cmeraki/elemento huggingface dataset:
Subject: chemistry
Question: The correct structure of ethylenediaminetetraacetic acid (EDTA) is
Choices: A) HOOC-CH2 | N-CH=CH-N | CH2-COOH, B) HOOC | N-CH2-CH2-N | COOH, C) HOOC-CH2 | N-CH2-CH2-N | CH2-COOH, D) HOOC-CH2 | CH2 | N-CH-CH-N | CH2-COOH
Answer: C
Subject: chemistry
Question: The ionization isomer of [Cr(H2O)4Cl(NO2)]Cl is
Choices: A) [Cr(H2O)4(O2N)]Cl2, B) [Cr(H2O)4Cl2](NO2), C) [Cr(H2O)4Cl(ONO)]Cl, D) [Cr(H2O)4Cl2(NO2)]·H2O
Answer: B
Subject: chemistry
Question: The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and an alkyne. The bromoalkane and alkyne respectively are
Choices: A) BrCH2CH2CH2CH2CH3 and CH3CH2C≡CH, B) BrCH2CH2CH3 and CH3CH2CH2C≡CH, C) BrCH2CH2CH2CH2CH3 and CH3C≡CH, D) BrCH2CH2CH2CH3 and CH3CH2C≡CH
Answer: D
Subject: chemistry
Question: Aqueous solutions of HNO3, KOH, CH3COOH, and CH3COONa of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)
Choices: A) HNO3 and CH3COOH, B) KOH and CH3COONa, C) HNO3 and CH3COONa, D) CH3COOH and CH3COONa
Answer: C and D
Subject: mathematics
Question: Equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is
Choices: A) x + 2y - 2z = 0, B) 3x + 2y - 2z = 0, C) x - 2y + z = 0, D) 5x + 2y - 4z = 0
Answer: C
Subject: mathematics
Question: Let ω be a complex cube root of unity with ω≠1. A fair die is thrown three times. If r1, r2 and r3 are the numbers obtained on the die, then the probability that ω¹ˡ +ω¹²+ω¹³=0 is
Choices: A) 1/18, B) 1/9, C) 2/9, D) 1/36
Answer: C
Subject: mathematics
Question: Let P, Q, R and S be the points on the plane with position vectors −2i−j, 4i, 3i+3j and −3i+2j respectively. The quadrilateral PQRS must be a
Choices: A) parallelogram, which is neither a rhombus nor a rectangle, B) square, C) rectangle, but not a square, D) rhombus, but not a square
Answer: A
Subject: mathematics
Question: Let p and q be real numbers such that p ≠ 0, p^3 ≠ q and p^3 ≠ -q . If α and β are nonzero complex numbers satisfying α + β = - p and α^2 + β^2 = q , then a quadratic equation having (α/β) and (α/α) as its roots is
Choices: A) (p^3 + q) x^2 - (p^3 + 2q)x + (p^3 + q) = 0, B) (p^3 + q) x^2 - (p^3 - 2q)x + (p^3 + q) = 0, C) (p^3 - q) x^2 - (5p^3 - 2q) x + (p^3 - q) = 0, D) (p^3 - q) x^2 - (5p^3 + 2q) x + (p^3 - q) = 0
Answer: B
Subject: mathematics
Question: Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = e^x + e^-x, g(x) = xe^x + e^-x and h(x) = x^2 e^x + e^-x. If a, b and c denote, respectively, the absolute maximum of f, g and h on [0, 1], then
Choices: A) a = b and c ≠ b, B) a = c and a ≠ b, C) a ≠ b and c ≠ b, D) a = b = c
Answer: D
Subject: mathematics
Question: Let ABC be a triangle such that ∠ACB = π/6 and let a, b and c denote the lengths of the sides opposite to A, B and C respectively. The value(s) of x for which a = x^2 + x + 1, b = x^2 - 1 and c = 2x + 1 is (are)
Choices: A) -(-2+√3), B) 1+√3, C) 2+√3, D) 4√3
Answer: B
Subject: mathematics
Question: Let z₁ and z₂ be two distinct complex numbers and let z = (1 - t) z₁ + tz₂ for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then
Choices: A) |z - z₁| + |z - z₂| = |z₁ - z₂|, B) Arg (z - z₁) = Arg (z - z₂), C) |z-z₁   z-z₂| = 0, D) Arg (z - z₁) = Arg(z₂ - z₁)|z₂-z₁  z₁-z₂|
Answer: A and C and D
Subject: mathematics
Question: Let f be a real-valued function defined on the interval (0, ∞) by f(x) = ∫(0 to x) t + sin t dt. Then which of the following statement(s) is (are) true?
