cmeraki/elemento huggingface dataset:
Subject: physics
Question: A resistance of 2 Ω is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 Ω, is connected across the other gap. When these resistances are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is
Choices: (A) 3 Ω (B) 4 Ω (C) 5 Ω (D) 6 Ω
Answer: A
Subject: physics
Question: In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then,
Choices: (A) x < f (B) f < x < 2f (C) x = 2f (D) x > 2f
Answer: B
Subject: physics
Question: Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' from the center P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes 2x, is
Choices: (A) F/2m √(a^2 - x^2) (B) F/2m √(a^2 - x^2) (C) Fx/2ma (D) F/2m √(a^2 - x^2) * x
Answer: B
Subject: physics
Question: A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.
Choices: (A) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder
(B) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
(C) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders
(D) No potential difference appears between the two cylinders when same charge density is given to both the cylinders
Answer: A
Subject: physics
Question: A ray of light traveling in water is incident on its surface open to air. The angle of incidence is θ, which is less than the critical angle. Then there will be
Choices: (A) only a reflected ray and no refracted ray
(B) only a refracted ray and no reflected ray
(C) a reflected ray and a refracted ray and the angle between them would be less than 180°– 2θ
(D) a reflected ray and a refracted ray and the angle between them would be greater than 180°– 2θ
Answer: C
Subject: chemistry
Question: In the options given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is
Choices: (A) E(92U) > E(137I) + E(97Y) + 2E(n)
(B) E(92U) < E(137I) + E(97Y) + 2E(n)
(C) E(92U) < E(140Ba) + E(94Kr) + 2E(n)
(D) E(92U) = E(140Ba) + E(94Kr) + 2E(n)
Answer: A
Subject: physics
Question: STATEMENT-1
A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

because

STATEMENT-2
The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Answer: C
Subject: physics
Question: STATEMENT-1
In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

because

STATEMENT-2
In an elastic collision, the linear momentum of the system is conserved.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
Answer: B
Subject: physics
Question: The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. because STATEMENT-2 Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.
Choices: A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 C) Statement-1 is True, Statement-2 is False D) Statement-1 is False, Statement-2 is True
Answer: C
Subject: physics
Question: STATEMENT-1 If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change. because STATEMENT-2 When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.
Choices: A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 C) Statement-1 is True, Statement-2 is False D) Statement-1 is False, Statement-2 is True
Answer: B
Subject: physics
Question: While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is
Choices: (A) (2P₀πR⁴)/(πR²P₀ + Mg) (2L), (B) (P₀πR²-Mg)/(πR²P₀) (2L), (C) (P₀πR² + Mg)/(πR²P₀) (2L), (D) (P₀πR²)/(πR²P₀ - Mg) (2L)
Answer: D
Subject: physics
Question: The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is ρ. In equilibrium, the height H of the water column in the cylinder satisfies
Choices: (A) ρg(L₀ - H)² + P₀(L₀ - H) + L₀P₀ = 0, (B) ρg(L₀ - H)² - P₀(L₀ - H) - L₀P₀ = 0, (C) ρg(L₀ - H)² + P₀(L₀ - H) - L₀P₀ = 0, (D) ρg(L₀ - H)² - P₀(L₀ - H) + L₀P₀ = 0
Answer: C
Subject: physics
Question: Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.
Choices: Column I: (A) GMeMe, G - universal gravitational constant, Me - mass of the earth, Ms - mass of the Sun
(B) 3RT/M, R - universal gas constant, T - absolute temperature, M - molar mass
(C) F^2/q^2B^2, F - force, q - charge, B - magnetic field
(D) GMe/Re, G - universal gravitational constant, Me - mass of the earth, Re - radius of the earth

