cmeraki/elemento huggingface dataset:
Subject: physics
Question: One end of a horizontal uniform beam of weight W and length L is hinged on a vertical wall at point O and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point Q, at a height L above the hinge at point O. A block of weight αW is attached at the point P of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of (2√2)W. Which of the following statement(s) is(are) correct?
Choices: A) The vertical component of reaction force at O does not depend on α
B) The horizontal component of reaction force at O is equal to W for α = 0.5
C) The tension in the rope is 2W for α = 0.5
D) The rope breaks if α > 1.5
Subject: physics
Question: A source, approaching with speed u towards the open end of a stationary pipe of length L, is emitting a sound of frequency fs. The farther end of the pipe is closed. The speed of sound in air is v and fo is the fundamental frequency of the pipe. For which of the following combination(s) of u and fs, will the sound reaching the pipe lead to a resonance?
Choices: A) u = 0.8v and fs = fo
B) u = 0.8v and fs = 2fo
C) u = 0.8v and fs = 0.5fo
D) u = 0.5v and fs = 1.5fo
Subject: physics
Question: For a prism of prism angle θ = 60°, the refractive indices of the left half and the right half are, respectively, n₁ and n₂ (n₂ ≥ n₁) as shown in the figure. The angle of incidence i is chosen such that the incident light rays will have minimum deviation if n₁ = n₂ = n = 1.5. For the case of unequal refractive indices, n₁ = n and n₂ = n + Δn (where Δn << n), the angle of emergence e = i + Δe. Which of the following statement(s) is(are) correct?
Choices: (A) The value of Δe (in radians) is greater than that of Δn

(B) Δe is proportional to Δn

(C) Δe lies between 2.0 and 3.0 milliradians, if Δn = 2.8 × 10^-3

(D) Δe lies between 1.0 and 1.6 milliradians, if Δn = 2.8 × 10^-3
Subject: physics
Question: A physical quantity S is defined as S = (E × B)/μ₀, where E is electric field, B is magnetic field and μ₀ is the permeability of free space. The dimensions of S are the same as the dimensions of  which of the following quantity(ies) ?
Choices: (A) Energy/Charge × Current

(B) Force/Length × Time

(C) Energy/Volume

(D) Power/Area
Subject: physics
Question: A heavy nucleus N, at rest, undergoes fission N → P + Q, where P and Q are two lighter nuclei. Let δ = MN − MP − MQ, where MP, MQ and MN are the masses of P, Q and N, respectively. EP and EQ are the kinetic energies of P and Q, respectively. The speeds of P and Q are vP and vQ, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?
Subject: physics
Question: Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I2 in the clockwise direction, with I2 > 2I1. B(x,y) denotes the magnetic field at a point (x,y) in the xy-plane. Which of the following statement(s) is(are) correct?
Choices: (A) B(x,y) is perpendicular to the xy-plane at any point in the plane (B) |B(x,y)| depends on x and y only through the radial distance r = √(x^2 + y^2) (C) |B (x,y)| is non-zero at all points for r < R (D) B (x,y) points normally outward from the xy-plane for all the points between the two loops
Answer: B,C
Subject: physics
Question: A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially the bottle is sealed at atmospheric pressure p0 = 10^5 Pa so that the volume of the trapped air is v0 = 3.3 cc. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p0 + Δp without changing its orientation. At this pressure, the volume of the trapped air is v0 − Δv. Let Δv = X cc and Δp = Y × 10^5 Pa.
Choices: NUMERICAL VALUE
Subject: physics
Question: In order to measure the internal resistance r1 of a cell of emf E, a meter bridge of wire resistance R0 = 50 Ω, a resistance R0/2, another cell of emf E/2 (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at l =72 cm, then the value of r1 is __ Ω.
Subject: physics
Question: In a photoemission experiment, the maximum kinetic energies of photoelectrons from metals P, Q and R are EP, EQ and ER, respectively, and they are related by EP = 2EQ = 2ER. In this experiment, the same source of monochromatic light is used for metals P and Q while a different source of monochromatic light is used for the metal R. The work functions for metals P, Q and R are 4.0 eV, 4.5 eV and 5.5 eV, respectively. The energy of the incident photon used for metal R, in eV, is ___.
Subject: chemistry
Question: For the following reaction\n2X + Y —> P\nthe rate of reaction is d[P]/dt = k[X]. Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the reaction mixture. The correct statement(s) about the reaction is(are)\n\n(Use: ln 2 = 0.693)
Choices: (A) The rate constant, k, of the reaction is 13.86 × 10^-4 s^-1.\n(B) Half-life of X is 50 s.\n(C) At 50 s, − d[X]/dt = 13.86 × 10^-3 mol L^-1 s^-1.\n(D) At 100 s, − d[Y]/dt = 3.46 × 10^-3 mol L^-1 s^-1.
Answer: A
Subject: chemistry
Question: Some standard electrode potentials at 298 K are given below:

