cmeraki/elemento huggingface dataset:
Subject: physics
Question: The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is
Choices: A) 5.112 cm, B) 5.124 cm, C) 5.136 cm, D) 5.148 cm
Answer: B
Subject: physics
Question: In the Young's double slit experiment using a monochromatic light of wavelength λ, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is
Choices: (A) (2n+1)λ/2 (B) (2n+1)λ/4 (C) (2n+1)λ/8 (D) (2n+1)λ/16
Answer: B
Subject: physics
Question: Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is
Choices: (A) 1 : 4 (B) 1 : 2 (C) 6 : 9 (D) 8 : 9
Answer: D
Subject: physics
Question: Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is
Choices: A) 2.0 s, B) 3.0 s, C) 4.5 s, D) 6.0 s
Answer: A
Subject: physics
Question: A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30 mW and the speed of light is 3 × 10^8 ms^-1. The final momentum of the object is
Choices: (A) 0.3 × 10^-17 kg ms^-1, (B) 1.0 × 10^-17 kg ms^-1, (C) 3.0 × 10^-17 kg ms^-1, (D) 9.0 × 10^-17 kg ms^-1
Answer: B
Subject: physics
Question: A particle of mass m is projected from the ground with an initial speed u0 at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed u0. The angle that the composite system makes with the horizontal immediately after the collision is
Choices: (A) π/4, (B) π/4+α, (C) π/2-α, (D) π/2
Answer: A
Subject: physics
Question: The work done on a particle of mass m by a force, K [ (x^2 + y^2)^(1/2) i + (x^2 + y^2)^(1/2) j] (K being a constant of appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is
Choices: A) 2Kπ/a, B) Kπ/a, C) Kπ/2a, D) 0
Answer: D
Subject: physics
Question: One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is
Choices: (A) 0.25 (B) 0.50 (C) 2.00 (D) 4.00
Answer: C
Subject: physics
Question: The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free space. The radius of the curved surface of the lens is
Choices: (A) 1 m (B) 2 m (C) 3 m (D) 6 m
Answer: C
Subject: physics
Question: A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, y(x, t) = (0.01 m) sin [(62.8 m^-1) x] cos [(628 s^-1)t]. Assuming π = 3.14, the correct statement(s) is (are)
Choices: (A) The number of nodes is 5. (B) The length of the string is 0.25 m. (C) The maximum displacement of the midpoint of the string, from its equilibrium position is 0.01 m. (D) The fundamental frequency is 100 Hz.
Answer: BC
Subject: physics
Question: A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k. The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct statement(s) is (are)
Choices: (A) the net elongation of the spring is 4πR^3ρg/3k. (B) the net elongation of the spring is 8πR^3ρg/3k. (C) the light sphere is partially submerged. (D) the light sphere is completely submerged.
Answer: AD
Subject: physics
Question: A particle of mass M and positive charge Q, moving with a constant velocity v₁ = 4i ms⁻¹, enters a region of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity v₂ = 2(√3i + j) ms⁻¹. The correct statement(s) is (are)
Choices: A) The direction of the magnetic field is -z direction. 
B) The direction of the magnetic field is +z direction. 
C) The magnitude of the magnetic field 50πM/3Q units. 
D) The magnitude of the magnetic field is 100πM/3Q units.
Answer: AC
Subject: physics
Question: Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ1 and ρ2 respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio ρ1/ρ2 can be
Choices: (A) -4, (B) -32/25, (C) 32/25, (D) 4
Answer: B
Subject: physics
Question: In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance C. The switch S1 is pressed first to fully charge the capacitor C1 and then released. The switch S2 is then pressed to charge the capacitor C2. After some time, S2 is released and then S3 is pressed. After some time,
Choices: (A) the charge on the upper plate of C1 is 2CV0; (B) the charge on the upper plate of C1 is CV0; (C) the charge on the upper plate of C2 is 0; (D) the charge on the upper plate of C2 is -CV0
Answer: BD
Subject: physics
Question: A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s^-1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching each other along the axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s^-1) of the system is
Choices: No response choices provided
Answer: 8
Subject: physics
Question: A bob of mass m, suspended by a string of length l1, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio l1/l2 is
Answer: 5
Subject: chemistry
Question: Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25 °C. For this process, the correct statement is
Choices: (A) The adsorption requires activation at 25 °C. (B) The adsorption is accompanied by a decrease in enthalpy. (C) The adsorption increases with increase of temperature. (D) The adsorption is irreversible.
Answer: B
Subject: chemistry
Question: The standard enthalpies of formation of CO₂(g), H₂O(l) and glucose(s) at 25 °C are –400 kJ/mol, –300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25 °C is
Choices: A) +2900 kJ, B) –2900 kJ, C) –16.11 kJ, D) +16.11 kJ
Answer: C
Subject: chemistry
Question: Consider the following complex ions, P, Q and R. P = [FeF6]3-, Q = [V(H2O)6]2+ and R = [Fe(H2O)6]2+. The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is
Choices: (A) R < Q < P, (B) Q < R < P, (C) R < P < Q, (D) Q < P < R
Answer: B
Subject: chemistry
Question: The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)
Choices: (A) [Cr(NH3)5Cl]Cl2 and [Cr(NH3)4Cl2]Cl
(B) [Co(NH3)4Cl2]+ and [Pt(NH3)2(H2O)Cl]+
(C) [CoBr2Cl2]2- and [PtBr2Cl2]2-
(D) [Pt(NH3)3(NO2)]Cl and [Pt(NH3)3Cl]Br
Answer: BD
Subject: chemistry
Question: The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to
Choices: (A) σ→p (empty) and σ→π* electron delocalisations. (B) σ→σ* and σ→π electron delocalisations. (C) σ→p (filled) and σ→π electron delocalisations. (D) p (filled)→σ* and σ→π* electron delocalisations.