Column II: (p) (volt) (coulomb) (metre)
(q) (kilogram) (metre)^3 (second)^-2
(r) (metre)^2 (second)^-2
(s) (farad) (volt)^2 (kg)^-1
Answer: A:pq, B:qr, C:rr, D:ss
Subject: physics
Question: Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4x4 matrix given in the ORS.
Choices: (A) A charged capacitor is connected to the ends of the wire, (B) The wire is moved perpendicular to its length with a constant velocity in a uniform magnetic field perpendicular to the plane of motion, (C) The wire is placed in a constant electric field that has a direction along the length of the wire, (D) A battery of constant emf is connected to the ends of the wire, (p) A constant current flows through the wire, (q) Thermal energy is generated in the wire, (r) A constant potential difference develops between the ends of the wire, (s) Charges of constant magnitude appear at the ends of the wire
Answer: D, p, q; B, q, r; C, r; A, s
Subject: physics
Question: Some laws / processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 x 4 matrix given in the ORS.
Choices: (A) Transition between two atomic energy levels, (B) Electron emission from a material, (C) Mosley's law, (D) Change of photon energy into kinetic energy of electrons, (p) Characteristic X-rays, (q) Photoelectric effect, (r) Hydrogen spectrum, (s) β-decay
Answer: A(p,b,c), B(a,d), C(r), D(s)
Subject: chemistry
Question: When 20 g of naphthoic acid (C11H8O2) is dissolved in 50 g of benzene (Kf = 1.72 K kg mol^-1), a freezing point depression of 2 K is observed. The van't Hoff factor (i) is
Choices: A) 0.5, B) 1, C) 2, D) 3
Answer: A
Subject: chemistry
Question: The value of log10K for a reaction A ⇌ B is (Given : ΔrH°298K = −54.07 kJ mol^-1, ΔrS°298K = 10 JK^-1 mol^-1 and R = 8.314 JK^-1 mol^-1, 2.303 × 8.314 × 298 = 5705)
Choices: A) 5, B) 10, C) 95, D) 100
Answer: B
Subject: chemistry
Question: STATEMENT-1 : Boron always forms covalent bond. because STATEMENT-2 : The small size of B3+ favours formation of covalent bond.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Answer: A
Subject: chemistry
Question: STATEMENT-1 : In water, orthoboric acid behaves as a weak monobasic acid. because STATEMENT-2 : In water, orthoboric acid acts as a proton donor.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Answer: C
Subject: chemistry
Question: STATEMENT-1 : p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid. because STATEMENT-2 : o-Hydroxybenzoic acid has intramolecular hydrogen bonding.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Answer: D
Subject: chemistry
Question: STATEMENT-1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC). because STATEMENT-2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Answer: B
Subject: chemistry
Question: Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
Choices: Column I: (A) [Co(NH3)4(H2O)2]Cl2, (B) [Pt(NH3)2Cl2], (C) [Co(H2O)6]Cl]Cl, (D) [Ni(H2O)6]Cl2 
 Column II: (p) geometrical isomers, (q) paramagnetic, (r) diamagnetic, (s) metal ion with +2 oxidation state
Answer: A: pq, B: qr, C: rs, D: ps
Subject: chemistry
Question: Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
Choices: Column I: (A) cellulose, (B) nylon-6, 6, (C) protein, (D) sucrose 
 Column II: (p) natural polymer, (q) synthetic polymer, (r) amide linkage, (s) glycoside linkage
Answer: A: p, s; B: q, q; C: r, r; D: s
Subject: chemistry
Question: Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
Choices: Column I: (A) hydrogen gas (P = 200 atm, T = 273 K), (B) hydrogen gas (P = 0, T= 273 K), (C) CO2 (P = 1 atm, T = 273 K), (D) real gas with very large molar volume 
 Column II: (p) compressibility factor ≠ 1, (q) attractive forces are dominant, (r) PV = nRT, (s) P(V-nb)=nRT
Answer: A: p, s; B: q; C: r, r; D: s
Subject: mathematics
Question: Let α, β be the roots of the equation x^2 - px + r = 0 and α/2, 2β be the roots of the equation x^2 - qx + r = 0. Then the value of r is
Choices: (A) 2/9 (p - q)(2q - p) (B) 2/9 (q - p)(2p - q) (C) 2/9 (q - 2p)(2q - p) (D) 2/9 (2p - q)(2q - p)
Answer: D
Subject: mathematics
Question: Let f(x) be differentiable on the interval (0, ∞) such that f(1) = 1, and lim (t^2 f(t) - x^2 f(x) / t^2 - x^2) = 1 for each x > 0. Then f(x) is
Choices: (A) 1/3x + 2x^2/3 (B) -1/x + 4x^2/3 (C) -1/x + 2/x^2 (D) 1/x
Answer: A
Subject: mathematics
Question: The tangent to the curve y = e^x drawn at the point (c, e^c) intersects the line joining the points (c -1, e^(c-1)) and (c + 1, e^(c+1))
