subject": "mathematics"}
{"id": 38, "question": "Let ABC be a triangle such that \u2220ACB = \u03c0/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x^2 + x + 1, b = x^2 - 1 and c = 2x + 1 is (are)", "response_choices": "A) -(-2+\u221a3), B) 1+\u221a3, C) 2+\u221a3, D) 4\u221a3", "answer": "B", "page_number": 11, "image_available": "no", "question_subject": "mathematics"}
{"id": 39, "question": "Let z\u2081 and z\u2082 be two distinct complex numbers and let z = (1 - t) z\u2081 + tz\u2082 for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then", "response_choices": "A) |z - z\u2081| + |z - z\u2082| = |z\u2081 - z\u2082|, B) Arg (z - z\u2081) = Arg (z - z\u2082), C) |z-z\u2081   z-z\u2082| = 0, D) Arg (z - z\u2081) = Arg(z\u2082 - z\u2081)|z\u2082-z\u2081  z\u2081-z\u2082|", "answer": "A and C and D", "page_number": 11, "image_available": "no", "question_subject": "mathematics"}
{"id": 40, "question": "Let f be a real-valued function defined on the interval (0, \u221e) by f(x) = \u222b(0 to x) t + sin t dt. Then which of the following statement(s) is (are) true?", "response_choices": "A) f'(x) exists for all x\u2208(0,\u221e) B) f'(x) exists for all x\u2208(0,\u221e) and f' is continuous on (0,\u221e), but not differentiable on (0,\u221e) C) there exists \u03b1 > 1 such that |f'(x)|<|f(x)| for all x\u2208(\u03b1,\u221e) D) there exists \u03b2 > 0 such that |f(x)|+|f'(x)|\u2264\u03b2 for all x\u2208(0,\u221e)", "answer": "B and C", "page_number": 12, "image_available": "no", "question_subject": "mathematics"}
{"id": 41, "question": "The value(s) of \u222b(0 to 1) x^4(1-x)^4/(1+x^2) dx is (are)", "response_choices": "A) 22/7 - \u03c0 B) 2/105 C) 0 D) 71/15 - 3\u03c0/2", "answer": "A", "page_number": 12, "image_available": "no", "question_subject": "mathematics"}
{"id": 42, "question": "Let p be an odd prime number and Tp be the following set of 2x2 matrices : Tp = {A= [a  b] : a,b,c \u2208 {0, 1, 2, ..., p-1}} The number of A in Tp such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is", "response_choices": "A) (p - 1)\u00b2 B) 2 (p - 1) C) (p - 1)\u00b2 + 1 D) 2p - 1", "answer": "D", "page_number": 12, "image_available": "no", "question_subject": "mathematics"}
{"id": 43, "question": "The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is [Note : The trace of a matrix is the sum of its diagonal entries.]", "response_choices": "A) (p - 1) (p\u00b2 - p + 1) B) p\u00b3 - (p - 1)\u00b2 C) (p - 1)\u00b2 D) (p - 1) (p\u00b2 - 2)", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "mathematics"}
{"id": 44, "question": "The number of A in Tp such that det (A) is not divisible by p is", "response_choices": "A) 2p^2 B) p^3 - 5p C) p^3 - 3p D) p^3 - p^2", "answer": "D", "page_number": 13, "image_available": "no", "question_subject": "mathematics"}
{"id": 45, "question": "Equation of a common tangent with positive slope to the circle as well as to the hyperbola is", "response_choices": "A) 2x-\u221a5y-20=0 B) 2x-\u221a5y+4=0 C) 3x-4y+8=0 D) 4x-3y+4=0", "answer": "B", "page_number": 13, "image_available": "yes", "question_subject": "mathematics"}
{"id": 46, "question": "Equation of the circle with AB as its diameter is", "response_choices": "A) x^2+y^2-12x+24=0 B) x^2+y^2+12x+24=0 C) x^2+y^2+24x-12=0 D) x^2+y^2-24x-12=0", "answer": "A", "page_number": 13, "image_available": "yes", "question_subject": "mathematics"}
{"id": 47, "question": "The number of values of \u03b8 in the interval (-(\u03c0/2),(\u03c0/2)) such that \u03b8 \u2260 l\u03c0/5 for n=0,\u00b11,\u00b12 and tan\u03b8=cot\u03b8 as well as sin2\u03b8=cos4\u03b8 is", "response_choices": "No explicit options given", "answer": "3", "page_number": 13, "image_available": "no", "question_subject": "mathematics"}
{"id": 48, "question": "The maximum value of the expression 1 / (sin^2 \u03b8 + 3 sin \u03b8 cos \u03b8 + 5cos^2 \u03b8) is", "response_choices": "", "answer": "2", "page_number": 14, "image_available": "no", "question_subject": "mathematics"}
{"id": 49, "question": "If \u0101 and b\u0304 are vectors in space given by \u0101 = i\u22122j\u0304/\u221a5 and b\u0304 = 2i\u0304 + j\u0304 + 3k\u0304/\u221a14, then the value of (2\u0101 + b\u0304) \u22c5 (\u0101 \u00d7 b\u0304) \u00d7 (\u0101 \u22122 b\u0304) is", "response_choices": "", "answer": "5", "page_number": 14, "image_available": "no", "question_subject": "mathematics"}
