cmeraki/elemento huggingface dataset:
Subject: mathematics
Question: Let α be a positive real number. Let f: ℝ → ℝ and g: (α, ∞) → ℝ be the functions defined by f(x) = sin((πx/12)) and g(x) = (2 logₐ(sqrt(x) - sqrt(α)))/logₐ(e^(sqrt(x)) - e^sqrt(α)). Then the value of lim[x→α+] f(g(x)) is _________.
Subject: mathematics
Question: In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of breathing problem, 330 persons had symptom of fever or cough or both, 350 persons had symptom of cough or breathing problem or both, 340 persons had symptom of fever or breathing problem or both, 30 persons had all three symptoms (fever, cough and breathing problem). If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is _________.
Subject: mathematics
Question: Let l1, l2 ..., l100 be consecutive terms of an arithmetic progression with common difference d1, and let w1, w2, ..., w100 be consecutive terms of another arithmetic progression with common difference d2 , where d1d2 = 10. For each i = 1, 2, ..., 100, let Ri be a rectangle with length li, width wi and area Ai. If A51 - A50 = 1000, then the value of A100 - A99 is _________.
Subject: mathematics
Question: Consider the equation ∫[e/(1 × (a – (log₀ x)^½)^2)] × (log₀ x)^(1/2) dx = 1, a ∈ (-∞, 0) ∪ (1, ∞). Which of the following statements is/are TRUE?
Choices: (A) No a satisfies the above equation, (B) An integer a satisfies the above equation, (C) An irrational number a satisfies the above equation, (D) More than one a satisfy the above equation
Answer: D
Subject: mathematics
Question: Let a1, a2, a3, ... be an arithmetic progression with a1 = 7 and common difference 8. Let T1, T2, T3, ... be such that T1 = 3 and Tn+1 - Tn = an for n ≥ 1. Then, which of the following is/are TRUE ?
Choices: (A) T20 = 1604, (B) Σ20k=1 Tk = 10510, (C) T30 = 3454, (D) Σ30k=1 Tk = 35610
Answer: (B) Σ20k=1 Tk = 10510
Subject: mathematics
Question: Let P1 and P2 be two planes given by P1: 10x + 15y + 12z - 60 = 0, P2: - 2x + 5y + 4z - 20 = 0. Which of the following straight lines can be an edge of some tetrahedron whose two faces lie on P1 and P2 ?
Choices: (A) x-1=y-1=z-1/5, (B) x-6/-5=y=z/3, (C) x/2=y-4/5=z/4, (D) x=y-4/-2=z/3
Answer: (B) x-6/-5=y=z/3
Subject: mathematics
Question: Let S be the reflection of a point Q with respect to the plane given by r = -(t + p)i + tj + (1 + p)k where t, p are real parameters and i, j, k are the unit vectors along the three positive coordinate axes. If the position vectors of Q and S are 10i + 15j + 20k and αi + βj + γk respectively, then which of the following is/are TRUE ?
Choices: (A) 3(α + β) = -101, (B) 3(β + γ) = -71, (C) 3(γ + α) = -86, (D) 3(α + β + γ) = -121
Answer: (B) 3(β + γ) = -71
Subject: mathematics
Question: Consider the parabola y^2 = 4x. Let S be the focus of the parabola. A pair of tangents drawn to the parabola from the point P = (−2, 1) meet the parabola at P1 and P2. Let Q1 and Q2 be points on the lines SP1 and SP2 respectively such that PQ1 is perpendicular to SP1 and PQ2 is perpendicular to SP2. Then, which of the following is/are TRUE ?