Answer: A
Subject: chemistry
Question: The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1M), at 25 °C. The Ka of HA is
Choices: (A) 1 × 10^-4, (B) 1 × 10^-5, (C) 1 × 10^-6, (D) 1 × 10^-3
Answer: A
Subject: chemistry
Question: A tetrapeptide has –COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences (primary structures) with –NH2 group attached to a chiral center is
Choices: No response choices provided
Answer: 4
Subject: mathematics
Question: Let complex numbers α and 1/α lie on circles (x - x0)2 + (y - y0)2 = r2 and (x - x0)2 + (y - y0)2 = 4r2, respectively. If z0 = x0 + iy0 satisfies the equation 2 |z0|2 = r2 + 2, then |α| =
Choices: A) 1/√2, B) 1/2, C) 1/√7, D) 1/3
Answer: C
Subject: mathematics
Question: Let f : [1/2, 1] → ℝ (the set of all real numbers) be a positive, non-constant and differentiable function such that f''(x) < 2 f'(x) and f(1/2) = 1. Then the value of [integral from 1/2 to 1 of f(x) dx] lies in the interval
Choices: (A) (2 e - 1, 2e)  (B) (e - 1, 2e - 1)  (C) ((e - 1) / 2, e - 1)  (D) (0, (e - 1) / 2)
Answer: D
Subject: mathematics
Question: The area enclosed by the curves y = sin x + cos x and y = |cos x - sin x| over the interval [0 , π/2] is
Choices: (A) 4(√2 - 1) (B) 2√2 (√2 - 1) (C) 2(√2 + 1) (D) 2√2 (√2 + 1)
Answer: B
Subject: mathematics
Question: A curve passes through the point (1 , π/6) . Let the slope of the curve at each point (x, y) be y/x + sec (y/x), x > 0. Then the equation of the curve is
Choices: (A) sin (y/x) = log x + 1/2 (B) cosec (y/x) = log x + 2 (C) sec (2y/x) = log x + 2 (D) cos (2y/x) = log x + 1/2
Answer: A
Subject: mathematics
Question: For a > b > c > 0, the distance between (1, 1) and the point of intersection of the lines ax + by + c = 0 and bx + ay + c = 0 is less than 2√2. Then
Choices: (A) a + b - c > 0, (B) a - b + c < 0, (C) a - b + c > 0, (D) a + b - c < 0
Answer: A or C or AC
Subject: mathematics
Question: Perpendiculars are drawn from points on the line x+2/2 = y+1/-1 = z/3 to the plane x + y + z = 3. The feet of perpendiculars lie on the line
Choices: (A) x/5 = y-1/8 = z-2/-13, (B) x/2 = y-1/3 = z-2/-5, (C) x/4 = y-1/3 = z-2/-7, (D) x/2 = y-1/-7 = z-2/5
Answer: D
Subject: mathematics
Question: Let PR = 3i + j - 2k and SQ = i - 3j - 4k determine diagonals of a parallelogram PQRS and PT = i + 2j + 3k be another vector. Then the volume of the parallelepipeddetermined by the vectors PT, PQ and PS is
Choices: (A) 5, (B) 20, (C) 10, (D) 30
Answer: C
Subject: mathematics
Question: For 3 x 3 matrices M and N, which of the following statement(s) is (are) NOT correct?
Choices: (A) N^TMN is symmetric or skew symmetric, according as M is symmetric or skew symmetric
(B) MN - NM is skew symmetric for all symmetric matrices M and N
(C) MN is symmetric for all symmetric matrices M and N
(D) (adj M) (adj N) = adj (MN) for all invertible matrices M and N
Answer: CD
Subject: mathematics
Question: Let f(x) = x sin πx, x > 0. Then for all natural numbers n, f'(x) vanishes at
Choices: A) a unique point in the interval (n, n + 1/2), B) a unique point in the interval (n + 1/2, n + 1), C) a unique point in the interval (n, n + 1), D) two points in the interval (n, n + 1)
Answer: BC
Subject: mathematics
Question: A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 3 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the rectangular sheet are
Choices: (A) 24 (B) 32 (C) 45 (D) 60
Answer: AC
Subject: mathematics
Question: A line l passing through the origin is perpendicular to the lines l1 : (3 + 0)i + (-1 + 2t)j + (4 + 2t)k , -∞ < t < ∞ l2 : (3 + 2s)i + (3 + 2s)j + (2 + s)k , -∞ < s < ∞ Then, the coordinate(s) of the point(s) on l2 at a distance of √17 from the point of intersection of l and l1 is (are)
Choices: (A) (7/3, 7/3, 3/3) (B) (-1, -1, 0) (C) (1, 1, 1) (D) (7/9, 7/9, 8/9)
Answer: BD
Subject: mathematics
Question: Of the three independent events E₁, E₂ and E₃, the probability that only E₁ occurs is α, only E₂ occurs is β and only E₃ occurs is γ. Let the probability p that none of events E₁, E₂ or E₃ occurs satisfy the equations (α − 2β) p = αβ and (β − 3γ) p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1). 

Then Probability of occurrence of E₁ / Probability of occurrence of E₃ =
Answer: 6
Subject: mathematics
Question: A vertical line passing through the point (h, 0) intersects the ellipse x^2/4 + y^2/3 = 1 at the points P and Q. Let the tangents to the ellipse at P and Q meet at the point R. If A(h) = area of the triangle PQR, A1 = max (1/2≤h≤1) A(h) and A2 = min (1/2≤h≤1) A(h), then 8/sqrt(5) A1 - 8A2 =
Choices: No multiple choice options given
Answer: 9