Pb2+/Pb	−0.13 V
Ni2+/Ni	−0.24 V
Cd2+/Cd	−0.40 V
Fe2+/Fe	−0.44 V

To a solution containing 0.001 M of X2+ and 0.1 M of Y2+, the metal rods X and Y are inserted (at 298 K) and connected by a conducting wire. This resulted in dissolution of X. The correct combination(s) of X and Y, respectively, is(are)

(Given: Gas constant, R = 8.314 J K−1 mol−1,
Faraday constant, F = 96500 C mol−1)
Choices: (A) Cd and Ni

(B) Cd and Fe

(C) Ni and Pb

(D) Ni and Fe
Answer: C
Subject: chemistry
Question: The pair(s) of complexes wherein both exhibit tetrahedral geometry is(are)

(Note: py = pyridine
Given: Atomic numbers of Fe, Co, Ni and Cu are 26, 27, 28 and 29, respectively)
Choices: (A) [FeCl4]− and [Fe(CO)4]2−		(B) [Co(CO)4]− and [CoCl4]2−

(C) [Ni(CO)4] and [Ni(CN)4]2−		(D) [Cu(py)4]+ and [Cu(CN)4]3−
Answer: B
Subject: chemistry
Question: At 298 K, the limiting molar conductivity of a weak monobasic acid is 4 × 10^2 S cm^2 mol^-1. At 298 K, for an aqueous solution of the acid the degree of dissociation is α and the molar conductivity is y × 10^2 S cm^2 mol^-1. At 298 K, upon 20 times dilution with water, the molar conductivity of the solution becomes 3y × 10^2 S cm^2 mol^-1. The value of α is ___.
Choices: No response choices provided.
Answer: Numeric value to be entered.
Subject: chemistry
Question: Reaction of x g of Sn with HCl quantitatively produced a salt. Entire amount of the salt reacted with y g of nitrobenzene in the presence of required amount of HCl to produce 1.29 g of an organic salt (quantitatively). (Use Molar masses (in g mol^-1) of H, C, N, O, Cl and Sn as 1, 12, 14, 16, 35 and 119, respectively).
Choices: No response choices provided.
Answer: Numeric values for x and y to be entered.
Subject: chemistry
Question: A sample (5.6 g) containing iron is completely dissolved in cold dilute HCl to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M KMnO4 solution to reach the end point. Number of moles of Fe2+ present in 250 mL solution is x × 10^-7 (consider complete dissolution of FeCl2). The amount of iron present in the sample is y% by weight. (Assume: KMnO4 reacts only with Fe2+ in the solution Use: Molar mass of iron as 56 g mol^-1) The value of x is ___.
Subject: chemistry
Question: A sample (5.6 g) containing iron is completely dissolved in cold dilute HCl to prepare a 250 mL of solution. Titration of 25.0 mL of this solution requires 12.5 mL of 0.03 M KMnO4 solution to reach the end point. Number of moles of Fe2+ present in 250 mL solution is x × 10^-7 (consider complete dissolution of FeCl2). The amount of iron present in the sample is y% by weight. (Assume: KMnO4 reacts only with Fe2+ in the solution Use: Molar mass of iron as 56 g mol^-1) The value of y is ___.
Subject: chemistry
Question: The amount of energy required to break a bond is same as the amount of energy released when the same bond is formed. In gaseous state, the energy required for homolytic cleavage of a bond is called Bond Dissociation Energy (BDE) or Bond Strength. BDE is affected by s-character of the bond and the stability of the radicals formed. Shorter bonds are typically stronger bonds. BDEs for some bonds are given below:
Choices: There are no multiple choice options provided.
Answer: The question shows values for 4 different bond dissociation energies: H3C-H (105 kcal mol^-1), Cl-Cl (58 kcal mol^-1), H3C-Cl (85 kcal mol^-1), H-Cl (103 kcal mol^-1).
Subject: chemistry
Question: Correct match of the C-H bonds (shown in bold) in Column J with their BDE in Column K is
Choices: A) P - iii, Q - iv, R - ii, S - i
B) P - i, Q - ii, R - iii, S - iv
C) P - iii, Q - ii, R - i, S - iv
D) P - ii, Q - i, R - iv, S - iii
Answer: B) P - i, Q - ii, R - iii, S - iv
Subject: chemistry
Question: For the following reaction

CH4(g) + Cl2(g) → CH3Cl(g) + HCl(g)

