question: For a first order reaction A→P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = -(2000)/T + 6.0. The pre-exponential factor A and the activation energy Ea, respectively, are

response_choices: (A) 1.0 × 10⁶ s⁻¹ and 9.2 kJ mol⁻¹ (B) 6.0 s⁻¹ and 16.6 kJ mol⁻¹ (C) 1.0 × 10⁶ s⁻¹ and 16.6 kJ mol⁻¹ (D) 1.0 × 10⁶ s⁻¹ and 38.3 kJ mol⁻¹

answer: D

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question_subject: chemistry


question: The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)₆ is

answer: A

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question_subject: chemistry


question: In the following carbocation, H₃CH₃ that is most likely to migrate to the positively charged carbon is

response_choices: (A) CH₃ at C-4 (B) H at C-4 (C) CH₃ at C-2 (D) H at C-2

answer: D

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question_subject: chemistry


question: The correct stability order of the following resonance structures is

answer: B

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question_subject: chemistry


question:
For the reduction of NO3- ion in an aqueous solution, E0 is +0.96 V. Values of E0 for some metal ions are given below

V2+(aq) + 2e- → V 						E0 = -1.19 V
Fe3+(aq) + 3e- → Fe 						E0 = -0.04 V
Au3+(aq) + 3e- → Au 						E0 = +1.40 V
Hg2+(aq) + 2e- → Hg 						E0 = +0.86 V

The pair(s) of metals that is(are) oxidized by NO3- in aqueous solution is(are)

response_choices:
(A)  V and Hg						(B)  Hg and Fe
(C)  Fe and Au						(D)  Fe and V

answer: AC

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question_subject: chemistry


question: Among the following, the state function(s) is(are)

response_choices:
(A)  Internal energy						(B)  Irreversible expansion work
(C)  Reversible expansion work				(D)  Molar enthalpy

answer: AD

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question_subject: chemistry


question:
In the reaction

2X + B2H6 → [BH2(X)2]2+ [BH4]-

the amine(s) X is(are)

answer: ABC

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question_subject: chemistry


question: The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)

answer: BC

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question_subject: chemistry


question: The correct statement(s) about the following sugars X and Y is(are)

response_choices:
(A) X is a reducing sugar and Y is a non-reducing sugar
(B) X is a non-reducing sugar and Y is a reducing sugar
(C) The glucosidic linkages in X and Y are α and β, respectively
(D) The glucosidic linkages in X and Y are β and α, respectively

answer: C

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question_subject: chemistry


question: Match each of the reactions given in Column I with the corresponding product(s) given in Column II

response_choices:
Column I: (A) Cu + dil HNO3, (B) Cu + conc HNO3, (C) Zn + dil HNO3, (D) Zn + conc HNO3
Column II: (p) NO, (q) NO2, (r) N2O, (s) Cu(NO3)2, (t) Zn(NO3)2

answer: p:q:r:s:t

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question_subject: chemistry


question: At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas Y at 60 K. The molecular weight of the gas Y is

answer: 4

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question_subject: chemistry


question: The dissociation constant of a substituted benzoic acid at 25°C is 1.0 × 10⁻⁴. The pH of a 0.01 M solution of its sodium salt is

answer: 8

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question_subject: chemistry


question: The total number of α and β particles emitted in the nuclear reaction ²³²U → ²¹⁴Pb is

answer: 8

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question_subject: chemistry


question: The oxidation number of Mn in the product of alkaline oxidative fusion of MnO₂ is

answer: 6

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question_subject: chemistry


question: The number of water molecule(s) directly bonded to the metal centre in CuSO₄·5H₂O is

answer: 5

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question_subject: chemistry


question: The coordination number of Al in the crystalline state of AlCl₃ is

answer: 6

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question_subject: chemistry


question: The total number of cyclic structural as well as stereo isomers possible for a compound with the molecular formula C₅H₁₀ is

answer: 7

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question_subject: chemistry


question: If the sum of first n terms of an A.P. is cn², then the sum of squares of these n terms is

answer: C

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question_subject: mathematics


question: A line with positive direction cosines passes through the point P(2, -1,2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

answer: C

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question_subject: mathematics


question: The normal at a point P on the ellipse x^2 + 4y^2 = 16 meets the x-axis at Q. If M is the mid point of the line segment PQ, then the locus of M intersects the latus rectums of the given ellipse at the points

