cmeraki/elemento huggingface dataset:
Subject: chemistry
Question: Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl-, CN- and H2O, respectively, are
Choices: (A) octahedral, tetrahedral and square planar, (B) tetrahedral, square planar and octahedral, (C) square planar, tetrahedral and octahedral, (D) octahedral, square planar and octahedral
Answer: B
Subject: chemistry
Question: Dissolving 120 g of urea (mol. wt. 60) in 1000 g of water gave a solution of density 1.15 g/mL. The molarity of the solution is
Choices: (A) 1.78 M, (B) 2.00 M, (C) 2.05 M, (D) 2.22 M
Answer: C
Subject: chemistry
Question: The correct statement(s) pertaining to the adsorption of a gas on a solid surface is (are)
Choices: (A) Adsorption is always exothermic. (B) Physisorption may transform into chemisorption at high temperature. (C) Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature. (D) Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation.
Answer: ABD
Subject: chemistry
Question: The final solution contains
Choices: (A) [Pb(NH3)4]2+ and [CoCl4]2- (B) [Al(NH3)4]3+ and [Cu(NH3)4]2+ (C) [Ag(NH3)2]+ and [Cu(NH3)4]+ (D) [Ag(NH3)2]+ and [Ni(NH3)6]2+
Answer: C
Subject: chemistry
Question: The work function (Φ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is
Choices: Metal: Li, Na, K, Mg, Cu, Ag, Fe, Pt, W; Φ (eV): 2.4, 2.3, 2.2, 3.7, 4.8, 4.3, 4.7, 6.3, 4.75
Answer: 4
Subject: physics
Question: A police car with a siren of frequency 8 kHz is moving with uniform velocity 36 km/hr towards a tall building which reflects the sound waves. The speed of sound in air is 320 m/s. The frequency of the siren heard by the car driver is
Choices: (A) 8.50 kHz (B) 8.25 kHz (C) 7.75 kHz (D) 7.50 kHz
Answer: A
Subject: physics
Question: 5.6 liter of helium gas at STP is adiabatically compressed to 0.7 liter. Taking the initial temperature to be T₁, the work done in the process is
Choices: (A) (9/8) R T₁ (B) (3/2) R T₁ (C) (15/8) R T₁ (D) (9/2) R T₁
Answer: A
Subject: physics
Question: The wavelength of the first spectral line in the Balmer series of hydrogen atom is 6561 Å. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is
Choices: (A) 1215 Å, (B) 1640 Å, (C) 2430 Å, (D) 4687 Å
Answer: A
Subject: physics
Question: A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is
Choices: (A) 9, (B) 18, (C) 27, (D) 36
Answer: D
Subject: physics
Question: A meter bridge is set-up as shown, to determine an unknown resistance 'X' using a standard 10 ohm resistor. The galvanometer shows null point when tapping-key is at 52 cm mark. The end-corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of 'X' is
Choices: (A) 10.2 ohm, (B) 10.6 ohm, (C) 10.8 ohm, (D) 11.1 ohm
Answer: B
Subject: physics
Question: A spherical metal shell A of radius RA and a solid metal sphere B of radius RB (< RA) are kept far apart and each is given charge '+Q'. Now they are connected by a thin metal wire. Then
Choices: (A) Einside = 0, (B) QA > QB, (C) σA = RB/RA * σB, (D) Eout surface A < Eout surface B
Answer: ABCD
Subject: physics
Question: An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?
Choices: (A) They will never come out of the magnetic field region, (B) They will come out travelling along parallel paths, (C) They will come out at the same time, (D) They will come out at different times.
Answer: BC, BD, BCD
Subject: physics
Question: A composite block is made of slabs A, B, C, D and E of different thermal conductivities (given in terms of a constant K) and sizes (given in terms of length, L) as shown in the figure. All slabs are of same width. Heat 'Q' flows only from left to right through the blocks. Then in steady state
Choices: A) heat flow through A and E slabs are same.
B) heat flow through slab E is maximum.
C) temperature difference across slab E is smallest.
D) heat flow through C = heat flow through B + heat flow through D.
Answer: D
Subject: physics
Question: A metal rod of length 'L' and mass 'm' is pivoted at one end. A thin disk of mass 'M' and radius 'R' (< L) is attached at its center to the free end of the rod. Consider two ways the disc is attached: (case A) The disc is not free to rotate about its center and (case B) the disc is free to rotate about its center. The rod-disc system performs SHM in vertical plane after being released from the same displaced position. Which of the following statement(s) is (are) true?
Choices: A) Restoring torque in case A = Restoring torque in case B
B) Restoring torque in case A < Restoring torque in case B
C) Angular frequency for case A > Angular frequency for case B.
D) Angular frequency for case A < Angular frequency for case B.
Answer: D
Subject: physics
Question: The phase space diagram for simple harmonic motion is a circle centered at the origin. In the figure, the two circles represent the same oscillator but for different initial conditions, and E1 and E2 are the total mechanical energies respectively. Then
Choices: (A) E1 = √2 E2, (B) E1 = 2 E2, (C) E1 = 4 E2, (D) E1 = 16 E2
Answer: C
Subject: physics
Question: Taking the electronic charge as 'e' and the permittivity as '\epsilon_0', use dimensional analysis to determine the correct expression for \omega_p.
Choices: (A) \sqrt{Ne/m\epsilon_0}, (B) \sqrt{m\epsilon_0/Ne}, (C) \sqrt{Ne^2/m\epsilon_0}, (D) \sqrt{m\epsilon_0/Ne^2}
Answer: C
Subject: physics
Question: Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N = 4 × 10^27 m^-3. Take \epsilon_0 = 10^-11 and m = 10^-30, where these quantities are in proper SI units.
