cmeraki/elemento huggingface dataset:
Subject: physics
Question: The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two jaws. The figure on the right shows the reading with a solid sphere held between the jaws. The correct diameter of the sphere is
Choices: (A) 3.07 cm (B) 3.11 cm (C) 3.15 cm (D) 3.17 cm
Answer: C
Subject: physics
Question: An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is
Choices: (A) 0.4, (B) 0.8, (C) 1.3, (D) 1.6
Answer: (C) 1.3
Subject: physics
Question: A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is
Choices: (A) 50, (B) 75, (C) 350, (D) 525
Answer: (C) 350
Subject: physics
Question: A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = -l, y = -h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s^2 along the positive x-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by L and τ, respectively. i, j and k are unit vectors along the positive x, y and z-directions, respectively. If k = i × j then which of the following statement(s) is(are) correct?
Choices: (A) The particle arrives at the point (x = l, y = -h) at time t = 2 s 

(B) τ = 2 k when the particle passes through the point (x = l, y = -h) 

(C) L = 4 k when the particle passes through the point (x = l, y = -h) 

(D) τ = k when the particle passes through the point (x = 0, y = -h)
Answer: B
Subject: physics
Question: Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?
Choices: (A) The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5 

(B) There is an overlap between the wavelength ranges of Balmer and Paschen series 

(C) The wavelengths of Lyman series are given by (1 + m^2/n^2) λ0, where λ0 is the shortest wavelength of Lyman series and m is an integer 

(D) The wavelength ranges of Lyman and Balmer series do not overlap
Answer: C
Subject: physics
Question: A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure). A resistor R = 1.4 Ω and a capacitor Co = 5.0 μF are connected in series between the rails. At time t = 0, Co is uncharged. Which of the following statement(s) is(are) correct? [μo = 4π × 10^-7 SI units. Take ln 2 = 0.7]
Choices: (A) Maximum current through R is 1.2 × 10^-6 ampere

