cmeraki/elemento huggingface dataset:
Subject: chemistry
Question: Among the following complexes (K–P), 
K3[Fe(CN)6] (K), [Co(NH3)6]Cl3 (L), Na3[Co(oxalate)3] (M), [Ni(H2O)6]Cl2 (N),
K3[Pt(CN)6] (O) and [Zn(H2O)6](NO3)2 (P)
the diamagnetic complexes are
Choices: (A) K, L, M, N	(B) K, M, O, P	(C) L, M, O, P	(D) L, M, N, O
Answer: C
Subject: chemistry
Question: Consider the following cell reaction:
2Fe(s) + O2(g) + 4H+(aq) → 2Fe3+(aq) + 2H2O(l)		E° = 1.67 V
At [Fe3+] = 10–3 M, P(O2) = 0.1 atm and pH = 3, the cell potential at 25 °C is
Choices: (A) 1.47 V	(B) 1.77 V	(C) 1.87 V	(D) 1.57 V
Answer: D
Subject: chemistry
Question: The freezing point (in °C) of a solution containing 0.1 g of K4[Fe(CN)6] (Mol. Wt. 329) in 100 g of water (Kf = 1.86 K kg mol^-1) is
Choices: (A) −2.3 × 10^-2  (B) −5.7 × 10^-2  (C) −5.7 × 10^-3  (D) −1.2 × 10^-2
Answer: A
Subject: chemistry
Question: For the first order reaction 

2N2O5(g) → 4NO2(g) + O2(g)
Choices: (A) the concentration of the reactant decreases exponentially with time.
(B) the half-life of the reaction decreases with increasing temperature.
(C) the half-life of the reaction depends on the initial concentration of the reactant. 
(D) the reaction proceeds to 99.6 % completion in eight half-life duration.
Answer: ABD
Subject: chemistry
Question: The correct functional group X and the reagent/reaction conditions Y in the following scheme are

X—(CH2)4—X    (i) Y
                  —————————————————>   condensation polymer
                        O        O
                (ii)    \C—(CH2)4—C/
                            \    /
                             HO  OH
                            heat
Choices: (A) X = COOCH3 , Y = H2/Ni/heat 
(B) X = CONH2 , Y = H2/Ni/heat
(C) X = CONH2 , Y = Br2/NaOH
(D) X = CN , Y = H2/Ni/heat
Answer: CD
Subject: chemistry
Question: In 1 L saturated solution of AgCl [Ksp(AgCl) = 1.6 × 10^-10], 0.1 mol of CuCl [Ksp(CuCl) = 1.0 × 10^-6] is added. The resultant concentration of Ag+ in the solution is 1.6 × 10^-x. The value of "x" is
Choices: <no multiple choice options provided>
Answer: 7
Subject: chemistry
Question: Match the transformations in column I with appropriate options in column II
Choices: Column I: (A) CO2(s) → CO2(g), (B) CaCO3(s) → CaO(s) + CO2(g), (C) 2 H• → H2(g), (D) P(white, solid) → P(red, solid) 