{"id": 50, "question": "The line 2x + y = 1 is tangent to the hyperbola x^2/a^2 - y^2/b^2 = 1. If this line passes through the point of intersection of the nearest directrix and the x-axis, then the eccentricity of the hyperbola is", "response_choices": "", "answer": "2", "page_number": 14, "image_available": "no", "question_subject": "mathematics"}
{"id": 51, "question": "If the distance between the plane Ax - 2y + z = d and the plane containing the lines x-1/2 = y-2/3 = z-3/4 and x-2/3 = y-3/4 = z-4/5 is \u221a6, then |d| is", "response_choices": "", "answer": "6", "page_number": 14, "image_available": "no", "question_subject": "mathematics"}
{"id": 52, "question": "For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = { x - [x] if [x] is odd, 1 + [x] - x if [x] is even}. Then the value of \u222b(10/-10) \u03c0^2 * 10 f(x) cos \u03c0x dx is", "response_choices": "", "answer": "4", "page_number": 14, "image_available": "no", "question_subject": "mathematics"}
{"id": 53, "question": "Let \u03c9 be the complex number cos 2\u03c0/3 + i sin 2\u03c0/3. Then the number of distinct complex numbers z satisfying |z+1 \u03c9 \u03c9^2; \u03c9 z+\u03c9^2 1; \u03c9^2 1 z+\u03c9| = 0 is equal to", "response_choices": "", "answer": "1", "page_number": 14, "image_available": "no", "question_subject": "mathematics"}
{"id": 54, "question": "Let Sk, k = 1, 2, ..., 100, denote the sum of the infinite geometric series whose first term is (k-1)/k! and the common ratio is 1/k. Then the value of 100^2 + (\u03a3 from k=1 to 100) [(k^2 - 3k + 1) Sk] is", "response_choices": "", "answer": "3", "page_number": 15, "image_available": "no", "question_subject": "mathematics"}
{"id": 55, "question": "The number of all possible values of \u03b8 , where 0 < \u03b8 < \u03c0, for which the system of equations (y + z) cos 3 \u03b8 = (xyz) sin 3 \u03b8, x sin 3\u03b8 = (2 cos 3\u03b8) / y, 2 sin 3\u03b8 / z, (xyz) sin 3 \u03b8 = (y + 2z) cos 3 \u03b8 + y sin 3 \u03b8 have a solution (x0, y0, z0) with y0 \u2260 0, is", "response_choices": "", "answer": "3", "page_number": 15, "image_available": "no", "question_subject": "mathematics"}
{"id": 56, "question": "Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1) = 1. If the y-intercept of the tangent at any point P(x, y) on the curve y = f(x) is equal to the cube of the abscissa of P, then the value of f(-3) is equal to", "response_choices": "", "answer": "9", "page_number": 15, "image_available": "no", "question_subject": "mathematics"}
{"id": 57, "question": "Consider a thin square sheet of side L and thickness t, made of a material of resistivity \u03c1. The resistance between two opposite faces, shown by the shaded areas in the figure is", "response_choices": "A) directly proportional to L, B) directly proportional to t, C) independent of L, D) independent of t", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"}
{"id": 58, "question": "A real gas behaves like an ideal gas if its", "response_choices": "A) pressure and temperature are both high, B) pressure and temperature are both low, C) pressure is high and temperature is low, D) pressure is low and temperature is high", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"}
{"id": 59, "question": "Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R\u2081\u2080\u2080, R\u2086\u2080 and R\u2084\u2080, respectively, the relation between these resistances is", "response_choices": "A) 1/R\u2081\u2080\u2080 = 1/R\u2086\u2080 + 1/R\u2084\u2080, B) R\u2081\u2080\u2080 = R\u2086\u2080 + R\u2084\u2080, C) R\u2081\u2080\u2080 > R\u2086\u2080 > R\u2084\u2080, D) 1/R\u2081\u2080\u2080 > 1/R\u2086\u2080 > 1/R\u2084\u2080", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"}
{"id": 60, "question": "To verify Ohm's law, a student is provided with a test resistor Rr, a high resistance R, a small resistance Rs, two identical galvanometers G1 and G2, and a variable voltage source V. The correct circuit to carry out the experiment is", "response_choices": "A) B) C) D)", "answer": "C", "page_number": 17, "image_available": "yes", "question_subject": "physics"}
{"id": 61, "question": "An AC voltage source of variable angular frequency \u03c9 and fixed amplitude Vo is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When \u03c9 is increased", "response_choices": "A) the bulb glows dimmer B) the bulb glows brighter C) total impedance of the circuit is unchanged D) total impedance of the circuit increases", "answer": "B", "page_number": 17, "image_available": "no", "question_subject": "physics"}
