cmeraki/elemento huggingface dataset:
Subject: physics
Question: At time t = 0, terminal A in the circuit shown in the figure is connected to B by a key and an alternating current i(t) = I0cos(ωt), with I0 = 1A and ω = 500 rad s-1 starts flowing in it with the initial direction shown in the figure. At t = 7π/6ω , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C=20μF, R= 10 Ω and the battery is ideal with emf of 50V, identify the correct statement (s).
Choices: (A) Magnitude of the maximum charge on the capacitor before t = 7π/6ω is 1 × 10−3 C, (B) The current in the left part of the circuit just before t = 7π/6ω is clockwise, (C) Immediately after A is connected to D, the current in R is 10A, (D) Q = 2 × 10−3 C.
Answer: (C) and (D)
Subject: physics
Question: A light source, which emits two wavelengths λ1 = 400 nm and λ2 = 600 nm, is used in a Young's double slit experiment. If recorded fringe widths for λ1 andλ2 areβ1 andβ2 © number of fringes for them within a distance yon one side of the central maximum are m1 and m2, respectively, then
Choices: (A)β2 > β1, (B)m2 > m1, (C) From the central maximum, 3rd maximum of λ2 overlaps with 5th minimum of λ1, (D)The angular separation of fringes for λ1 is greater than λ2
Answer: (A), (B) and (C)
Subject: physics
Question: One end of a taut string of length 3m along the x axis is fixed at x=0.The speed of the waves in the string is 100 ms−1. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is(are)
Choices: (A)y(t) = A sin πx/6 cos 50πt/3, (B)y(t) = A sin πx/3 cos 100πt/3, (C) y(t) = A sin 5πx/6 cos 250πt/3, (D) y(t) = A sin 5πx/2 cos 250πt
Answer: (A) , (C) and (D)
Subject: physics
Question: A parallel plate capacitor has a dielectric slab of dielectric constant K between its plates that covers 1/3 of the area of its plates, as shown in the figure. The total capacitance of the capacitor is C while that of the portion with dielectric in between is C1. When the capacitor is charged, the plate area covered by the dielectric gets charge Q1 and the rest of the area gets charge Q2. The electric field in the dielectric is E1 and that in the other portion is E2. Choose the correct option/options, ignoring edge effects.
Choices: (A) E1/E2 = 1, (B) E1/E2 = 1/K, (C) Q1/Q2 = 3/K, (D) C/C1 = 2+K/K
Answer: (A) and (D)
Subject: physics
Question: Let E1(r), E2(r) and E3(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, and an infinite plane with uniform surface charge density σ. If E1(r0) = E2(r0) = E3(r0) at a given distance r0, then
Choices: (A) Q = 4πr0^2, (B) r0 = λ/2πσ, (C) E1(r0/2)= 2E2(r0/2), (D) E2(r0/2)=4E3(r0/2)
Answer: (C)
Subject: physics
Question: A student is performing an experiment using a resonance column and a tuning fork of frequency 244s^-1. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is (0.350 ± 0.005) m, the gas in the tube is
Choices: (A)Neon(M=20,(10⁄20=7⁄10)),​(B)Nitrogen(M=28,(10⁄28=3⁄5)),​(C)Oxygen(M=32,​(10⁄√32=9⁄16)),​(D)Argon(M=36,(10⁄√36=17⁄32))
Answer: (D)
Subject: physics
Question: Heater of an electric kettle is made of a wire of length L and diameter d. It takes 4 minutes to raise the temperature of 0.5kgwater by 40K. This heater is replaced by a new heater having two wires of the same material, each of length L and diameter 2d.The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by 40 K?