Column II: (p) phase transition, (q) allotropic change, (r) ΔH is positive, (s) ΔS is positive, (t) ΔS is negative
Answer: A: p, r and s
B: r and s
C: t
D: p, q and t
Subject: physics
Question: A satellite is moving with a constant speed 'V' in a circular orbit about the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its ejection, the kinetic energy of the object is
Choices: (A) 1/2 mV^2, (B) mV^2, (C) 3/2 mV^2, (D) 2mV^2
Answer: B
Subject: physics
Question: A long insulated copper wire is closely wound as a spiral of 'N' turns. The spiral has inner radius 'a' and outer radius 'b'. The spiral lies in the X-Y plane and a steady current 'I' flows through the wire. The Z-component of the magnetic field at the center of the spiral is
Choices: (A) (μ₀N I / 2(b-a)) ln (b/a), (B) (μ₀N I / 2(b-a)) ln ((b+a)/(b-a)), (C) (μ₀N I / 2b) ln (b/a), (D) (μ₀N I / 2b) ln ((b+a)/(b-a))
Answer: A
Subject: physics
Question: A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x₁(t) = A sin ωt and x₂(t) = A sin (ωt + 2π/3). Adding a third sinusoidal displacement x₃(t) = B sin (ωt + ϕ) brings the mass to a complete rest. The values of B and ϕ are
Choices: (A) √2 A, 3π/4, (B) A, 4π/3, (C) √3 A, 5π/6, (D) A, π/3
Answer: B
Subject: physics
Question: A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is
Choices: (A) 250 m/s, (B) 250√2 m/s, (C) 400 m/s, (D) 500 m/s
Answer: D
Subject: physics
Question: The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is
Choices: (A) 0.9%, (B) 2.4%, (C) 3.1%, (D) 4.2%
Answer: C
Subject: physics
Question: A wooden block performs SHM on a frictionless surface with frequency, v0. The block carries a charge +Q on its surface. If now a uniform electric field E is switched-on as shown, then the SHM of the block will be
Choices: A) of the same frequency and with shifted mean position. B) of the same frequency and with the same mean position. C) of changed frequency and with shifted mean position. D) of changed frequency and with the same mean position.
Answer: A
Subject: physics
Question: Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
Choices: (A) dA < dF, (B) dB > dF, (C) dA > dF, (D) dA + dB = 2 dF
Answer: ABD
Subject: physics
Question: A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?
Choices: (A) IRA > IRB, (B) IRA < IRB, (C) VCA > VCB, (D) VCA < VCB
Answer: BC
Subject: physics
Question: Which of the following statement(s) is/are correct?
Choices: (A) If the electric field due to a point charge varies as r^-2.5 instead of r^-2, then the Gauss law will still be valid. (B) The Gauss law can be used to calculate the field distribution around an electric dipole. (C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same. (D) The work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB - VA).
Answer: CD
Subject: physics
Question: A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
Choices: (A) the ring has pure rotation about its stationary CM. (B) the ring comes to a complete stop. (C) friction between the ring and the ground is to the left. (D) there is no friction between the ring and the ground.
Answer: A OR AC
Subject: physics
Question: A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s^2, is
Choices: No response choices provided
Answer: 5
Subject: physics
Question: A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is
Choices: No response choices provided
Answer: 4
Subject: physics
Question: Water (with refractive index = 4/3) in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature 'R = 6 cm' as shown. Consider oil to act as a thin lens. An object 'S' is placed 24 cm above water surface. The location of its image is at 'x' cm above the bottom of the tank. Then 'x' is
Choices: No response choices provided
Answer: 2
Subject: physics
Question: A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A × 10 (where 1 < A < 10). The value of 'Z' is
Choices: No response choices provided
Answer: 7
Subject: physics
Question: Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λ1. Match each system with statements given in Column II describing the nature and wavelength of the standing waves.
Choices: (A) Pipe closed at one end, (B) Pipe open at both ends, (C) Stretched wire clamped at both ends, (D) Stretched wire clamped at both ends and at mid-point