Choices: (A) SQ1 = 2 (B) Q1Q2 = 3√10/5 (C) PQ1 = 3 (D) SQ2 = 1
Answer: C
Subject: mathematics
Question: Let |M| denote the determinant of a square matrix M. Let g: [0, π] → ℝ be the function defined by g(θ) = √(f(θ) − 1 + √((π − θ)/2 − θ) − 1) where f(θ) = 1/2 [1 -sin θ sin θ 1; -sin θ -1 sin θ; 1 -sin θ 1] + [sin π cos (θ + π/4) tan (θ - π/4); -cos π/4 -logE (π/4) tan π; cot (θ + π/4) logB (π/4)]  Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g(θ), and p(2) = 2 - √2 . Then, which of the following is/are TRUE ?
Choices: (A) p (3+√2/4) < 0 (B) p (1+3√2/4) > 0 (C) p (5√2-1/4) > 0 (D) p (5-√2/4) < 0
Answer: C
Subject: mathematics
Question: Consider the following lists: [List-I with four sets of equations given] [List-II with descriptions of set sizes P, Q, R, S, T]
Choices: (A) (I) → (P); (II) → (S); (III) → (P); (IV) → (S) 
(B) (I) → (P); (II) → (P); (III) → (T); (IV) → (R) 
(C) (I) → (Q); (II) → (P); (III) → (T); (IV) → (S) 
(D) (I) → (Q); (II) → (S); (III) → (P); (IV) → (R)
Answer: (B) (I) → (P); (II) → (P); (III) → (T); (IV) → (R)
Subject: mathematics
Question: Two players, P1 and P2, play a game against each other. In every round of the game, each player rolls a fair die once, where the six faces of the die have six distinct numbers. Let x and y denote the readings on the die rolled by P1 and P2, respectively. If x > y, then P1 scores 5 points and P2 scores 0 point. If x = y, then each player scores 2 points. If x < y, then P1 scores 0 point and P2 scores 5 points. Let Xl and Yl be the total scores of P1 and P2, respectively, after playing the lth round.
Choices: (A) (I) → (Q); (II) → (R); (III) → (T); (IV) → (S) 
 (B) (I) → (Q); (II) → (R); (III) → (T); (IV) → (T) 
 (C) (I) → (P); (II) → (R); (III) → (Q); (IV) → (S) 
 (D) (I) → (P); (II) → (R); (III) → (Q); (IV) → (T)
Answer: (C) (I) → (P); (II) → (R); (III) → (Q); (IV) → (S)
Subject: mathematics
Question: Let p, q, r be nonzero real numbers that are, respectively, the 10th, 100th and 1000th terms of a harmonic progression. Consider the system of linear equations x + y + z = 1, 10x + 100y + 1000z = 0, qr x + pr y + pq z = 0.
Choices: (A) (I) → (T); (II) → (R); (III) → (S); (IV) → (T) | (B) (I) → (Q); (II) → (S); (III) → (S); (IV) → (R) | (C) (I) → (Q); (II) → (R); (III) → (P); (IV) → (R) | (D) (I) → (T); (II) → (S); (III) → (P); (IV) → (T)
Answer: (C) (I) → (Q); (II) → (R); (III) → (P); (IV) → (R)
Subject: mathematics
Question: Consider the ellipse (x^2)/4 + (y^2)/3 = 1. Let H(α, 0), 0 < α < 2, be a point. A straight line drawn through H parallel to the y-axis crosses the ellipse and its auxiliary circle at points E and F respectively, in the first quadrant. The tangent to the ellipse at the point E intersects the positive x-axis at a point G. Suppose the straight line joining F and the origin makes an angle ϕ with the positive x-axis.
Choices: List-I: (I) If ϕ = π/4, then the area of the triangle FGH is, (II) If ϕ = π/3, then the area of the triangle FGH is, (III) If ϕ = π/6, then the area of the triangle FGH is, (IV) If ϕ = π/12, then the area of the triangle FGH is; List-II: (P) (√3-1)^4/8, (Q) 1, (R) 3/4, (S) 1/2√3, (T) 3√3/2
Answer: D
Subject: physics
Question: Two spherical stars A and B have densities ρA and ρB, respectively. A and B have the same radius, and their masses MA and MB are related by MB = 2MA. Due to an interaction process, star A loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains ρA. The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being ρA. If vA and vB are the escape velocities from A and B after the interaction process, the ratio vB/vA = √[10n/(3√π)]. The value of n is _____.