answer: C

image_available: yes

question_subject: mathematics


question: The locus of the orthocentre of the triangle formed by the lines (1 + p)x - py + p(1 + p) = 0, (1 + q)x - qy + q(1 + q) = 0, and y = 0, where p ≠ q, is

response_choices: (A) a hyperbola (B) a parabola (C) an ellipse (D) a straight line

answer: D

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question_subject: mathematics


question: If In = ∫ (sin nx / (1 + x^8))sin x dx, n = 0, 1, 2, ..., then

answer: A,B,C

image_available: yes

question_subject: mathematics


question: An ellipse intersects the hyperbola 2x^2 - 2y^2 - 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

response_choices: (A) Equation of ellipse is x^2 + 2y^2 = 2 (B) The foci of ellipse are (±1, 0) (C) Equation of ellipse is x^2 - 2y^2 = 4 (D) The foci of ellipse are (±√2, 0)

answer: A, B

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question_subject: mathematics


question: For the function f(x) = x cos ^1/x, x ≥ 1,

response_choices: (A) for at least one x in the interval [1, ∞), f(x + 2) - f(x) < 2 (B) lim f'(x) = 1 x→∞ (C) for all x in the interval [1, ∞), f(x + 2) - f(x) > 2 (D) f'(x) is strictly decreasing in the interval [1, ∞)

answer: B, C, D

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question_subject: mathematics


question: The tangent PT and the normal PN to the parabola y^2 = 4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose

response_choices: (A) vertex is (2a/3, 0) (B) directrix is x = 0 (C) latus rectum is 2a/3 (D) focus is (a, 0)

answer: A, D

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question_subject: mathematics


question: For 0 < θ < π/2 , the solution(s) of Σcosec(θ + (m - 1)π/4)cosec(θ + mπ/4) = 4√2 m = 1 5 is(are)

answer: C, D

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question_subject: mathematics


question: Match the statements/expressions given in Column I with the values given in Column II.

response_choices: A: p, B: q, C: r, D: s, AND t

answer: A: p, q, r, s, t; B: p, q, r, s, t; C: p, q, r, s, t; D: p, q, r, s, t

image_available: yes

question_subject: mathematics


question: Match the statements/expressions given in Column I with the values given in Column II.

response_choices: A) The number of solutions of the equation x^(5/3) - cos x = 0 in the interval (0, π/2); B) Value(s) of k for which the planes kx + 4y + z = 0, 4x + ky + 2z = 0 and 2x + 2y + z = 0 intersect in a straight line; C) Value(s) of k for which |x - 1| + |x - 2| + |x + 1| + |x + 2| = 4k has integer solution(s); D) If y' = y + 1 and y(0) = 1, then value(s) of y(ln 2)

answer: p: 1, q: 2, r: 3, s: 4, t: 5

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question_subject: mathematics


question: The maximum value of the function f(x) = 2x^3 - 15x^2 + 36x - 48 on the set A = {x | x^2 + 20 ≤ 9x} is

answer: 7

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question_subject: mathematics


question: Let (x, y, z) be points with integer coordinates satisfying the system of homogeneous equations: 3x - y - z = 0, -3x + z = 0, -3x + 2y + z = 0. Then the number of such points for which x^2 + y^2 + z^2 ≤ 100 is

answer: 7

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question_subject: mathematics


question: Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2√2 and angle B = 30°. The absolute value of the difference between the areas of these triangles is

answer: 4

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question_subject: mathematics


question: Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and lim [1 + p(x)/x^2] = 2. Then the value of p(2) is

answer: 6

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question_subject: mathematics


question: Let f: R → R be a continuous function which satisfies f(x) = ∫[f(t)/t]dt. Then the value of f(ln 5) is

answer: 4

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question_subject: mathematics


question: The centres of two circles C1 and C2 each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1 and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is

answer: 8

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question_subject: mathematics


question: The smallest value of k, for which both the roots of the equation x^2 - 5kx + 16 (k^2 - k + 1) = 0 are real, distinct and have values at least 4, is

answer: 2

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question_subject: mathematics


question: If the function f(x) = x^4 + e^2 and g(x) = f'^-1(x), then the value of g'(1) is

