| {"id": 1, "question": "The complex showing a spin-only magnetic moment of 2.82 B.M. is", "response_choices": "A) Ni(CO)4 B) [NiCl4]2- C) Ni(PPh3)4 D) [Ni(CN)4]2-", "answer": "B", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 2, "question": "The species having pyramidal shape is", "response_choices": "A) SO3 B) BrF3 C) SiO32- D) OSF2", "answer": "D", "page_number": 1, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 3, "question": "In the reaction H3C-(ring structure)-C-NH2 (1) NaOH/Br2 T (2) (ring structure)-C-Cl the structure of the Product T is", "response_choices": "A) (structure) B) (structure) C) (structure) D) (structure)", "answer": "C", "page_number": 1, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 4, "question": "The compounds P, Q and S were separately subjected to nitration using HNO3/H2SO4 mixture. The major product formed in each case respectively, is", "response_choices": "A) HO-NO2, H3C-NO2, O2N-; B) HO-NO2, H3C-NO2, -NO2; C) HO-NO2, H3C-NO2, -NO2; D) HO-NO2, H3C-NO2, O-NO2", "answer": "C", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 5, "question": "The packing efficiency of the two-dimensional square unit cell shown below is", "response_choices": "A) 39.27%; B) 68.02%; C) 74.05%; D) 78.54%", "answer": "D", "page_number": 2, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 6, "question": "Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule B2 is", "response_choices": "A) 1 and diamagnetic, B) 0 and diamagnetic, C) 1 and paramagnetic, D) 0 and paramagnetic", "answer": "A", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 7, "question": "The total number of diprotic acids among the following is H3PO4, H2SO4, H3PO3, H2CO3, H2S2O7, H3BO3, H3PO2, H2CrO4, H2SO3", "response_choices": "", "answer": "6", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 8, "question": "Total number of geometrical isomers for the complex [RhCl(CO)(PPh3)(NH3)] is", "response_choices": "", "answer": "3", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 9, "question": "Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, Na, Ti", "response_choices": "", "answer": "2", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 10, "question": "Silver (atomic weight = 108 g mol\u207b\u00b9) has a density of 10.5 g cm\u207b\u00b3. The number of silver atoms on a surface of area 10\u207b\u00b9\u00b2 m\u00b2 can be expressed in scientific notation as y \u00d7 10^x. The value of x is", "response_choices": "", "answer": "7", "page_number": 3, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 11, "question": "One mole of an ideal gas is taken from a to b along two paths denoted by the solid and the dashed lines as shown in the graph below. If the work done along the solid line path is ws and that along the dotted line path is wd, then the integer closest to the ratio wd/ws is", "response_choices": "Not Available", "answer": "2", "page_number": 4, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 12, "question": "The compounds P and Q respectively are", "response_choices": "A) H3C-CH2-CH-C-H and H3C-C-H, B) H3C-CH-C-H and C-H, C) H3C-CH2-CH-C-H and H3C-C-H, D) H3C-CH2-CH-C-H and H-C-H", "answer": "B", "page_number": 5, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 13, "question": "The compound R is", "response_choices": "A) H3C-C-C-H, B) H3C-C=C-H, CH3, C-CH-CH, CH3, OH, D) H3C-CH-CH-H, CH3, CH2-OH", "answer": "A", "page_number": 6, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 14, "question": "The compound S is", "response_choices": "A) H3C-CH-CH-H, CH2-CN, B) H3C-C-H, CH2-CN, C) H3C-CH-CH-OH, CH3, CN, CH2-OH, D) H3C-CH-OH, CH3-OH", "answer": "D", "page_number": 6, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 15, "question": "The state S1 is", "response_choices": "A) 1s, B) 2s, C) 2p, D) 3s", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 16, "question": "Energy of the state S1 in units of the hydrogen atom ground state energy