cmeraki/elemento huggingface dataset:
Subject: mathematics
Question: Consider the two curves C1 : y^2 = 4x, C2 : x^2 + y^2 - 6x + 1 = 0. Then,
Choices: (A) C1 and C2 touch each other only at one point, (B) C1 and C2 touch each other exactly at two points, (C) C1 and C2 intersect (but do not touch) at exactly two points, (D) C1 and C2 neither intersect nor touch each other
Answer: B
Subject: mathematics
Question: If 0 < x < 1, then sqrt(1 + x^2) ( [x cos (cot^-1 x) + sin (cot^-1 x)]^2 - 1 )^2 =
Choices: (A) x/sqrt(1+x^2), (B) x, (C) x*sqrt(1+x^2), (D) sqrt(1+x^2)
Answer: C
Subject: mathematics
Question: The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors â, b̂, ĉ such that â.b̂ = b̂.ĉ = ĉ.â = 1/2. Then, the volume of the parallelopiped is
Choices: (A) 1/sqrt(2), (B) 1/2sqrt(2), (C) sqrt(3)/2, (D) 1/sqrt(3)
Answer: A
Subject: mathematics
Question: Let a and b be non-zero real numbers. Then, the equation (a x^2 + b y^2 + c) (x^2 - 5 x y + 6 y^2) = 0 represents
Choices: (A) four straight lines, when c = 0 and a, b are of the same sign, (B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a, (C) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a, (D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a
Answer: B
Subject: mathematics
Question: Let g(x) = (x-1)^n/(log cos^m (x-1)), 0<x<2, m and n are integers, m≠0, n>0, and let p be the left hand derivative of |x-1| at x=1. If lim g(x)=p, then
Choices: (A) n=1, m=1 (B) n=1, m=-1 (C) n=2, m=2 (D) n>2, m=n
Answer: C
Subject: mathematics
Question: A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
Choices: (A) 1/PS + 1/ST < 2/√QS×SR (B) 1/PS + 1/ST > 2/√QS×SR (C) 1/PS + 1/ST < 4/QR (D) 1/PS + 1/ST > 4/QR
Answer: B, D
Subject: mathematics
Question: Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the latus rectum of the ellipse x^2 + 4y^2 = 4. The equations of parabolas with latus rectum PQ are
Choices: (A) x^2 + 2√3 y = 3 + √3, (B) x^2 - 2√3 y = 3 + √3, (C) x^2 + 2√3 y = 3 - √3, (D) x^2 - 2√3 y = 3 - √3
Answer: C
Subject: mathematics
Question: Let S_n = Σ(n/(n^2 + kn + k^2)) and T_n = Σ((n-1)/(n^2 + kn + k^2)), for n = 1, 2, 3, .... Then,
Choices: (A) S_n < π/3√3, (B) S_n > π/3√3, (C) T_n < π/3√3, (D) T_n > π/3√3
Answer: A,D
Subject: mathematics
Question: Let f(x) be a non-constant twice differentiable function defined on (-∞, ∞) such that f(x) = f(1 - x) and f''(1/4) = 0. Then,
Choices: (A) f''(x) vanishes at least twice on [0, 1], (B) f'(1/2) = 0, (C) ∫(1/2)(-1/2) f(x + 1/2) sin x dx = 0, (D) ∫(1/2)(0) f(t) e^sin πt dt = ∫(1/2)(0) f(1 - t) e^sin πt dt
Answer: A,B,C,D
Subject: mathematics
Question: Let f and g be real valued functions defined on interval (- 1, 1) such that g''(x) is continuous, g(0) ≠ 0, g'(0) = 0, g''(0) ≠ 0, and f(x) = g(x)sin x. STATEMENT-1 : lim [g(x) cot x - g(0) cosec x] = f''(0) . and STATEMENT-2 : f'(0) = g(0) .
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: mathematics
Question: Consider three planes P1 :x - y + z = 1 P2 : x + y - z = -1 P3 :x - 3y + 3z = 2. Let L1, L2, L3 be the lines of intersection of the planes P2 and P3, P3 and P1, and P1 and P2, respectively. STATEMENT-1 : At least two of the lines L1, L2 and L3 are non-parallel. and STATEMENT-2 : The three planes do not have a common point.