{"id": 62, "question": "A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is", "response_choices": "A) IBL, B) IBL/\u03c0, C) IBL/2\u03c0, D) IBL/4\u03c0", "answer": "C", "page_number": 18, "image_available": "yes", "question_subject": "physics"}
{"id": 63, "question": "A block of mass m is on an inclined plane of angle \u03b8. The coefficient of friction between the block and the plane is \u03bc and tan\u03b8>\u03bc. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P\u2081= mg(sin\u03b8 - \u03bc cos\u03b8) to P\u2082= mg(sin\u03b8 + \u03bc cos\u03b8), the frictional force f versus P graph will look like", "response_choices": "A) [Graph A], B) [Graph B], C) [Graph C], D) [Graph D]", "answer": "A", "page_number": 18, "image_available": "yes", "question_subject": "physics"}
{"id": 64, "question": "A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is", "response_choices": "A) 2GM(4\u221a2-5)/7R   B) -2GM(4\u221a2-5)/7R   C) GM/4R   D) 2GM(\u221a2-1)/5R", "answer": "A", "page_number": 19, "image_available": "yes", "question_subject": "physics"}
{"id": 65, "question": "A few electric field lines for a system of two charges Q\u2081 and Q\u2082 fixed at two different points on the x-axis are shown in the figure. These lines suggest that", "response_choices": "A) |Q\u2081| > |Q\u2082|   B) |Q\u2081| < |Q\u2082|   C) at a finite distance to the left of Q\u2081 the electric field is zero   D) at a finite distance to the right of Q\u2082 the electric field is zero", "answer": "A and D", "page_number": 19, "image_available": "yes", "question_subject": "physics"}
{"id": 66, "question": "A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true ?", "response_choices": "A) Error \u0394T in measuring T, the time period, is 0.05 seconds   B) Error \u0394T in measuring T, the time period, is 1 second   C) Percentage error in the determination of g is 5%   D) Percentage error in the determination of g is 2.5%", "answer": "A and C", "page_number": 19, "image_available": "no", "question_subject": "physics"}
{"id": 67, "question": "A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms\u207b\u00b9. Which of the following statement(s) is (are) correct for the system of these two masses ?", "response_choices": "A) Total momentum of the system is 3 kg ms\u207b\u00b9\nB) Momentum of 5 kg mass after collision is 4 kg ms\u207b\u00b9\nC) Kinetic energy of the centre of mass is 0.75 J\nD) Total kinetic energy of the system is 4 J", "answer": "A and C", "page_number": 20, "image_available": "no", "question_subject": "physics"}
{"id": 68, "question": "A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60\u00b0 (see figure). If the refractive index of the material of the prism is \u221a5, which of the following is (are) correct ?", "response_choices": "A) The ray gets totally internally reflected at face CD\nB) The ray comes out through face AD\nC) The angle between the incident ray and the emergent ray is 90\u00b0\nD) The angle between the incident ray and the emergent ray is 120\u00b0", "answer": "A and B and C", "page_number": 20, "image_available": "yes", "question_subject": "physics"}
{"id": 69, "question": "One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is PA. Choose the correct option(s) from the following", "response_choices": "A) Internal energies at A and B are the same\nB) Work done by the gas in process AB is PAVB ln 4\nC) Pressure at C is P0/4\nD) Temperature at C is T0/4", "answer": "A and B and C and D", "page_number": 20, "image_available": "yes", "question_subject": "physics"}
{"id": 70, "question": "If the total energy of the particle is E, it will perform periodic motion only if", "response_choices": "A) E < 0, B) E > 0, C) Vo > E > 0, D) E > Vo", "answer": "B or C or (B and C)", "page_number": 21, "image_available": "yes", "question_subject": "physics"}
{"id": 71, "question": "For periodic motion of small amplitude A, the time period T of this particle is proportional to", "response_choices": "A) A\u221a(m/\u03b1), B) 1/A\u221a(\u03b1/m), C) A\u221a(\u03b1/m), D) 1/A\u221a(\u03b1/m)", "answer": "B", "page_number": 21, "image_available": "yes", "question_subject": "physics"}
{"id": 72, "question": "The acceleration of this particle for |x|>Xo is", "response_choices": "B) proportional to (Vo/mXo), A) proportional to Vo, C) proportional to \u221a(Vo/mXo), D) zero", "answer": "D", "page_number": 21, "image_available": "yes", "question_subject": "physics"}