Choices: (A) 800 nm, (B) 600 nm, (C) 300 nm, (D) 200 nm
Answer: B
Subject: physics
Question: A boy is pushing a ring of mass 2 kg and radius 0.5 m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 m/s². The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is
Answer: 4
Subject: physics
Question: Steel wire of length 'L' at 40°C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^(-5) /°C, Young's modulus of steel is 10^11 N/m^2 and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is nearly
Answer: 3
Subject: physics
Question: A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 ohm and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as I = I0 cos (300 t) where I0 is constant. If the magnetic moment of the loop is N d0 I0 sin (300 t), then 'N' is
Choices: (No response choices provided)
Answer: 6
Subject: mathematics
Question: Let a⃗=i⃗+j⃗+k⃗, b⃗=i⃗−j⃗+k⃗ and c⃗=i⃗−j⃗−k⃗ be three vectors. A vector v⃗ in the plane of a⃗ and b⃗, whose projection on c⃗ is 1/√3, is given by
Choices: A) i⃗−3j⃗+3k⃗, B) −3i⃗−3j⃗−k⃗, C) 3i⃗−j⃗+3k⃗, D) i⃗+3j⃗−3k⃗
Answer: C
Subject: mathematics
Question: Let the straight line x=b divide the area enclosed by y=(1−x)², y=0, and x=0 into two parts R₁ (0≤x≤b) and R₂ (b≤x≤1) such that R₁−R₂=1/4. Then b equals
Choices: A) 3/4, B) 1/2, C) 1/3, D) 1/4
Answer: B
Subject: mathematics
Question: Let α and β be the roots of x^2 - 6x - 2 = 0, with α > β. If a_n = α^n - β^n for n≥1, then the value of (a_0 - 2a_1)/2a_0 is
Choices: (A) 1, (B) 2, (C) 3, (D) 4
Answer: C
Subject: mathematics
Question: A straight line L through the point (3,-2) is inclined at an angle 60° to the line √3x + y = 1. If L also intersects the x-axis, then the equation of L is
Choices: (A) y + √3x + 2 - 3√3 = 0, (B) y - √3x + 2 + 3√3 = 0, (C) √3y - x + 3 + 2√3 = 0, (D) √3y + x - 3 + 2√3 = 0
Answer: B
Subject: mathematics
Question: The vector(s) which is/are coplanar with vectors \vec{i} + \vec{j} + 2\vec{k} and \vec{i} + 2\vec{j} + \vec{k}, and perpendicular to the vector \vec{i} + \vec{j} + \vec{k} is/are
Choices: (A) \vec{j} - \vec{k}, (B) -\vec{i} + \vec{j}, (C) \vec{i} - \vec{j}, (D) -\vec{j} + \vec{k}
Answer: AD
Subject: mathematics
Question: Let M and N be two 3x3 non-singular skew-symmetric matrices such that MN = NM . If P^T denotes the transpose of P, then M^2N^2 (M^TN)^-1 (MN^-1)^T is equal to
Choices: (A) M^2, (B) -N^2, (C) -M^2, (D) MN
Answer: MARKS TO ALL
Subject: mathematics
Question: Let the eccentricity of the hyperbola x^2/a^2 - y^2/b^2 = 1 be reciprocal to that of the ellipse x^2 + 4y^2 = 4 . If the hyperbola passes through a focus of the ellipse, then
Choices: (A) the equation of the hyperbola is x^2/3 - y^2/2 = 1, (B) a focus of the hyperbola is (2, 0), (C) the eccentricity of the hyperbola is \sqrt{5}/3, (D) the equation of the hyperbola is x^2 - 3y^2 = 3
Answer: BD
Subject: mathematics
Question: Let f : R → R be a function such that f(x + y) = f(x) + f(y), ∀x, y ∈ R. If f(x) is differentiable at x = 0, then
Choices: (A) f(x) is differentiable only in a finite interval containing zero, (B) f(x) is continuous ∀x ∈ R, (C) f'(x) is constant ∀x ∈ R, (D) f(x) is differentiable except at finitely many points
Answer: BC,BCD
Subject: mathematics
Question: Let ω be a solution of x^3 - 1 = 0 with Im(ω) > 0. If a = 2 with b and c satisfying (E), then the value of (3/ω^4) + (1/ω^6) + (3/ω^5) is equal to
Choices: (A) -2, (B) 2, (C) 3, (D) -3
Answer: A
Subject: mathematics
Question: Let b = 6, with a and c satisfying (E). If α and β are the roots of the quadratic equation ax^2 + bx + c = 0, then Σ[(1/α)^n + (1/β)^n] is
Choices: (A) 6, (B) 7, (C) 6/7, (D) ∞
Answer: B
Subject: mathematics
Question: Consider the parabola y² = 8x. Let A₁ be the area of the triangle formed by the end points of its latus rectum and the point P(1, 2) on the parabola, and A₂ be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum. Then A₁/A₂ is
Answer: 2
Subject: mathematics
Question: Let a₁, a₂, a₃, ..., a₁₀₀ be an arithmetic progression with a₁ = 3 and S₅ = Σⁿᵖ=¹ aᵖ , 1 ≤ p ≤ 100. For any integer n with 1 ≤ n ≤ 20, let m = 5n. If S_m/S₅ does not depend on n, then a₅ is
Answer: 3, 9, 3 & 9 BOTH