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: Consider the system of equations x - 2y + 3z = -1 -x + y - 2z = k x - 3y + 4z = 1 STATEMENT-1 : The system of equations has no solution for k ≠ 3 and STATEMENT-2 : The determinant | 1 3 -1| |-1 -2 k| ≠ 0, for k ≠ 3. |1 4 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: A
Subject: mathematics
Question: Consider the system of equations ax + b y = 0 , c x + d y = 0 , where a, b, c, d ϵ {0, 1} . STATEMENT-1 : The probability that the system of equations has a unique solution is 3/8 . and STATEMENT-2 : The probability that the system of equations has a solution is 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: B
Subject: mathematics
Question: The equation of circle C is
Choices: (A) (x - 2√3)^2 + (y - 1)^2 = 1, (B) (x - 2√3)^2 + (y + 1/2)^2 = 1, (C) (x - √3)^2 + (y + 1)^2 = 1, (D) (x - √3)^2 + (y - 1)^2 = 1
Answer: D
Subject: mathematics
Question: Points E and F are given by
Choices: (A) (√3/2 , 2), (√3, 0), (B) (√3/2 , 1/2), (√3, 0), (C) (√3/2 , 2), (√3/2 , 1/2), (D) (3/2, √3/2), (√3/2 , 1/2)
Answer: A
Subject: mathematics
Question: Equations of the sides QR , RP are
Choices: (A) y = -2/√3 x + 1, y = -2/√3 x - 1, (B) y = 1/√3 x, y = 0, (C) y = √3/2 x + 1, y = -√3/2 x - 1, (D) y = √3 x, y = 0
Answer: D
Subject: mathematics
Question: The area of the region bounded by the curve y = f(x), the x-axis, and the lines x = a and x = b, where -∞ < a < b < -2, is
Choices: (A) ∫ₐ^b [x / (3((f(x))² - 1))] dx + b f(b) - a f(a), (B) -∫ₐ^b [x / (3((f(x))² - 1))] dx + b f(b) - a f(a), (C) ∫ₐ^b [x / (3((f(x))² - 1))] dx - b f(b) + a f(a), (D) -∫ₐ^b [x / (3((f(x))² - 1))] dx - b f(b) + a f(a)
Answer: A
Subject: physics
Question: Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table. Least count for length = 0.1 cm Least count for time = 0.1 s [Table with data for Student, Length of the pendulum (cm), Number of oscillations (n), Total time for (n) oscillations (s), Time period (s)] If E1, EII and EIII are the percentage errors in g, i.e., (Δg/g×100) for students I, II and III, respectively,
Choices: (A) EI = 0, (B) EI is minimum, (C) EI = EII, (D) EII is maximum
Answer: B
Subject: physics
Question: Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then
Choices: (A) P1 > P2 > P3, (B) P1 > P3 > P2, (C) P2 > P1 > P3, (D) P3 > P2 > P1
Answer: C
Subject: physics
Question: Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?
Choices: (A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases, (B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target, (C) Intensity of the characteristic X-rays depends on the electrical power given to the X-ray tube, (D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube
Answer: B
Subject: physics
Question: A spherically symmetric gravitational system of particles has a mass density ρ=ρ0 for r≤R, 0 for r>R where ρ0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r (0<r<∞) from the centre of the system is represented by
Choices: (A) (B) (C) (D)
Answer: C
Subject: physics
Question: Two balls, having linear momenta p⃗1=pi⃗ and p⃗2=−pi⃗, undergo a collision in free space. There is no external force acting on the balls. Let p'⃗1 and p'⃗2 be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of p, a1, a2, b1, b2, c1 and c2 :
Choices: (A) p'⃗1=a1i⃗+b1j⃗+c1k⃗ p'⃗2=a2i⃗+b2j⃗ (B) p'⃗1=c1k⃗ p'⃗2=c2k⃗ (C) p'⃗1=a1i⃗+b1j⃗+c1k⃗ p'⃗2=a2i⃗+b2j⃗−c1k⃗ (D) p'⃗1=a1i⃗+b1j⃗ p'⃗2=a2i⃗+b1j⃗
Answer: A,D
Subject: physics
Question: Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.
Choices: (A) Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy, (B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy, (C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into two equal fragments, (D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two equal fragments
Answer: C,D
Subject: physics
Question: A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B, perpendicular to the plane of the paper. The length of the Region II is l. Choose the correct choice(s).
Choices: (A) The particle enters Region III only if its velocity V > q*B/m, (B) The particle enters Region III only if its velocity V < q*B/m, (C) Path length of the particle in Region II is maximum when velocity V = q*B/m, (D) Time spent in Region II is same for any velocity V as long as the particle returns to Region I
Answer: B,C
Subject: physics
Question: In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is λ. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).
Choices: (A) If d = λ, the screen will contain only one maximum
(B) If λ < d < 2λ, at least one more maximum (besides the central maximum) will be observed on the screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase
Answer: B
Subject: physics
Question: STATEMENT-1
In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
and
STATEMENT-2
Resistance of a metal increases with increase in temperature.
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: physics
Question: STATEMENT-1
An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT-2
An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.
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: physics
Question: STATEMENT-1
Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

and

STATEMENT-2
By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
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: physics
Question: STATEMENT-1
The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT-2
In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.