is", "response_choices": "A) 0.75, B) 1.50, C) 2.25, D) 4.50", "answer": "C", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 17, "question": "The orbital angular momentum quantum number of the state S2 is", "response_choices": "A) 0, B) 1, C) 2, D) 3", "answer": "B", "page_number": 7, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 18, "question": "Match the reactions in Column I with appropriate options in Column II.", "response_choices": "A) r and s, B) t, C) p and q, D) r", "answer": "A: r and s, B: t, C: p and q, D: r", "page_number": 7, "image_available": "yes", "question_subject": "chemistry"} | |
| {"id": 19, "question": "All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.", "response_choices": "Column I: A) (CH3)2SiCl2, B) XeF4, C) Cl2, D) VCl3 \n Column II: p) Hydrogen halide formation, q) Redox reaction, r) Reacts with glass, s) Polymerization, t) O2 formation", "answer": "A: p and s, B: p and q and r and t, C: p and q, D: p", "page_number": 8, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 20, "question": "For r = 0, 1, ..., 10, let Ar, Br and Cr denote, respectively, the coefficient of xr in the expansions of (1+x)10, (1+x)20 and (1+x)30. Then \n 10 \u2211 Ar (B10Br - C10Ar)\nr=1 \nis equal to", "response_choices": "A) B10 - C10, B) A10 (B102 - C10A10), C) 0, D) C10 - B10", "answer": "D", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 21, "question": "Let S = {1, 2, 3, 4}. The total number of unordered pairs of disjoint subsets of S is equal to", "response_choices": "A) 25, B) 34, C) 42, D) 41", "answer": "D", "page_number": 8, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 22, "question": "Let f be a real-valued function defined on the interval (-1, 1) such that e^-x f(x) = 2 + \u222b(\u221a(t^4 + 1 dt), for all x \u2208 (-1, 1), and let f^-1 be the inverse function of f. Then (f^-1)' (2) is equal to", "response_choices": "A) 1, B) 1/3, C) 1/2, D) 1/e", "answer": "B", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 23, "question": "If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = \u03b1 , where \u03b1 > 0, is 5, then the foot of the perpendicular from P to the plane is", "response_choices": "A) (8/3, 4/3, 7/3), B) (4/3, 4/3, 1/3), C) (1/3, 2/3, 10/3), D) (2/3, 1/3, 5/2)", "answer": "A", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 24, "question": "Two adjacent sides of a parallelogram ABCD are given by AB = 2i + 10j + 11k and AD = - i + 2j + 2k The side AD is rotated by an acute angle \u03b1 in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle \u03b1 is given by", "response_choices": "A) 8/9, B) \u221a17/9, C) 1/9, D) 4\u221a5/9", "answer": "B", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 25, "question": "A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is green, then the probability that the original signal was green is", "response_choices": "A) 3/5, B) 6/7, C) 20/23, D) 9/20", "answer": "C", "page_number": 9, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 26, "question": "Two parallel chords of a circle of radius 2 are at a distance \u221a3 + 1 apart. If the chords subtend at the center, angles of \u03c0/k and 2\u03c0/k, where k > 0, then the value of [k] is [Note : [k] denotes the largest integer less than or equal to k]", "response_choices": "NA", "answer": "3", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 27, "question": "Consider a triangle ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively. Suppose a = 6, b = 10 and the area of the triangle is 15\u221a3. If \u2220ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r^2 is equal to", "response_choices": "NA", "answer": "3", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 28, "question": "Let f be a function defined on R (the set of all real numbers) such that f(x)=2010(x\u22122009)(x\u22122010)^2(x\u22122011)^3(x\u22122012)^4, for all x \u2208 R. If g is a function defined on R with values in the interval (0, \u221e) such