Choices: A) f'(x) exists for all x∈(0,∞) B) f'(x) exists for all x∈(0,∞) and f' is continuous on (0,∞), but not differentiable on (0,∞) C) there exists α > 1 such that |f'(x)|<|f(x)| for all x∈(α,∞) D) there exists β > 0 such that |f(x)|+|f'(x)|≤β for all x∈(0,∞)
Answer: B and C
Subject: mathematics
Question: Let p be an odd prime number and Tp be the following set of 2x2 matrices : Tp = {A= [a  b] : a,b,c ∈ {0, 1, 2, ..., p-1}} The number of A in Tp such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is
Choices: A) (p - 1)² B) 2 (p - 1) C) (p - 1)² + 1 D) 2p - 1
Answer: D
Subject: mathematics
Question: The number of A in Tp such that the trace of A is not divisible by p but det (A) is divisible by p is [Note : The trace of a matrix is the sum of its diagonal entries.]
Choices: A) (p - 1) (p² - p + 1) B) p³ - (p - 1)² C) (p - 1)² D) (p - 1) (p² - 2)
Answer: C
Subject: mathematics
Question: If ā and b̄ are vectors in space given by ā = i−2j̄/√5 and b̄ = 2ī + j̄ + 3k̄/√14, then the value of (2ā + b̄) ⋅ (ā × b̄) × (ā −2 b̄) is
Answer: 5
Subject: mathematics
Question: For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the interval [-10, 10] by f(x) = { x - [x] if [x] is odd, 1 + [x] - x if [x] is even}. Then the value of ∫(10/-10) π^2 * 10 f(x) cos πx dx is
Answer: 4
Subject: mathematics
Question: The number of all possible values of θ , where 0 < θ < π, for which the system of equations (y + z) cos 3 θ = (xyz) sin 3 θ, x sin 3θ = (2 cos 3θ) / y, 2 sin 3θ / z, (xyz) sin 3 θ = (y + 2z) cos 3 θ + y sin 3 θ have a solution (x0, y0, z0) with y0 ≠ 0, is
Answer: 3
Subject: physics
Question: Incandescent bulbs are designed by keeping in mind that the resistance of their filament increases with the increase in temperature. If at room temperature, 100 W, 60 W and 40 W bulbs have filament resistances R₁₀₀, R₆₀ and R₄₀, respectively, the relation between these resistances is
Choices: A) 1/R₁₀₀ = 1/R₆₀ + 1/R₄₀, B) R₁₀₀ = R₆₀ + R₄₀, C) R₁₀₀ > R₆₀ > R₄₀, D) 1/R₁₀₀ > 1/R₆₀ > 1/R₄₀
Answer: D
Subject: physics
Question: A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is
Choices: A) IBL, B) IBL/π, C) IBL/2π, D) IBL/4π
Answer: C
Subject: physics
Question: A block of mass m is on an inclined plane of angle θ. The coefficient of friction between the block and the plane is μ and tanθ>μ. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from P₁= mg(sinθ - μ cosθ) to P₂= mg(sinθ + μ cosθ), the frictional force f versus P graph will look like
Choices: A) [Graph A], B) [Graph B], C) [Graph C], D) [Graph D]
Answer: A
Subject: physics
Question: A thin uniform annular disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass from point P on its axis to infinity is
Choices: A) 2GM(4√2-5)/7R   B) -2GM(4√2-5)/7R   C) GM/4R   D) 2GM(√2-1)/5R
Answer: A
Subject: physics
Question: A few electric field lines for a system of two charges Q₁ and Q₂ fixed at two different points on the x-axis are shown in the figure. These lines suggest that
Choices: A) |Q₁| > |Q₂|   B) |Q₁| < |Q₂|   C) at a finite distance to the left of Q₁ the electric field is zero   D) at a finite distance to the right of Q₂ the electric field is zero
Answer: A and D
Subject: physics
Question: A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true ?