{"id": 73, "question": "In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B2 (dashed line). If B2 is larger than B1, which of the following graphs shows the correct variation of R with T in these fields?", "response_choices": "Options A), B), C), and D) are shown in the image graphs.", "answer": "A", "page_number": 22, "image_available": "yes", "question_subject": "physics"}
{"id": 74, "question": "A superconductor has Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when", "response_choices": "A) B = 5 Tesla, Tc (B) = 80 K, B) B = 5 Tesla, 75 K < Tc (B) < 100 K, C) B = 10 Tesla, 75 K < Tc (B) < 100 K, D) B = 10 Tesla, Tc (B) = 70 K", "answer": "B", "page_number": 22, "image_available": "yes", "question_subject": "physics"}
{"id": 75, "question": "The focal length of a thin biconvex lens is 20cm. When an object is moved from a distance of 25cm in front of it to 50cm, the magnification of its image changes from m25 to m50. The ratio m25/m50 is", "response_choices": "", "answer": "6", "page_number": 23, "image_available": "no", "question_subject": "physics"}
{"id": 76, "question": "An \u03b1-particle and a proton are accelerated from rest by a potential difference of 100V. After this, their de Broglie wavelengths are \u03bb\u03b1 and \u03bbp respectively. The ratio \u03bbp/\u03bb\u03b1, to the nearest integer, is", "response_choices": "", "answer": "3", "page_number": 23, "image_available": "no", "question_subject": "physics"}
{"id": 77, "question": "When two identical batteries of internal resistance 1\u03a9 each are connected in series across a resistor R, the rate of heat produced in R is J1. When the same batteries are connected in parallel across R, the rate is J2. If J1 = 2.25 J2, then the value of R in \u03a9 is", "response_choices": "", "answer": "4", "page_number": 23, "image_available": "no", "question_subject": "physics"}
{"id": 78, "question": "Two spherical bodies A (radius 6 cm) and B (radius 18 cm) are at temperatures T1 and T2, respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?", "response_choices": "", "answer": "9", "page_number": 23, "image_available": "no", "question_subject": "physics"}
{"id": 79, "question": "When two progressive waves y1 = 4 sin(2x - 6t) and y2 = 3 sin(2x-6t - \u03c0/2) are superimposed, the amplitude of the resultant wave is", "response_choices": "", "answer": "5", "page_number": 23, "image_available": "no", "question_subject": "physics"}
{"id": 80, "question": "A 0.1 kg mass is suspended from a wire of negligble mass. The length of the wire is 1m and its cross-sectional area is 4.9\u00d710^-7m\u00b2. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s\u207b\u00b9. If the Young's modulus of the material of the wire is n\u00d710^9Nm\u207b\u00b2, the value of n is", "response_choices": "No response choices provided.", "answer": "4", "page_number": 24, "image_available": "no", "question_subject": "physics"}
{"id": 81, "question": "A binary star consists of two stars A (mass 2.2M_\u29bf) and B (mass 11M_\u29bf), where M_\u29bf is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is", "response_choices": "No response choices provided.", "answer": "6", "page_number": 24, "image_available": "no", "question_subject": "physics"}
{"id": 82, "question": "Gravitational acceleration on the surface of a planet is \u221a(5/11)g , where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms\u207b\u00b9, the escape speed on the surface of the planet in kms\u207b\u00b9 will be", "response_choices": "No response choices provided.", "answer": "3", "page_number": 24, "image_available": "no", "question_subject": "physics"}
{"id": 83, "question": "A piece of ice (heat capacity = 2100 J kg\u207b\u00b9 \u00b0C\u207b\u00b9 and latent heat = 3.36 \u00d7 10\u2075 J kg\u207b\u00b9) of mass m grams is at -5\u00b0C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is", "response_choices": "No response choices provided.", "answer": "8", "page_number": 24, "image_available": "no", "question_subject": "chemistry"}
{"id": 84, "question": "A stationary source is emitting sound at a fixed frequency f\u2080, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f\u2080. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms\u207b\u00b9.", "response_choices": "No response choices provided.", "answer": "7", "page_number": 24, "image_available": "no", "question_subject": "physics"}