that f(x) = \u2113n (g (x)), for all x \u2208 R, then the number of points in R at which g has a local maximum is", "response_choices": "NA", "answer": "1", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 29, "question": "Let a1, a2, a3, ... , a11 be real numbers satisfying a1 = 15, 27 - 2a2 > 0 and ak = 2ak-1 - ak-2 for k = 3, 4, ..., 11. If (a1^2 + a2^2 + ... + a11^2)/11 = 90, then the value of (a1 + a2 + ... + a11)/11 is equal to", "response_choices": "NA", "answer": "0", "page_number": 10, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 30, "question": "Let k be a positive real number and let A= [2k-1 \u221a2k 2\u221ak; 2\u221ak 1 -2k; -2\u221ak 2k -1] and B=[0 2k-1 \u221ak; 1-2k 0 2\u221ak; -\u221ak -2\u221ak 0] If det (adj A) + det(adj B) =10^6, then [k] is equal to", "response_choices": "Note: adj M denotes the adjoint of a square matrix M and [k] denotes the largest integer less than or equal to [k].", "answer": "4", "page_number": 11, "image_available": "yes", "question_subject": "mathematics"} | |
| {"id": 31, "question": "The real number s lies in the interval", "response_choices": "A) (-1/4,0) B) (-11,-3/4) C) (-3/4,1/2) D) (0,1/4)", "answer": "C", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 32, "question": "The area bounded by the curve y = f(x) and the lines x = 0, y = 0 and x = t, lies in the interval", "response_choices": "A) (3/4,3) B) (21/64,11/16) C) (9,10) D) (0,21/64)", "answer": "A", "page_number": 11, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 33, "question": "The function f(x) is", "response_choices": "A) increasing in (\u2212t, -1/4) and decreasing in (\u22121/4, t)\nB) decreasing in (\u2212t, -1/4) and increasing in (\u22121/4, t)\nC) increasing in (-t, t)\nD) decreasing in (-t, t)", "answer": "B", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 34, "question": "The coordinates of A and B are", "response_choices": "A) (3, 0) and (0, 2)\nB) (-8 \u221a161/5, 15) and (-9 8/5, 5)\nC) (-8 \u221a161/5, 15) and (0, 2)\nD) (3, 0) and (-9 8/5, 5)", "answer": "D", "page_number": 12, "image_available": "yes", "question_subject": "mathematics"} | |
| {"id": 35, "question": "The orthocenter of the triangle PAB is", "response_choices": "A) (5, 8/7)\nB) (7, 25/5, 8)\nC) (11, 8/5, 5)\nD) (8, 7/25, 5)", "answer": "C", "page_number": 12, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 36, "question": "The equation of the locus of the point whose distances from the point P and the line AB are equal, is", "response_choices": "A) 9x^2 + y^2 - 6xy - 54x - 62y + 241 = 0, B) x^2 + 9y^2 + 6xy - 54x + 62y - 241 = 0, C) 9x^2 + 9y^2 - 6xy - 54x - 62y - 241 = 0, D) x^2 + y^2 - 2xy + 27x + 31y - 120 = 0", "answer": "A", "page_number": 13, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 37, "question": "Match the statements in Column-I with those in Column-II. [Note: Here z takes values in the complex plane and Im z and Re z denote, respectively, the imaginary part and the real part of z.]", "response_choices": "Column I: A) The set of points z satisfying |z-1|z|=|z+1|z|, B) The set of points z satisfying |z+4|+|z-4|=10, C) If |w|=2, then the set of points z=w-1/w, D) If |w|=1, then the set of points z=w+1/w; Column II: p) an ellipse with eccentricity 4/5, q) the set of points z satisfying Im z=0, r) the set of points z satisfying |Im z|\u22641, s) the set of points z satisfying |Re z|\u22642, t) the set of points z satisfying |z|\u22643", "answer": "A: q and r, B: p, C: p and s and t, D: q and r and s and t", "page_number": 13, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 38, "question": "Match the statements in Column-I with the values in Column-II.", "response_choices": "A) A line from the origin meets the lines x-2=y-1=z+1 and x-8/3=y+3/2=-z-1/1 at P and Q respectively. If length PQ = d, then d^2 is p) - 4\nB) The values of x satisfying tan^-1 (x + 3) - tan^-1 (x - 3) = sin^-1 (3/5) are q) 0\nC) Non-zero vectors \u0101, b\u0304 and c\u0304 satisfy \u0101.b\u0304 = 0, (b\u0304 - \u0101).(b\u0304 + c\u0304) = 0 and 2|b\u0304 + c\u0304| = |b\u0304 - \u0101|. If \u0101 = \u03bcb\u0304 + 4c\u0304, then the possible values of \u03bc are r) 4\nD) Let f be the function on [-\u03c0, \u03c0] given by f(0) = 9 and f(x) = sin((9x/2)/sin(x/2)) for x \u2260 0. The value of (2/\u03c0) \u222b[-\u03c0]^\u03c0 f(x) dx is s) 5\nt) 6", "answer": "A: t\nB: p and r\nC: either q or (q and s)\nD: r", "page_number": 14, "image_available": "no", "question_subject": "mathematics"} | |