Choices: A) Error ΔT in measuring T, the time period, is 0.05 seconds   B) Error ΔT in measuring T, the time period, is 1 second   C) Percentage error in the determination of g is 5%   D) Percentage error in the determination of g is 2.5%
Answer: A and C
Subject: physics
Question: A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 ms⁻¹. Which of the following statement(s) is (are) correct for the system of these two masses ?
Choices: A) Total momentum of the system is 3 kg ms⁻¹
B) Momentum of 5 kg mass after collision is 4 kg ms⁻¹
C) Kinetic energy of the centre of mass is 0.75 J
D) Total kinetic energy of the system is 4 J
Answer: A and C
Subject: physics
Question: A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60° (see figure). If the refractive index of the material of the prism is √5, which of the following is (are) correct ?
Choices: A) The ray gets totally internally reflected at face CD
B) The ray comes out through face AD
C) The angle between the incident ray and the emergent ray is 90°
D) The angle between the incident ray and the emergent ray is 120°
Answer: A and B and C
Subject: physics
Question: One mole of an ideal gas in initial state A undergoes a cyclic process ABCA, as shown in the figure. Its pressure at A is PA. Choose the correct option(s) from the following
Choices: A) Internal energies at A and B are the same
B) Work done by the gas in process AB is PAVB ln 4
C) Pressure at C is P0/4
D) Temperature at C is T0/4
Answer: A and B and C and D
Subject: physics
Question: In the graphs below, the resistance R of a superconductor is shown as a function of its temperature T for two different magnetic fields B1 (solid line) and B2 (dashed line). If B2 is larger than B1, which of the following graphs shows the correct variation of R with T in these fields?
Choices: Options A), B), C), and D) are shown in the image graphs.
Answer: A
Subject: physics
Question: A superconductor has Tc (0) = 100 K. When a magnetic field of 7.5 Tesla is applied, its Tc decreases to 75 K. For this material one can definitely say that when
Choices: A) B = 5 Tesla, Tc (B) = 80 K, B) B = 5 Tesla, 75 K < Tc (B) < 100 K, C) B = 10 Tesla, 75 K < Tc (B) < 100 K, D) B = 10 Tesla, Tc (B) = 70 K
Answer: B
Subject: physics
Question: A 0.1 kg mass is suspended from a wire of negligble mass. The length of the wire is 1m and its cross-sectional area is 4.9×10^-7m². If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency 140 rad s⁻¹. If the Young's modulus of the material of the wire is n×10^9Nm⁻², the value of n is
Choices: No response choices provided.
Answer: 4
Subject: physics
Question: A binary star consists of two stars A (mass 2.2M_⦿) and B (mass 11M_⦿), where M_⦿ is the mass of the sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is
Choices: No response choices provided.
Answer: 6
Subject: physics
Question: Gravitational acceleration on the surface of a planet is √(5/11)g , where g is the gravitational acceleration on the surface of the earth. The average mass density of the planet is 2/3 times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms⁻¹, the escape speed on the surface of the planet in kms⁻¹ will be
Choices: No response choices provided.
Answer: 3
Subject: chemistry
Question: A piece of ice (heat capacity = 2100 J kg⁻¹ °C⁻¹ and latent heat = 3.36 × 10⁵ J kg⁻¹) of mass m grams is at -5°C at atmospheric pressure. It is given 420 J of heat so that the ice starts melting. Finally when the ice-water mixture is in equilibrium, it is found that 1 gm of ice has melted. Assuming there is no other heat exchange in the process, the value of m is
Choices: No response choices provided.
Answer: 8
Subject: physics
Question: A stationary source is emitting sound at a fixed frequency f₀, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2% of f₀. What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ms⁻¹.
Choices: No response choices provided.
Answer: 7