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: physics
Question: As the bubble moves upwards, besides the buoyancy force the following forces are acting on it
Choices: (A) Only the force of gravity
(B) The force due to gravity and the force due to the pressure of the liquid
(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
(D) The force due to gravity and the force due to viscosity of the liquid
Answer: D
Subject: physics
Question: When the gas bubble is at a height y from the bottom, its temperature is
Choices: (A) T0 ( P0 + ρ ⋅ g ⋅ H ) ^ (2/5) / ( P0 + ρi ⋅ g ⋅ y )
(B) T0 ( P0 + ρ ⋅ g ⋅ (H - y) ) ^ (2/5) / ( P0 + ρ ⋅ g ⋅ H )
(C) T0 ( P0 + ρ ⋅ g ⋅ H ) ^ (3/5) / ( P0 + ρi ⋅ g ⋅ y )
(D) T0 ( P0 + ρ ⋅ g ⋅ (H - y) ) ^ (3/5) / ( P0 + ρ ⋅ g ⋅ H )
Answer: B
Subject: physics
Question: The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)
Choices: (A) ρ ₙ R g Tₒ [(Pₒ + ρ ₐ g H )²⁄₅] / [(Pₒ + ρ ₐ g y)¹⁄₅], (B) [ρ ₙ R g Tₒ] / [(Pₒ + ρ ₐ g H )²⁄₅ [(Pₒ + ρ ₐ g (H - y))³⁄₅]], (C) ρ ₙ R g Tₒ [(Pₒ + ρ ₐ g H )³⁄₅] / [(Pₒ + ρ ₐ g y)⁵⁄₃], (D) [ρ ₙ R g Tₒ] / [(Pₒ + ρ ₐ g H )³⁄₅ [(Pₒ + ρ ₐ g (H - y))²⁄₅]]
Answer: B
Subject: physics
Question: The wavelength of light emitted in the visible region by He⁺ ions after collisions with H atoms is
Choices: (A) 6.5 x 10⁻⁷ m, (B) 5.6 x 10⁻⁷ m, (C) 4.8 x 10⁻⁷ m, (D) 4.0 x 10⁻⁷ m
Answer: C
Subject: chemistry
Question: Under the same reaction conditions, initial concentration of 1.386 mol dm^3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio (k1/k0) of the rate constants for first order (k1) and zero order (k0) of the reactions is
Choices: (A) 0.5 mol^-1 dm^3 (B) 1.0 mol dm^-3 (C) 1.5 mol dm^-3 (D) 2.0 mol^-1 dm^3
Answer: A
Subject: chemistry
Question: 2.5 mL of 2/5 M weak monoacidic base (Kb = 1 x 10^-12 at 25°C) is titrated with 2/15 M HCl in water at 25°C. The concentration of H+ at equivalence point is (Kw = 1 x 10^-14 at 25°C)
Choices: (A) 3.7 x 10^-13 M, (B) 3.2 x 10^-7 M, (C) 3.2 x 10^-2 M, (D) 2.7 x 10^-2 M
Answer: D
Subject: chemistry
Question: A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is (are)
Choices: (A) NH4NO3, (B) NH4NO2, (C) NH4Cl, (D) (NH4)2SO4
Answer: B
Subject: chemistry
Question: A gas described by van der Waals equation (A) behaves similar to an ideal gas in the limit of large molar volumes (B) behaves similar to an ideal gas in the limit of large pressures (C) is characterised by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature (D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally
Choices: (A), (C) OR (A), (C), (D)
Answer: (A), (C)
Subject: chemistry
Question: STATEMENT-1 : Bromobenzene upon reaction with Br2/Fe gives 1,4-dibromobenzene as the major product. and STATEMENT-2 : In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile. (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: chemistry
Question: STATEMENT-1 : Pb⁺⁺ compounds are stronger oxidizing agents than Sn⁺⁺ compounds. and STATEMENT-2 : The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.
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 : The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45° slope as the atomic number is increased. and STATEMENT-2 : Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.
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 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero. and STATEMENT-2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs 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: D
Subject: chemistry
Question: Among the following, the correct statement is (A) Phosphates have no biological significance in humans (B) Between nitrates and phosphates, phosphates are less abundant in earth's crust (C) Between nitrates and phosphates, nitrates are less abundant in earth's crust (D) Oxidation of nitrates is possible in soil
Choices: (A) Phosphates have no biological significance in humans, (B) Between nitrates and phosphates, phosphates are less abundant in earth's crust, (C) Between nitrates and phosphates, nitrates are less abundant in earth's crust, (D) Oxidation of nitrates is possible in soil
Answer: C
Subject: chemistry
Question: Among the following, the correct statement is (A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional (B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional (C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional (D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional
Choices: (A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional, (B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional, (C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional, (D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional
Answer: C