answer: 2

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question_subject: mathematics


question: The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is

answer: D

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question_subject: physics


question: A piece of wire is bent in the shape of a parabola y = kx^2 (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is

answer: B

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question_subject: physics


question: Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions ξp = 2.0 eV, ξq = 2.5 eV and ξr = 3.0 eV, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensities illuminates each of the plates. The correct I-V graph for the experiment is

response_choices: (A), (B), (C), (D) [Graph options]

answer: A

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question_subject: physics


question: A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle θ in one direction and released. The frequency of oscillation is

response_choices: 1 ⁄ √(2k ⁄ M), 1 ⁄ √(k ⁄ M), 1 ⁄ √(6k ⁄ M), 1 ⁄ √(24k ⁄ M)

answer: C

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question_subject: physics


question: Two metallic rings A and B, identical in shape and size but having different resistivities ρA and ρB, are kept on top of two identical solenoids as shown in the figure. When current I is switched on in both the solenoids in identical manner, the rings A and B jump to heights hA and hB, respectively, with hA > hB. The possible relation(s) between their resistivities and their masses mA and mB is(are)

response_choices: ρA > ρB and mA = mB, ρA < ρB and mA = mB, ρA > ρB and mA > mB, ρA < ρB and mA < mB

answer: BC

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question_subject: physics


question: A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then,

response_choices: the intensity of the sound heard at the first resonance was more than that at the second resonance, the prongs of the tuning fork were kept in a horizontal plane above the resonance tube, the amplitude of vibration of the ends of the prongs is typically around 1 cm, the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air

answer: AD

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question_subject: physics


question: The figure shows the P-V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse. Then,

response_choices:
(A) the process during the path A → B is isothermal
(B) heat flows out of the gas during the path B → C → D
(C) work done during the path A → B → C is zero
(D) positive work is done by the gas in the cycle ABCDA

answer: BD

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question_subject: physics


question: Under the influence of the Coulomb field of charge +Q, a charge –q is moving around it in an elliptical orbit. Find out the correct statement(s).

response_choices:
(A) The angular momentum of the charge –q is constant
(B) The linear momentum of the charge –q is constant
(C) The angular velocity of the charge –q is constant
(D) The linear speed of the charge –q is constant

answer: A

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question_subject: physics


question: A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then,

response_choices:
(A) ⃗VC - ⃗VA = 2(⃗VB - ⃗VC)	(B) ⃗VC - ⃗VB = ⃗VB - ⃗VA
(C) |⃗VC - ⃗VA| = 2|⃗VB - ⃗VC|	(D) |⃗VC - ⃗VA| = 4|⃗VB|

answer: BC

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question_subject: physics


question: Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the system. Match the statements in Column I to the appropriate process(es) from Column II

response_choices:
A. The energy of the system is increased
B. Mechanical energy is provided to the system, which is converted into energy of random motion of its parts
C. Internal energy of the system is converted into its mechanical energy
D. Mass of the system is decreased

answer:
A: p q r s t
B: p q r s l
C: p q r s l
D: p q r s l

image_available: yes

question_subject: physics


question: Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits S1 and S2. In each of these cases S1P1 - S2P1 = λ/4 and S1P2 - S2P2 = λ/3, where λ is the wavelength of the light used. In the cases B, C and D, a transparent sheet of refractive index μ and thickness t is pasted on slit S2. The thicknesses of the sheets are different in different cases. The phase difference between the light waves reaching a point P on the screen from the two slits is denoted by δ(P) and the intensity by I(P). Match each situation given in Column I with the statement(s) in Column II valid for that situation.

answer:
A: p,q,r,s,t
B: p,q,r,s,t
C: p,q,r,s,f
D: p,q,f,s,t

image_available: yes

question_subject: physics


question: A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k(μ₀I / 48πx), find the value of k.

answer: 7

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question_subject: physics


question: A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s², find the work done (in Joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.

answer: 8

image_available: yes

question_subject: physics


question: A solid sphere of radius R has a charge Q distributed in its volume with a charge density ρ = kr⁴, where k and a are constants and r is the distance from its centre. If the electric field at r = R/2 is 3 times that at r = R, find the value of a.

answer: 2

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question_subject: physics


question: A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.

answer: 5

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question_subject: physics