Choices: (A)4 if wires are in parallel​(B) 2 if wires are in series​(C) 1 if wires are in series​(D)0.5 if wires are in parallel
Answer: (B) and (D)
Subject: physics
Question: In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle θ with the horizontal floor. The coefficient of friction between the wall and the ladder is μ₁ and that between the floor and the ladder is μ₂. The normal reaction of the wall on the ladder is N₁ and that of the floor is N₂. If the ladder is about to slip, then
Choices: (A)μ₁ = 0 μ₂ ≠ 0andN₂ tanθ = mg/2, (B) μ₁ ≠ 0 μ₂ = 0andN₁ tanθ = mg/2, (C)μ₁ ≠ 0 μ₂ ≠ 0andN₂ = mg/1+μ₁μ₂, (D)μ₁ = 0 μ₂ ≠ 0andN₁ tanθ = mg/2
Answer: (C) and (D)
Subject: physics
Question: A transparent thin film of uniform thickness and refractive index n₁= 1.4 is coated on the convex spherical surface of radius Rat one end of a long solid glass cylinder of refractive index n₂ = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then
Choices: (A) |f₁| =3R, (B)|f₁| = 2.8R, (C)|f₂|=2R, (D)|f₂| = 1.4R
Answer: (A) and (C)
Subject: physics
Question: Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if
Choices: (A) V1 = V2 and R1 = R2 = R3, (B) V1 = V2 and R1 = 2R2 = R3, (C) V1 = 2V2 and 2R1 = 2R2 = R3, (D) 2V1 = V2 and 2R1 = R2 = R3
Answer: (A), (B) and (D)
Subject: physics
Question: Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30° and 60° with respect to the horizontal respectively as shown in figure. The speed of A is 100√3 ms⁻¹. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = t₀, A just escapes being hit by B, t₀ in seconds is
Choices: No response choices provided.
Answer: 5
Subject: physics
Question: During Searle's experiment, zero of the Vernier scale lies between 3.20 × 10⁻² m and 3.25 × 10⁻² m of the main scale. The 20ᵗʰ division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of 2 kg is applied to the wire, the zero of the Vernier scale still lies between 3.20 × 10⁻² m and 3.25 × 10⁻² m of the main scale but now the 45ᵗʰ division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is 2 m and its cross-sectional area is 8 × 10⁻⁷ m². The least count of the Vernier scale is 1.0 × 10⁻⁵ m. The maximum percentage error in the Young's modulus of the wire is
Choices: No response choices provided.
Answer: 4
Subject: physics
Question: A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in rad s^-1 is
Choices: No response choices provided
Answer: 2
Subject: physics
Question: Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same direction, the radius of curvature of the path of the point charge is R1. In contrast, if the currents I in the two wires have directions opposite to each other, the radius of curvature of the path is R2. If X0/X1 = 3, the value of R1/R2 is
Choices: No response choices provided
Answer: 3
Subject: physics
Question: A galvanometer gives full scale deflection with 0.006 A current. By connecting it to a 4990 Ω resistance, it can be converted into a voltmeter of range 0 - 30 V. If connected to a 249/2Ω resistance, it becomes an ammeter of range 0 - 1.5 A. The value ofn is
Choices: No response choices provided
Answer: 5
Subject: physics