(B) Maximum current through R is 3.8 × 10^-6 ampere

(C) Maximum charge on capacitor Co is 8.4 × 10^-12 coulomb

(D) Maximum charge on capacitor Co is 2.4 × 10^-12 coulomb
Subject: physics
Question: A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle θ = 45°. P1 and P2 are pressures at points 1 and 2, respectively, located at the base of the tube. Let β = (P1 − P2)/(ρgd), where ρ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?
Choices: A) β = 0 when a = g/√2, B) β > 0 when a = g/√2, C) β = √2-1/√2 when a = g/2, D) β = 1/√2 when a = g/2
Subject: physics
Question: An α-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the α-particle and the sulfur ion move in circular orbits of radii rα and rS, respectively. The ratio (rS/rα) is ___.
Subject: physics
Question: A thin rod of mass M and length a is free to rotate in horizontal plane about a fixed vertical axis passing through point O. A thin circular disc of mass M and of radius a/4 is pivoted on this rod with its center at a distance a/4 from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity Ω and the disc rotating about its vertical axis with angular velocity 4Ω. The total angular momentum of the system about the point O is (Ma^2Ω)/48 n. The value of n is ___.
Subject: physics
Question: A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t = t1 and 50 K at t = t2. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio (t2/t1) is ____.
Choices: No response choices provided.
Answer: ____
Subject: chemistry
Question: The calculated spin only magnetic moments of [Cr(NH3)6]3+ and [CuF6]3- in BM, respectively, are (Atomic numbers of Cr and Cu are 24 and 29, respectively)
Choices: (A) 3.87 and 2.84, (B) 4.90 and 1.73, (C) 3.87 and 1.73, (D) 4.90 and 2.84
Answer: B
Subject: chemistry
Question: The correct statement(s) related to colloids is(are)
Choices: (A) The process of precipitating colloidal sol by an electrolyte is called peptization. (B) Colloidal solution freezes at higher temperature than the true solution at the same concentration. (C) Surfactants form micelle above critical micelle concentration (CMC). CMC depends on temperature. (D) Micelles are macromolecular colloids.
Subject: chemistry
Question: The correct statement(s) related to the metal extraction processes is(are)
Choices: (A) A mixture of PbS and PbO undergoes self-reduction to produce Pb and SO2. (B) In the extraction process of copper from copper pyrites, silica is added to produce copper silicate. (C) Partial oxidation of sulphide ore of copper by roasting, followed by self-reduction produces blister copper. (D) In cyanide process, zinc powder is utilized to precipitate gold from Na[Au(CN)2].
Subject: chemistry
Question: A mixture of two salts is used to prepare a solution S, which gives the following results:
Choices: (A) Pb(NO3)2 and Zn(NO3)2 (B) Pb(NO3)2 and Bi(NO3)3 (C) AgNO3 and Bi(NO3)3 (D) Pb(NO3)2 and Hg(NO3)2
Subject: mathematics
Question: Consider a triangle A whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of A is (1, 1), then the equation of the circle passing through the vertices of the triangle A is
Choices: (A) x^2 + y^2 - 3x + y = 0, (B) x^2 + y^2 + x + 3y = 0, (C) x^2 + y^2 + 2y - 1 = 0, (D) x^2 + y^2 + x + y = 0
Answer: D
Subject: mathematics
Question: The area of the region {(x, y) : 0 ≤ x ≤ 9/4, 0 ≤ y ≤ 1, x ≥ 3y, x + y ≥ 2} is
Choices: (A) 11/32, (B) 35/96, (C) 37/96, (D) 13/32
Answer: C
Subject: mathematics
Question: Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 - S1 and F2 = F1 ∪ S1. Now two elements are chosen at random, without replacement, from the set F2 and let S2 denote the set of these chosen elements. Let G2 = G1 ∪ S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements. Let E3 = E2 ∪ S3. Given that E1= E3, let p be the conditional probability of the event S1 = {1, 2}. Then the value of p is
Choices: (A) 1/5, (B) 2/5, (C) 1/2, (D) 2/5
Answer: B
Subject: mathematics
Question: For any 3 × 3 matrix M, let |M| denote the determinant of M. Let E = [1 2 3; 2 3 4; 8 13 18], P = [1 0 0; 0 0 1; 0 1 0] and F = [1 3 2; 8 18 13; 2 4 3]. If Q is a nonsingular matrix of order 3 × 3, then which of the following statements is (are) TRUE?
Choices: Options A, B, C, D (not provided in the image)
Answer: Not provided
Subject: mathematics
Question: (A) F = PEP and P^2 = [1 0 0; 0 1 0; 0 0 1] (B) |EQ + PFQ^-1| = |EQ| + |PFQ^-1| (C) |(EF)^3| > |EF|^2 (D) Sum of the diagonal entries of P^-1FP + F is equal to the sum of diagonal entries of E + P^-1FP
Choices: No options given
Answer: No answer given
Subject: mathematics
Question: Let f: R → R be defined by f(x) = (x^2 - 3x - 6) / (x^2 + 2x + 4). Then which of the following statements is (are) TRUE? (A) f is decreasing in the interval (-2, -1) (B) f is increasing in the interval (1, 2) (C) f is onto (D) Range of f is [-3/2, 2]
Choices: (A), (B), (C), (D)
Answer: No answer given
Subject: mathematics
Question: Let E, F and G be three events having probabilities P(E) = 1/8, P(F) = 1/6 and P(G) = 1/4, and let P(E ∩ F ∩ G) = 1/10. For any event H, if H^c denotes its complement, then which of the following statements is (are) TRUE? (A) P(E ∩ F ∩ G^c) ≤ 1/40 (B) P(E^c ∩ F ∩ G) ≤ 1/15 (C) P(E ∪ F ∪ G) ≤ 13/24 (D) P(E^c ∩ F^c ∩ G^c) ≤ 5/12
Choices: (A), (B), (C), (D)
Answer: No answer given
Subject: mathematics
Question: For any 3 × 3 matrix M, let |M| denote the determinant of M. Let I be the 3 × 3 identity matrix. Let E and F be two 3 × 3 matrices such that (I - EF) is invertible. If G = (I - EF)^-1, then which of the following statements is (are) TRUE? (A) |FE| = |I - FE||FGE| (B) (I - FE)(I + FGE) = I
Choices: (A), (B)
Answer: No answer given
Subject: mathematics
Question: For any positive integer n, let Sn: (0,∞) → ℝ be defined by Sn(x) = ∑(n)(k=1) cot^(-1)((1 + k(k + 1)x^2)/x), where for any x ∈ ℝ, cot^(-1)(x) ∈ (0,π) and tan^(-1)(x) ∈ (-π/2,π/2). Then which of the following statements is (are) TRUE?
Choices: (A) S10(x) = π/2 = tan^(-1)((1+11x^2)/(10x)), for all x > 0
(B) lim cot(Sn(x)) = x, for all x > 0
n→∞
(C) The equation S3(x) = π/4 has a root in (0,∞)
(D) tan(Sn(x)) ≤ 1/2, for all n ≥ 1 and x > 0
Subject: mathematics
Question: For any complex number w = c + id, let arg(w) ∈ (-π,π], where i = √(-1) . Let α and β be real numbers such that for all complex numbers z = x + iy satisfying arg((z+α)/(z+β)) = π/4, the ordered pair (x,y) lies on the circle x^2 + y^2 + 5x - 3y + 4 = 0. Then which of the following statements is (are) TRUE?
Choices: (A) α = -1
(B) αβ = 4
(C) αβ = -4
(D) β = 4
Subject: mathematics
Question: Let ⃗u, ⃗v and ⃗w be vectors in three-dimensional space, where ⃗u and ⃗v are unit vectors which are not perpendicular to each other and ⃗u · ⃗w = 1, ⃗v · ⃗w = 1, ⃗w · ⃗w = 4 If the volume of the parallelopiped, whose adjacent sides are represented by the vectors ⃗u, ⃗v and ⃗w, is √2 , then the value of |3 ⃗u +5 ⃗v | is ___.
Choices: None provided
Answer: Must enter an integer