Choices: No response choices provided
Answer: Numerical Value
Subject: physics
Question: The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction 15N + 4He → 3H + 18O in a laboratory frame is n (in MeV). Assume that 15N is at rest in the laboratory frame. The masses of 15N, 4He, 3H and 18O can be taken to be 16.006 u, 4.003 u, 1.008 u and 19.003 u, respectively, where 1 u = 930 MeV/c^2. The value of n is _____.
Choices: No response choices provided
Answer: Numerical Value
Subject: physics
Question: A rod of length 2 cm makes an angle 2π/3 rad with the principal axis of a thin convex lens. The lens has a focal length of 10 cm and is placed at a distance of 40/3 cm from the object as shown in the figure. The height of the image is 30√3/13 cm and the angle made by it with respect to the principal axis is α rad. The value of α is π/n rad, where n is _______.
Choices: No response choices provided
Answer: Numerical Value
Subject: physics
Question: At time t = 0, a disk of radius 1 m starts to roll without slipping on a horizontal plane with an angular acceleration of α = 5 rad s^-2. A small stone is stuck to the disk. At t = 0, it is at the contact point of the disk and the plane. Later, at time t = √6 s, the stone detaches itself and flies off tangentially from the disk. The maximum height (in m) reached by the stone measured from the plane is ½ + √6/10. The value of x is _____. [Take g = 10 m s^-2.]
Choices: No response choices provided
Answer: No answer provided
Subject: physics
Question: A solid sphere of mass 1 kg and radius 1 m rolls without slipping on a fixed inclined plane with an angle of inclination θ = 30° from the horizontal. Two forces of magnitude 1 N each, parallel to the incline, act on the sphere, both at distance r = 0.5 m from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ___ ms^-2. (Take g = 10 m s^-2.)
Choices: No response choices provided
Answer: No answer provided
Subject: physics
Question: Consider an LC circuit, with inductance L = 0.1 H and capacitance C = 10^-3 F, kept on a plane. The area of the circuit is 1 m². It is placed in a constant magnetic field of strength B0 which is perpendicular to the plane of the circuit. At time t = 0, the magnetic field strength starts increasing linearly as B = B0 + βt with β = 0.04 Ts^-1. The maximum magnitude of the current in the circuit is ___ mA.
Choices: No response choices provided
Answer: No answer provided
Subject: physics
Question: A projectile is fired from horizontal ground with speed v and projection angle θ. When the acceleration due to gravity is g, the range of the projectile is d. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is g' = v²/g.π², then the new range is d' = π.d. The value of n is _____.
Choices: No response choices provided
Answer: No answer provided
Subject: physics
Question: A medium having dielectric constant K >1 fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is d. The capacitor is connected to a battery of voltage V, as shown in Figure (a). Now, both the plates are moved by a distance of d/2 from their original positions, as shown in Figure (b). In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?
Choices: (A) The electric field inside the dielectric material is reduced by a factor of 2K. (B) The capacitance is decreased by a factor of (1+d/2)/(1+d). (C) The voltage between the capacitor plates is increased by a factor of (K + 1). (D) The work done in the process DOES NOT depend on the presence of the dielectric material.
Answer: B
Subject: physics
Question: An ideal gas of density ρ = 0.2 kg m^-3 enters a chimney of height h at the rate of α = 0.8 kg s^-1 from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is A1 = 0.1 m^2 and the upper end is A2 = 0.4 m^2. The pressure and the temperature of the gas at the lower end are 600 Pa and 300 K, respectively, while its temperature at the upper end is 150 K. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take g = 10 m s^-2 and the ratio of specific heats of the gas γ = 2. Ignore atmospheric pressure. Which of the following statement(s) is(are) correct?