Question: Consider an elliptically shaped rail PQ in the vertical plane with OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the rail from P to Q with a force of 18 N, which is always parallel to line PQ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches Q is (n × 10)Joules. The value of n is (take acceleration due to gravity = 10 ms^-2)
Choices: No response choices provided
Answer: 5
Subject: physics
Question: A rocket is moving in a gravity free space with a constant acceleration of 2 ms^-2 along +x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in +x direction with a speed of 0.3 ms^-1 relative to the rocket. At the same time, another ball is thrown in –x direction with a speed of 0.2 ms^-1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is
Choices: No response choices provided
Answer: 2 OR 8
Subject: physics
Question: A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 ms^-1 with respect to the ground. The rotational speed of the platform inrads^-1 after the balls leave the platform is
Choices: Answer: 4
Answer: 4
Subject: physics
Question: A thermodynamic system is taken from an initial state i with internal energy Ui = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are Waf = 200 J, Wib = 50 J and Wbf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Qiaf, Qib and Qbf respectively. If the internal energy of the system in the state b is Ub = 200 J and  Qiaf = 500 J, the ratio Qbf /Qib is
Choices: Answer : 2
Answer: 2
Subject: chemistry
Question: The correct combination of names for isomeric alcohols with molecular formula C4H10O is/are
Choices: (A) tert-butanol and 2-methylpropan-2-ol, (B) tert-butanol and 1, 1-dimethylethan-1-ol, (C) n-butanol and butan-1-ol, (D) isobutyl alcohol and 2-methylpropan-1-ol
Answer: (A), (C) and (D)
Subject: chemistry
Question: he reactivity of compound Z with different halogens under appropriate conditions is given below:, The observed pattern of electrophilic substitution can be explained by
Choices: (A) the steric effect of the halogen, (B) the steric effect of the tert-butyl group, (C) the electronic effect of the phenolic group, (D) the electronic effect of the tert-butyl group
Answer: (A), (B) and (C)
Subject: physics
Question: An ideal gas in a thermally insulated vessel at internal pressure = P1, volume = V1, and absolute temperature = T1 expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are P2, V2 and T2 respectively. For this expansion,
Choices: (A) q = 0 (B) T2 = T1 (C) P2V2 = P1V1 (D) P2V2' = P1V1'
Answer: (A), (B) and (C)
Subject: chemistry
Question: For the reaction: I⁻ + ClO₃⁻ + H₂SO₄ → Cl⁻ + HSO₄⁻ + I₂ The correct statement(s) in the balanced equation is/are:
Choices: (A) Stoichiometric coefficient of HSO₄⁻ is 6. (B) Iodide is oxidized. (C) Sulphur is reduced. (D) H₂O is one of the products.
Answer: (A), (B) and (D) OR (A) and (D)*
Subject: chemistry
Question: A list of species having the formula XZ4 is given below. XeF4, SF4, SiF4, BF4, BrF4, [Cu(NH3)4]2+, [FeCI4]2-, [CoCl4]2- and [PtCl4]2-. Defining shape on the basis of the location of X and Z atoms, the total number of species having a square planar shape is
Answer: 4
Subject: mathematics
Question: Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠ N2 and M2 = N4, then
Choices: (A) determinant of (M2 + MN2) is 0