Choices: (A) on the left of x = c (B) on the right of x = c (C) at no point (D) at all points
Answer: A
Subject: mathematics
Question: A hyperbola, having the transverse axis of length 2 sin θ, is confocal with the ellipse 3x^2 + 4y^2 = 12. Then its equation is
Choices: (A) x^2 cosec^2 θ - y^2 sec^2 θ = 1, (B) x^2 sec^2 θ - y^2 cosec^2 θ = 1, (C) x^2 sin^2 θ - y^2 cos^2 θ = 1, (D) x^2 cos^2 θ - y^2 sin^2 θ = 1
Answer: A
Subject: mathematics
Question: A man walks a distance of 3 units from the origin towards the north-east (N 45°E) direction. From there, he walks a distance of 4 units towards the north-west (N 45°W) direction to reach a point P. Then the position of P in the Argand plane is
Choices: (A) 3e^(i/4) + 4i, (B) (3 - 4i)e^(i/4), (C) (4 + 3i)e^(i/4), (D) (3 + 4i)e^(i/4)
Answer: D
Subject: mathematics
Question: Let H1, H2, ..., Hn be mutually exclusive and exhaustive events with P(Hi) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1. STATEMENT-1 : P(Hi | E) > P(E | Hi). P(Hi) for i = 1, 2, ..., n. because STATEMENT-2 : ΣP(Hi) = 1.
Choices: (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, (C) Statement-1 is True, Statement-2 is False, (D) Statement-1 is False, Statement-2 is True
Answer: D
Subject: mathematics
Question: Tangents are drawn from the point (17, 7) to the circle x^2 + y^2 = 169 . STATEMENT-1 : The tangents are mutually perpendicular. because STATEMENT-2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is x^2 + y^2 = 338 . (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Choices: A, B, C, D
Answer: A
Subject: mathematics
Question: Let the vectors PQ , QR , RS , ST , TU and UP represent the sides of a regular hexagon. STATEMENT-1 : PQ × (RS + ST) ≠ 0 . because STATEMENT-2 : PQ × RS = 0 and PQ × ST ≠ 0 . (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Choices: A, B, C, D
Answer: C
Subject: mathematics
Question: Let F(x) be an indefinite integral of sin^2 x. STATEMENT-1 : The function F(x) satisfies F(x + π) = F(x) for all real x. because STATEMENT-2 : sin^2(x + π) = sin^2 x for all real x. (A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Choices: A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1, B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1, C) Statement-1 is True, Statement-2 is False, D) Statement-1 is False, Statement-2 is True
Answer: D
Subject: mathematics
Question: Let Vr denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is (2r - 1). Let Tr = Vr+1 - Vr - 2 and Qr = Tr+1 - Tr for r = 1, 2,... The sum V1 + V2 + ... + Vn is (A) 1/12 n(n + 1)(3n^2 - n + 1) (B) 1/12 n(n + 1)(3n^2 + n + 2) (C) 1/2 n(2n^2 - n + 1) (D) 1/3 (2n^3 - 2n + 3)
Choices: A) 1/12 n(n + 1)(3n^2 - n + 1), B) 1/12 n(n + 1)(3n^2 + n + 2), C) 1/2 n(2n^2 - n + 1), D) 1/3 (2n^3 - 2n + 3)
Answer: B
Subject: mathematics
Question: Which one of the following is a correct statement? (A) Q1, Q2, Q3,... are in A.P. with common difference 5 (B) Q1, Q2, Q3,... are in A.P. with common difference 6 (C) Q1, Q2, Q3,... are in A.P. with common difference 11 (D) Q1 - Q2 = Q3 - ...
Choices: (A) Q1, Q2, Q3,... are in A.P. with common difference 5, (B) Q1, Q2, Q3,... are in A.P. with common difference 6, (C) Q1, Q2, Q3,... are in A.P. with common difference 11, (D) Q1 - Q2 = Q3 - ...
Answer: B
Subject: mathematics
Question: Consider the following linear equations ax + by + cz = 0 bx + cy + az = 0 cx + ay + bz = 0 Match the conditions/expressions in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the 4 x 4 matrix given in the ORS.
Choices: Column I: (A) a + b + c ≠ 0 and a^2 + b^2 + c^2 = ab + bc + ca (B) a + b + c = 0 and a^2 + b^2 + c^2 ≠ ab + bc + ca (C) a + b + c ≠ 0 and a^2 + b^2 + c^2 ≠ ab + bc + ca (D) a + b + c = 0 and a^2 + b^2 + c^2 = ab + bc + ca Column II: (p) the equations represent planes meeting only at a single point. (q) the equations represent the line x = y = z. (r) the equations represent identical planes. (s) the equations represent the whole of the three dimensional space.
Answer: C-r, B-q, A-p, D-s
Subject: mathematics
Question: Match the functions in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the 4 × 4 matrix given in the ORS.
Choices: Column I: (A) x⌊x⌋, (B) √x, (C) x+⌊x⌋, (D) ⌊x-1⌋+⌊x+1⌋ 
 Column II: (p) continuous in (-1, 1), (q) differentiable in (-1, 1), (r) strictly increasing in (-1, 1), (s) not differentiable at least at one point in (-1, 1)
Answer: A: pqr, B: qs, C: rs, D: pq