the correct statement is
Choices: A) Initiation step is exothermic with ΔH° = -58 kcal mol-1.
B) Propagation step involving •CH3 formation is exothermic with ΔH° = -2 kcal mol-1.
C) Propagation step involving CH3Cl formation is endothermic with ΔH° = +27 kcal mol-1.
D) The reaction is exothermic with ΔH° = -25 kcal mol-1.
Answer: D) The reaction is exothermic with ΔH° = -25 kcal mol-1
Subject: mathematics
Question: Let S1 = {(i, j, k) : i, j, k ∈ {1,2, ...,10}}, S2 = {(i, j) : 1 ≤ i < j + 2 ≤ 10, i, j ∈ {1,2, ..., 10}}, S3 = {(i, j, k, l) : 1 ≤ i < j < k < l, i, j, k, l ∈ {1,2, ...,10}} and S4 = {(i, j, k, l) : i, j, k and l are distinct elements in {1,2, ...,10}}. If the total number of elements in the set Sr is nr, r = 1,2,3,4, then which of the following statements is (are) TRUE ?
Choices: (A) n1 = 1000 (B) n2 = 44 (C) n3 = 220 (D) n4 = 420
Answer: (D) n4 = 420
Subject: mathematics
Question: Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE ?
Choices: (A) cos P ≥ 1 - p^2/2qr, (B) cos R ≥ (q-r)/(q+r) cos P + (p-r)/(p+r) cos Q, (C) (q+r)/p < 2 √(sin Q sin R/sin P), (D) If p < q and p < r, then cos Q > p/r and cos R > p/q
Subject: mathematics
Question: Let f: [- π/2, π] → ℝ be a continuous function such that f(0) = 1 and ∫(π/2)^0 f(t)dt = 0. Then which of the following statements is (are) TRUE ?
Choices: (A) The equation f(x) - 3 cos 3x = 0 has at least one solution in (0, π/3), (B) The equation f(x) - 3 sin 3x = - 6/π has at least one solution in (0, π/3), (C) lim x→1- ∫x/0 f(t)dt/(1-e^x^2) = -1, (D) lim x→0 sin x ∫0^x f(t)dt/x^2 = -1
Subject: mathematics
Question: For any real numbers α and β, let yα,β(x), x ∈ ℝ, be the solution of the differential equation dy/dx + αy = xeβx, y(1) = 1. Let S = {yα,β (x) : α,β ∈ ℝ}. Then which of the following functions belong(s) to the set S?
Choices: (A) f(x) = (x²/2) e^-x + (e - 1/2) e^-x, (B) f(x) = -x² e^-x + (e + 1/2) e^-x, (C) f(x) = e^x (x - 1/2) + (e - e²/4) e^-x, (D) f(x) = e^x (1 - x)/2 + (e + e²/4) e^-x
Subject: mathematics
Question: Let O be the origin and OA⃗ = 2i⃗ + 2j⃗ + k⃗, OB⃗ = i⃗ - 2j⃗ + 2k⃗ and OC⃗ = 1/λ (OB⃗ - λ OA⃗) for some λ > 0. If |OB⃗ × OC⃗| = 9/2 , then which of the following statements is (are) TRUE?
Choices: (A) Projection of OC⃗ on OA⃗ is -3/2, (B) Area of the triangle OAB is 9/2, (C) Area of the triangle ABC is 9/2, (D) The acute angle between the diagonals of the parallelogram with adjacent sides OA⃗ and OC⃗ is π/3
Subject: mathematics
Question: Let E denote the parabola y^2 = 8x. Let P = (-2, 4), and let Q and Q' be two distinct points on E such that the lines PQ and PQ' are tangents to E. Let F be the focus of E. Then which of the following statements is (are) TRUE ?
Choices: (A) The triangle PFQ is a right-angled triangle

(B) The triangle QPQ' is a right-angled triangle

(C) The distance between P and F is 5√2

(D) F lies on the line joining Q and Q'
Subject: mathematics
Question: Consider M with r = 1025/513. Let k be the number of all those circles Cn that are inside M. Let l be the maximum possible of circles among these k circles such that no two circles intersect. Then
Choices: (A) k + 2l = 22, (B) 2k + l = 26, (C) 2k + 3l = 34, (D) 3k + 2l = 40
Answer: (B) 2k + l = 26
Subject: mathematics
Question: Which of the following statements is TRUE ?
Choices: (A) f(√ln 3) + g(√ln 3) = 1⁄2
(B) For every x > 1, there exists an α ∈ (1, x) such that ψ1(x) = 1 + αx
(C) For every x > 0, there exists a β ∈ (0, x) such that ψ2(x) = 2x(ψ1(β) − 1)
(D) f is an increasing function on the interval [0, 2]
Subject: mathematics
Question: Which of the following statements is TRUE ?
Choices: (A) ψ1(x) ≤ 1, for all x > 0
(B) ψ2(x) ≤ 0, for all x > 0
(C) f(x) ≥ 1 − e^(-x^2) − 2⁄3 x^3 + 2⁄5 x^5, for all x ∈ (0, 1⁄2)
(D) g(x) ≤ 3⁄4 x^3 − 2⁄5 x^5 + 1⁄7 x^7, for all x ∈ (0, 1⁄2)
Subject: mathematics
Question: Let E be the ellipse (x^2)/16 + (y^2)/9 = 1. For any three distinct points P, Q and Q' on E, let M(P, Q) be the mid-point of the line segment joining P and Q, and M(P, Q') be the mid-point of the line segment joining P and Q'. Then the maximum possible value of the distance between M(P, Q) and M(P, Q'), as P, Q and Q' vary on E, is ___.