Answer: A : p and t, B : p and s, C : q and s, D : q and r
Subject: mathematics
Question: Let P(6,3) be a point on the hyperbola (x^2/a^2) - (y^2/b^2) = 1. If the normal at the point P intersects the x-axis at (9,0), then the eccentricity of the hyperbola is
Choices: (A) √5/2, (B) √3/2, (C) √2, (D) √3
Answer: B
Subject: mathematics
Question: Let ω ≠ 1 be a cube root of unity and S be the set of all non-singular matrices of the form [1 a b; ω 1 c; ω^2 ω 1], where each of a, b, and c is either ω or ω^2. Then the number of distinct matrices in the set S is
Choices: (A) 2, (B) 6, (C) 4, (D) 8
Answer: A
Subject: mathematics
Question: If lim [1+𝑥ln(1+𝑏²)] = 2𝑏sin²𝜃, 𝑏>0 and 𝜃∈(-𝜋,𝜋], then the value of 𝜃 is
Choices: A) ±𝜋/4, B) ±𝜋/3, C) ±𝜋/6, D) ±𝜋/2
Answer: D
Subject: mathematics
Question: Let f:[-1,2]→(0,∞) be a continuous function such that f(x)=f(1-x) for all x∈[-1,2]. Let R₁= ∫xf(x)dx, and R₂ be the area of the region bounded by y=f(x), x=-1, x=2, and the x-axis. Then
Choices: A) R₁=2R₂, B) R₁=3R₂, C) 2R₁=R₂, D) 3R₁=R₂
Answer: C
Subject: mathematics
Question: Let f(x)=x³ and g(x)=sinx for all x∈R. Then the set of all x satisfying (f∘g∘g∘f)(x)=(g∘g∘f)(x), where (f∘g)(x)=f(g(x)), is
Choices: A) ±√n𝜋, n∈{0,1,2,...}, B) ±√n𝜋, n∈{1,2,...}, C) 𝜋/2+2n𝜋, n∈{...,-2,-1,0,1,2,...}, D) 2n𝜋, n∈{...,-2,-1,0,1,2,...}
Answer: A
Subject: mathematics
Question: Let (x,y) be any point on the parabola y²=4x. Let P be the point that divides the line segment from (0,0) to (x,y) in the ratio 1:3. Then the locus of P is
Choices: A) x²=y, B) y²=2x, C) y²=x, D) x²=2y
Answer: C
Subject: mathematics
Question: If f(x)={ −x, π/2 ≤ x≤ π/2; −cos x, −π/2 < x ≤ 0; x−1, 0 < x ≤ 1; ln x, x>1,}, then
Choices: (A) f(x) is continuous at x = π/2, (B) f(x) is not differentiable at x = 0, (C) f(x) is differentiable at x = 1, (D) f(x) is differentiable at x = 3/2
Answer: ABCD
Subject: mathematics
Question: Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then
Choices: (A) P(E)=4/5, P(F)=3/5, (B) P(E)=1/5, P(F)=2/5, (C) P(E)=2/5, P(F)=1/5, (D) P(E)=3/5, P(F)=4/5
Answer: AD
Subject: mathematics
Question: Let L be a normal to the parabola y^2 = 4x. If L passes through the point (9, 6), then L is given by
Choices: (A) y - x + 3 = 0, (B) y + 3x - 33 = 0, (C) y + x - 15 = 0, (D) y - 2x + 12 = 0
Answer: ABD
Subject: mathematics
Question: Let f : (0,1) → R be defined by f(x) = (b - x)/(1 - bx), where b is a constant such that 0 < b < 1. Then
Choices: (A) f is not invertible on (0, 1), (B) f ≠ f^-1 on (0, 1) and f'(b) = 1/f'(0), (C) f = f^-1 on (0, 1) and f'(b) = 1/f'(0), (D) f^-1 is differentiable on (0, 1)
Answer: A
Subject: mathematics
Question: Let ω = e^(2i/3), and a, b, c, x, y, z be non-zero complex numbers such that a + b + c = x, a + bω + cω^2 = y, a + bω^2 + cω = z. Then the value of |x|^2 + |y|^2 + |z|^2 / |a|^2 + |b|^2 + |c|^2 is
Answer: MARKS TO ALL
Subject: mathematics
Question: Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ∈ ℝ, where f'(x) denotes d f(x)/dx and g(x) is a given non-constant differentiable function on ℝ with g(0) = g(2) = 0. Then the value of y(2) is
Answer: 0
Subject: mathematics
Question: Match the statements given in Column I with the values given in Column II
Choices: (A) If ā = j + √3 k̄ , b̄ = - j + √3 k̄ and c̄ = 2√3 k̄ form a triangle, then the internal angle of the triangle between ā and b̄ is 
(B) If ∫_0^π (f(x) - 3x)dx = a^2 - b^2, then the value of f(π/6) is 
(C) The value of ∫_(π/3)^(5π/6) (π^2/9) sec(πx) dx is 
(D) The maximum value of |Arg (1/(1-z))| for |z|=1, z≠1 is given by
Answer: A : q
B : p or p, q, r, s and t
C : s
D : t
Subject: mathematics
Question: Match the statements given in Column I with the intervals/union of intervals given in Column II
Choices: (A) The set {Re(2iz / (1-z^2)) : z is a complex number, |z|=1, z != +1} is (p) (-∞, -1) ∪ (1, ∞) 

(B) The domain of the function f(x) = sin^-1 (8(3)^(x+3) / (1-3^(x+1))) is (q) (-∞, 0) ∪ (0, ∞)

(C) If f(θ) = [-tan θ   tan θ   1 / -1   -tan θ   1], then the set {f(θ) : 0 ≤ θ < π/2} is (r) [2, ∞) 

(D) If f(x) = x^(2/3) (3x-10), x ≥ 0, then f(x) is increasing in (s) (-∞, -1] ∪ [1, ∞)
Answer: A: s
B: t
C: r
D: r