cmeraki/elemento huggingface dataset:
Subject: chemistry
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
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
Subject: chemistry
Question: The compounds P and Q respectively are
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
Subject: chemistry
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.
Choices: Column I: A) (CH3)2SiCl2, B) XeF4, C) Cl2, D) VCl3 
 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
Subject: mathematics
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 
 10 ∑ Ar (B10Br - C10Ar)
r=1 
is equal to
Choices: A) B10 - C10, B) A10 (B102 - C10A10), C) 0, D) C10 - B10
Answer: D
Subject: mathematics
Question: Let f be a real-valued function defined on the interval (-1, 1) such that e^-x f(x) = 2 + ∫(√(t^4 + 1 dt), for all x ∈ (-1, 1), and let f^-1 be the inverse function of f. Then (f^-1)' (2) is equal to
Choices: A) 1, B) 1/3, C) 1/2, D) 1/e
Answer: B
Subject: mathematics
Question: If the distance of the point P(1, -2, 1) from the plane x + 2y - 2z = α , where α > 0, is 5, then the foot of the perpendicular from P to the plane is
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
Subject: mathematics
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 α 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 α is given by
Choices: A) 8/9, B) √17/9, C) 1/9, D) 4√5/9
Answer: B
Subject: mathematics
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
Choices: A) 3/5, B) 6/7, C) 20/23, D) 9/20
Answer: C
Subject: mathematics
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√3. If ∠ACB is obtuse and if r denotes the radius of the incircle of the triangle, then r^2 is equal to
Choices: NA
Answer: 3
Subject: mathematics
Question: Let f be a function defined on R (the set of all real numbers) such that f(x)=2010(x−2009)(x−2010)^2(x−2011)^3(x−2012)^4, for all x ∈ R. If g is a function defined on R with values in the interval (0, ∞) such that f(x) = ℓn (g (x)), for all x ∈ R, then the number of points in R at which g has a local maximum is
Choices: NA
Answer: 1
Subject: mathematics
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
Choices: NA
Answer: 0
Subject: mathematics
Question: Let k be a positive real number and let A= [2k-1 √2k 2√k; 2√k 1 -2k; -2√k 2k -1] and B=[0 2k-1 √k; 1-2k 0 2√k; -√k -2√k 0] If det (adj A) + det(adj B) =10^6, then [k] is equal to
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
Subject: mathematics
Question: The coordinates of A and B are
Choices: A) (3, 0) and (0, 2)
B) (-8 √161/5, 15) and (-9 8/5, 5)
C) (-8 √161/5, 15) and (0, 2)
D) (3, 0) and (-9 8/5, 5)
Answer: D
Subject: mathematics
Question: The equation of the locus of the point whose distances from the point P and the line AB are equal, is
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
Subject: mathematics
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.]
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|≤1, s) the set of points z satisfying |Re z|≤2, t) the set of points z satisfying |z|≤3
Answer: A: q and r, B: p, C: p and s and t, D: q and r and s and t
Subject: mathematics
Question: Match the statements in Column-I with the values in Column-II.
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
B) The values of x satisfying tan^-1 (x + 3) - tan^-1 (x - 3) = sin^-1 (3/5) are q) 0
C) Non-zero vectors ā, b̄ and c̄ satisfy ā.b̄ = 0, (b̄ - ā).(b̄ + c̄) = 0 and 2|b̄ + c̄| = |b̄ - ā|. If ā = μb̄ + 4c̄, then the possible values of μ are r) 4
D) Let f be the function on [-π, π] given by f(0) = 9 and f(x) = sin((9x/2)/sin(x/2)) for x ≠ 0. The value of (2/π) ∫[-π]^π f(x) dx is s) 5
t) 6
Answer: A: t
B: p and r
C: either q or (q and s)
D: r
Subject: physics
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
Choices: A) 0.02 mm, B) 0.05 mm, C) 0.1 mm, D) 0.2 mm
Answer: D
Subject: physics
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
Choices: A) 5 grams, B) 10 grams, C) 20 grams, D) 40 grams
Answer: B
Subject: physics
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
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
Subject: physics
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
Choices: A) 4.50 J, B) 7.50 J, C) 5.06 J, D) 14.06 J
Answer: C
Subject: physics
Question: A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of strength 81π/104 Vm−1. When the field is switched off, the drop is observed to fall with terminal velocity 2 × 10−3 m s−1. Given g = 9.8 m s−2, viscosity of the air = 1.8 × 10−5 Ns m−2 and the density of oil = 900 kg m−3, the magnitude of q is
Choices: A) 1.6 × 10−19 C, B) 3.2 × 10−19 C, C) 4.8 × 10−19 C, D) 8.0 × 10−19 C
Answer: D
Subject: physics
Question: A uniformly charged thin spherical shell of radius R carries uniform surface charge density of σ per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to
Choices: A) (1/ε0)*σ^2*R^2, B) (1/ε0)*σ*R, C) (1/ε0*R)*σ^2, D) (1/ε0*R^2)*σ^2
Answer: A
Subject: physics
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
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
Subject: physics
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
Choices: A) 1/n^2 * (h^2 / 8π^2 I), B) 1/n * (h^2 / 8π^2 I), C) n * (h^2 / 8π^2 I), D) n^2 * (h^2 / 8π^2 I)
Answer: D
Subject: physics
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/π×10¹¹ Hz. Then the moment of inertia of CO molecule about its center of mass is close to (Take ℏ = 2 π x 10^-34 J s)
Choices: A) 2.76×10^-46 kg m2, B) 1.87×10^-46 kg m2, C) 4.67×10^-47 kg m2, D) 1.17×10^-47 kg m2
Answer: B
Subject: chemistry
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. = 5/3×10^-27 kg, is close to
Choices: A) 2.4×10^-10 m, B) 1.9×10^-10 m, C) 1.3×10^-10 m, D) 4.4×10^-11 m
Answer: C
Subject: physics
Question: Two transparent media of refractive indices μ1 and μ3 have a solid lens shaped transparent material of refractive index  μ2 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 μ1, μ2 and μ3 are given. Match them to the ray diagrams shown in Column I
Choices: A) μ1 < μ2, B) μ1 > μ2, C) μ2 = μ3, D) μ2 > μ3
Answer: A: p and r, B: q and s and t, C: p and r and t, D: q and s
Subject: physics
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
Choices: A) I ≠ 0, V1 is proportional to I
B) I ≠ 0, V2 > V1
C) V1 = 0, V2 = V
D) I ≠ 0, V2 is proportional to I
Answer: A: r and s and t
B: q and r and s and t
C: p and q
D: q and r and s and t