| {"id": 39, "question": "A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is", "response_choices": "A) 0.02 mm, B) 0.05 mm, C) 0.1 mm, D) 0.2 mm", "answer": "D", "page_number": 15, "image_available": "no", "question_subject": "physics"} | |
| {"id": 40, "question": "A hollow pipe of length 0.8 m is closed at one end. At its open end a 0.5 m long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is 50 N and the speed of sound is 320 ms^-1, the mass of the string is", "response_choices": "A) 5 grams, B) 10 grams, C) 20 grams, D) 40 grams", "answer": "B", "page_number": 15, "image_available": "no", "question_subject": "physics"} | |
| {"id": 41, "question": "A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is", "response_choices": "A) virtual and at a distance of 16 cm from the mirror, B) real and at a distance of 16 cm from the mirror, C) virtual and at a distance of 20 cm from the mirror, D) real and at a distance of 20 cm from the mirror", "answer": "B", "page_number": 15, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 42, "question": "A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards it is subjected to a time-dependent force F(t) in the x direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the block after 4.5 seconds is", "response_choices": "A) 4.50 J, B) 7.50 J, C) 5.06 J, D) 14.06 J", "answer": "C", "page_number": 16, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 43, "question": "A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81\u03c0/104 Vm\u22121. When the field is switched off, the drop is observed to fall with terminal velocity 2 \u00d7 10\u22123 m s\u22121. Given g = 9.8 m s\u22122, viscosity of the air = 1.8 \u00d7 10\u22125 Ns m\u22122 and the density of oil = 900 kg m\u22123, the magnitude of q is", "response_choices": "A) 1.6 \u00d7 10\u221219 C, B) 3.2 \u00d7 10\u221219 C, C) 4.8 \u00d7 10\u221219 C, D) 8.0 \u00d7 10\u221219 C", "answer": "D", "page_number": 16, "image_available": "no", "question_subject": "physics"} | |
| {"id": 44, "question": "A uniformly charged thin spherical shell of radius R carries uniform surface charge density of \u03c3 per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to", "response_choices": "A) (1/\u03b50)*\u03c3^2*R^2, B) (1/\u03b50)*\u03c3*R, C) (1/\u03b50*R)*\u03c3^2, D) (1/\u03b50*R^2)*\u03c3^2", "answer": "A", "page_number": 17, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 45, "question": "A diatomic ideal gas is compressed adiabatically to (1/32) of its initial volume. In the initial temperature of the gas is T\u2081 (in Kelvin) and the final temperature is \u03b1T\u2081, the value of \u03b1 is", "response_choices": "", "answer": "4", "page_number": 17, "image_available": "no", "question_subject": "physics"} | |
| {"id": 46, "question": "At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V ?", "response_choices": "[Take : \u2113n 5 = 1.6, \u2113n 3 = 1.1]", "answer": "2", "page_number": 17, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 47, "question": "Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from (25/3) m to (50/7) m in 30 seconds. What is the speed of the object in km per hour ?", "response_choices": "", "answer": "3", "page_number": 17, "image_available": "no", "question_subject": "physics"} | |
| {"id": 48, "question": "A large glass slab (\u03bc = 5/3) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ?", "response_choices": "", "answer": "6", "page_number": 18, "image_available": "no", "question_subject": "physics"} | |