Choices: (A) The pressure of the gas at the upper end of the chimney is 300 Pa.
(B) The velocity of the gas at the lower end of the chimney is 40 m s^-1 and at the upper end is 20 m s^-1.
(C) The height of the chimney is 590 m.
(D) The density of the gas at the upper end is 0.05 kg m^-3.
Subject: physics
Question: Three plane mirrors form an equilateral triangle with each side of length L. There is a small hole at a distance l > 0 from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle θ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane. Which of the following statement(s) is(are) correct?
Choices: (A) The ray of light will come out for θ = 30°, for 0 < l < L.
(B) There is an angle for l = L/2 at which the ray of light will come out after two reflections.
(C) The ray of light will NEVER come out for θ = 60°, and l = L/3.
(D) The ray of light will come out for θ = 60°, and 0 < l < L/2 after six reflections.
Subject: physics
Question: A small circular loop of area A and resistance R is fixed on a horizontal xy-plane with the center of the loop always on the axis n̂ of a long solenoid. The solenoid has m turns per unit length and carries current I counterclockwise as shown in the figure. The magnetic field due to the solenoid is in n̂ direction. List-I gives time dependences of n̂ in terms of a constant angular frequency ω. List-II gives the torques experienced by the circular loop at time t = π/ω. Let α = A^2R^2nm^2/2R.
Choices: (A) I->Q, II->P, III->S, IV->T 
(B) I->S, II->T, III->Q, IV->P 
(C) I->Q, II->P, III->S, IV->R 
(D) I->T, II->Q, III->P,IV->R
Answer: (C) I->Q, II->P, III->S, IV->R
Subject: physics
Question: List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities (in m s^-1) at time t = π/3 s.
Choices: (A) I → R, II → T, III → P, IV → S
(B) I → S, II → P, III → Q, IV → R
(C) I → S, II → T, III → P, IV → R
(D) I → T, II → P, III → R, IV → S
Answer: C
Subject: physics
Question: List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process. Which one of the following options is correct?
Choices: (A) I → T, II → R, III → S, IV → Q, (B) I → S, II → P, III → T, IV → P, (C) I → P, II → R, III → T, IV → Q, (D) I → Q, II → R, III → S, IV → T,
Answer: (D)
Subject: physics
Question: Which one of the following options is correct?
Choices: (A) (I) → P; (II) → R; (III) → Q; (IV) → T
(B) (I) → Q; (II) → P; (III) → T; (IV) → S
(C) (I) → P; (II) → T; (III) → R; (IV) → Q
(D) (I) → T; (II) → S; (III) → Q; (IV) → R
Answer: (C)
Subject: chemistry
Question: 2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of O2 at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of Hg(g) are 20.00 kJ K^-1 and 61.32 kJ mol^-1 at 298 K, respectively, the calculated standard molar enthalpy of formation of HgO(s) at 298 K is X kJ mol^-1. The value of [X] is _____. [Given: Gas constant R = 8.3 J K^-1 mol^-1]
Choices: Numerical Value
Answer: Numerical Value
Subject: chemistry
Question: For diatomic molecules, the correct statement(s) about the molecular orbitals formed by the overlap of two 2pz orbitals is(are)
Choices: (A) σ orbital has a total of two nodal planes.
(B) σ* orbital has one node in the xz-plane containing the molecular axis.
(C) π orbital has one node in the plane which is perpendicular to the molecular axis and goes through the center of the molecule.
(D) π* orbital has one node in the xy-plane containing the molecular axis.
Subject: chemistry
Question: The correct option(s) related to adsorption processes is(are)
Choices: (A) Chemisorption results in a unimolecular layer.
(B) The enthalpy change during physisorption is in the range of 100 to 140 kJ mol¯¹.
(C) Chemisorption is an endothermic process.
(D) Lowering the temperature favors physisorption processes.