(B) there is a 3 × 3 non-zero matrix U such that (M2 + MN2)U is the zero matrix

(C) determinant of (M2 + MN2) ≥ 1

(D) for a 3 × 3 matrix U, if (M2 + MN2)U equals the zero matrix then U is the zero matrix
Answer: (A), (B)
Subject: mathematics
Question: For every pair of continuous functions f, g: [0, 1] → R such that

max {f(x): x ∈ [0, 1]} = max {g(x): x ∈ [0, 1]},

the correct statement(s) is(are):
Choices: (A) (f(c))2 + 3f(c) = (g(c))2 + 3g(c) for some c ∈ [0, 1]

(B) (f(c))2 + f(c) = (g(c))2 + 3g(c) for some c ∈ [0, 1]

(C) (f(c))2 + 3f(c) = (g(c))2 + g(c) for some c ∈ [0, 1]

(D) (f(c))2 = (g(c))2 for some c ∈ [0, 1]
Answer: (A), (D)
Subject: mathematics
Question: Let f : (0, ∞) → ℝ be given by  f(x) = ∫(x/2)^x e^(-(t+1)/t) dt/t
Choices: (A) f(x) is monotonically increasing on (1, ∞)
(B) f(x) is monotonically decreasing on (0, 1)
(C) f(x) + f(1/t) = 0, for all x ∈ (0, ∞)
(D) f(2^x) is an odd function of x on ℝ
Answer: (A), (C), (D)
Subject: mathematics
Question: Let a ∈ ℝ and let f : ℝ → ℝ be given by f(x) = x^5 - 5x + a.
Choices: (A) f(x) has three real roots if a > 4
(B) f(x) has only one real root if a > 4
(C) f(x) has three real roots if a < -4
(D) f(x) has three real roots if -4 < a < 4
Answer: (B), (D)
Subject: mathematics
Question: Let f: [a, b] → [1, ∞) be a continuous function and let g: ℝ → ℝ be defined as (see image for mathematical expression)
Choices: (A) g(x) is continuous but not differentiable at a, (B) g(x) is differentiable on ℝ, (C) g(x) is continuous but not differentiable at b, (D) g(x) is continuous and differentiable at either a or b but not both
Answer: (A), (C)
Subject: mathematics
Question: Let f: (−π/2, π/2) → ℝ be given by f(x) = (log(sec x + tan x))³. Then (see image for options)
Choices: (A) f(x) is an odd function, (B) f(x) is a one-one function, (C) f(x) is an onto function, (D) f(x) is an even function
Answer: (A), (B) and (C)
Subject: mathematics
Question: From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x, z = 1 and y = −x, z = −1. If P is such that ∠QPR is a right angle, then the possible value(s) of λ is(are)
Choices: (A) √2, (B) 1, (C) −1, (D) −√2
Answer: (C)
Subject: mathematics
Question: Let 𝑥⃗, 𝑦⃗ and 𝑧⃗ be three vectors each of magnitude √2 and the angle between each pair of them is π/4. If 𝑎⃗ is a nonzero vector perpendicular to 𝑥⃗ and 𝑦⃗ × 𝑧⃗ and 𝑏⃗ is a nonzero vector perpendicular to 𝑦⃗ and 𝑧⃗ × 𝑥⃗, then
Choices: (A) 𝑏⃗ = (𝑏⃗ · 𝑧⃗)(𝑧⃗ − 𝑥⃗), (B) 𝑎⃗ = (𝑎⃗ · 𝑦⃗)(𝑦⃗ − 𝑧⃗), (C) 𝑎⃗ · 𝑏⃗ = −(𝑎⃗ · 𝑦⃗)(𝑏⃗ · 𝑧⃗), (D) 𝑎⃗ = (𝑎⃗ · 𝑦⃗)(𝑧⃗ − 𝑦⃗)
Answer: (A), (B) and (C)
Subject: mathematics
Question: A circle S passes through the point (0,1) and is orthogonal to the circles (x − 1)2 + y2 = 16 and x2 + y2 = 1. Then
Choices: (A) radius of S is 8, (B) radius of S is 7, (C) centre of S is (−7,1), (D) centre of S is (−8,1)
Answer: (B), (C)
Subject: mathematics
Question: Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if
Choices: (A) the first column of M is the transpose of the second row of M
(B) the second row of M is the transpose of the first column of M
(C) M is a diagonal matrix with nonzero entries in the main diagonal
(D) the product of entries in the main diagonal of M is not the square of an integer
Answer: (C), (D)
Subject: mathematics
Question: Let f: R → R and g: R → R be respectively given by f(x) = |x| + 1 and g(x) = x^2 + 1. Define h: R → R by h(x) = { max {f(x), g(x)} if x ≤ 0, min {f(x), g(x)} if x > 0. The number of points at which h(x) is not differentiable is
Answer: 3
Subject: mathematics
Question: For a point P in the plane, let d₁(P) and d₂(P) be the distances of the point P from the lines x - y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ≤ d₁(P) + d₂(P) ≤ 4, is
Answer: 6
Subject: mathematics
Question: Let a⃗, b⃗, and c⃗ be three non-coplanar unit vectors such that the angle between every pair of them is π/3. If a⃗ × b⃗ + b⃗ × c⃗ = pa⃗ + qb⃗ + rc⃗, where p, q and r are scalars, then the value of (p²+2q²+r²)/q² is
Answer: 4