| {"id": 49, "question": "To determine the half life of a radioactive element, a student plots a graph of |dN(t)/dt| versus t. Here dN(t)/dt is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is", "response_choices": "", "answer": "8", "page_number": 18, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 50, "question": "If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r<<R) is", "response_choices": "A) 2\u03c0rT, B) 2\u03c0RT, C) 2\u03c0^2T/R, D) 2\u03c0R^2T/r", "answer": "C", "page_number": 18, "image_available": "no", "question_subject": "physics"} | |
| {"id": 51, "question": "If r = 5x10^-4 m, p = 10^3 kgm^-3, g = 10 ms^-2, T = 0.11 Nm^-1, the radius of the drop when it detaches from the dropper is approximately", "response_choices": "A) 1.4 x 10^-3 m, B) 3.3 x 10^-3 m, C) 2.0 x 10^-3 m, D) 4.1 x 10^-3 m", "answer": "A", "page_number": 19, "image_available": "no", "question_subject": "physics"} | |
| {"id": 52, "question": "After the drop detaches, its surface energy is", "response_choices": "A) 1.4 x 10^-6 J, B) 2.7 x 10^-6 J, C) 5.4 x 10^-6 J, D) 8.1 x 10^-6 J", "answer": "B", "page_number": 19, "image_available": "no", "question_subject": "physics"} | |
| {"id": 53, "question": "A diatomic molecule has moment of inertia I. By Bohr's quantization condition its rotational energy in the nth level (n = 0 is not allowed) is", "response_choices": "A) 1/n^2 * (h^2 / 8\u03c0^2 I), B) 1/n * (h^2 / 8\u03c0^2 I), C) n * (h^2 / 8\u03c0^2 I), D) n^2 * (h^2 / 8\u03c0^2 I)", "answer": "D", "page_number": 19, "image_available": "no", "question_subject": "physics"} | |
| {"id": 54, "question": "It is found that the excitation frequency from ground to the first excited state of rotation for the CO molecule is close to 4/\u03c0\u00d710\u00b9\u00b9 Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take \u210f = 2 \u03c0 x 10^-34 J s)", "response_choices": "A) 2.76\u00d710^-46 kg m2, B) 1.87\u00d710^-46 kg m2, C) 4.67\u00d710^-47 kg m2, D) 1.17\u00d710^-47 kg m2", "answer": "B", "page_number": 20, "image_available": "no", "question_subject": "physics"} | |
| {"id": 55, "question": "In a CO molecule, the distance between C (mass = 12 a.m.u.) and O (mass = 16 a.m.u.), where 1 a.m.u. = 5/3\u00d710^-27 kg, is close to", "response_choices": "A) 2.4\u00d710^-10 m, B) 1.9\u00d710^-10 m, C) 1.3\u00d710^-10 m, D) 4.4\u00d710^-11 m", "answer": "C", "page_number": 20, "image_available": "no", "question_subject": "chemistry"} | |
| {"id": 56, "question": "Two transparent media of refractive indices \u03bc1 and \u03bc3 have a solid lens shaped transparent material of refractive index \u03bc2 between them as shown in figures in Column II. A traversing these media is also shown in the figures. In Column I different relationship between \u03bc1, \u03bc2 and \u03bc3 are given. Match them to the ray diagrams shown in Column I", "response_choices": "A) \u03bc1 < \u03bc2, B) \u03bc1 > \u03bc2, C) \u03bc2 = \u03bc3, D) \u03bc2 > \u03bc3", "answer": "A: p and r, B: q and s and t, C: p and r and t, D: q and s", "page_number": 21, "image_available": "yes", "question_subject": "physics"} | |
| {"id": 57, "question": "You are given many resistances, capacitors and inductors. These are connected to variable DC voltage source (the first two circuits) or an AC voltage source of 50 Hz frequency (the next three circuits) in different ways as shown in Column II. When a current (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V1 and V2. (indicated in circuits) are related as shown in column I. Match the two", "response_choices": "A) I \u2260 0, V1 is proportional to I\nB) I \u2260 0, V2 > V1\nC) V1 = 0, V2 = V\nD) I \u2260 0, V2 is proportional to I", "answer": "A: r and s and t\nB: q and r and s and t\nC: p and q\nD: q and r and s and t", "page_number": 22, "image_available": "yes", "question_subject": "physics"} | |