Subject: chemistry
Question: The electrochemical extraction of aluminum from bauxite ore involves
Choices: (A) the reaction of Al2O3 with coke (C) at a temperature > 2500 °C. (B) the neutralization of aluminate solution by passing CO2 gas to precipitate hydrated alumina (Al2O3·3H2O). (C) the dissolution of Al2O3 in hot aqueous NaOH. (D) the electrolysis of Al2O3 mixed with Na3AlF6 to give Al and CO2.
Subject: chemistry
Question: Considering the reaction sequence given below, the correct statement(s) is(are)
Choices: (A) P can be reduced to a primary alcohol using NaBH4. (B) Treating P with conc. NH4OH solution followed by acidification gives Q. (C) Treating Q with a solution of NaNO2 in aq. HCl liberates N2. (D) P is more acidic than CH3CH2COOH.
Answer: B
Subject: chemistry
Question: Considering the following reaction sequence, the correct option(s) is(are)
Choices: A) P = H2/Pd, ethanol R = NaNO2/HCl U = 1. H3PO2 2. KMnO4 - KOH, heat B) P = Sn/HCl R = HNO2 S = (image) C) S = (image) T = (image) U = 1. CH3CH2OH 2. KMnO4 - KOH, heat D) Q = (image) R = H2/Pd, ethanol T = (image)
Answer: C
Subject: chemistry
Question: Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. X, and k are constants having appropriate units.
Choices: A) I → P, II → Q, III → S, IV → T
B) I → R, II → S, III → S, IV → T
C) I → P, II → Q, III → Q, IV → R
D) I → R, II → S, III → Q, IV → R
Answer: B
Subject: chemistry
Question: LIST-I contains compounds and LIST-II contains reactions

LIST-I
(I) H₂O₂
(II) Mg(OH)₂
(III) BaCl₂
(IV) CaCO₃

LIST-II
(P) Mg(HCO₃)₂ + Ca(OH)₂ →
(Q) BaO₂ + H₂SO₄ →
(R) Ca(OH)₂ + MgCl₂ →
(S) BaO₂ + HCl →
(T) Ca(HCO₃)₂ + Ca(OH)₂ →

Match each compound in LIST-I with its formation reaction(s) in LIST-II, and choose the correct option
Choices: (A) I → Q; II → P; III → S; IV → R
(B) I → T; II → P; III → Q; IV → R
(C) I → T; II → R; III → Q; IV → P
(D) I → Q; II → R; III → S; IV → P
Answer: D
Subject: chemistry
Question: LIST-I contains metal species and LIST-II contains their properties.

LIST-I
(I) [Cr(CN)₆]³⁻
(II) [RuCl₆]²⁻
(III) [Cr(H₂O)₆]³⁺
(IV) [Fe(H₂O)₆]³⁺

LIST-II
(P) t₂g orbitals contain 4 electrons
(Q) μ (spin-only) = 4.9 BM
(R) low spin complex ion
(S) metal ion in 4+ oxidation state
(T) d³ species

[Given: Atomic number of Cr = 24, Ru = 44, Fe = 26]

Match each metal species in LIST-I with their properties in LIST-II, and choose the correct option
Choices: (A) I → R, T; II → P, S; III → Q, T; IV → P, Q
(B) I → R, S; II → P, T; III → P, Q; IV → Q, T
(C) I → P, R; II → R, S; III → R, T; IV → P, T
(D) I → Q, T; II → S, T; III → P, T; IV → Q, R
Answer: B
Subject: chemistry
Question: Match the compounds in LIST-I with the observations in LIST-II, and choose the correct option.
Choices: (A) I→P,Q; II→S; III→Q,R; IV→P
(B) I→P; II→R,S; III→R; IV→Q,S
(C) I→Q,S; II→P,T; III→P; IV→S
(D) I→P,S; II→T; III→Q,R; IV→P