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KVPY Exam Pattern, KVPY Questions with Answers Page 12

(#M40027219) KVPY QUESTION Physical Ability Test Keep an EYE

XeF6 hydrolyses to give an oxide. The structure of XeF6 and the oxide, respectively, are-
(A) octahedral and tetrahedral
(B) distorted octahedral and pyramidal
(C) octahedral and pyramidal
(D) distorted octahedral and tetrahedral

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(#M40027218) KVPY QUESTION Physical Ability Test Keep an EYE

At a distance l from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity u in the direction perpendicular to the wire. When the particle reaches a distance 2l from the wire
its speed is found to be sqrt(2) u . The magnitude of the velocity, when it is a distance 4l away from the wire, is
(ignore gravity)

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(#M40027216) KVPY QUESTION Physical Ability Test Keep an EYE

One mole of an ideal gas at initial temperature T, undergoes a quasi-static process during which the volume
V is doubled. During the process the internal energy U obeys the equation U = aV3, where a is a constant.
The work done during this process is-
(A) 3RT / 2 (B) 5RT / 2 (C) 5RT / 3 (D) 7RT / 3

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(#M40027215) KVPY QUESTION Physical Ability Test Keep an EYE

The surface of a planet is found to be uniformly charged. When a particle of mass m and no charge is thrown
at an angle from the surface of the planet, it has a parabolic trajectory as in projectile motion with horizontal
range L. A particle of mass m and charge q, with the same initial conditions has a range L/2. The range of
particle of mass m and charge 2q with the same initial conditions is-
(A) L (B) L/2 (C) L/3 (D) L/4

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(#M40027214) KVPY QUESTION Mental Ability Keep an EYE

arithmetic mean and the geometric mean of two distinct 2-digit numbers x and y are two integers one of
which can be obtained by reversing the digits of the other (in base 10 representation). Then x + y equals-
(A) 82 (B) 116 (C) 130 (D) 148

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(#M40027213) KVPY QUESTION Mental Ability Keep an EYE

The maximum possible value of x^2 + y^2 – 4x – 6y, x, y real, subject to the condition | x + y | + | x – y | = 4
(A) is 12 (B) is 28 (C) is 72 (D) does not exist

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(#M40027212) KVPY QUESTION Mental Ability Keep an EYE

Let f(x) = x^12 – x^9 + x^4 – x + 1. Which of the following is true ?
(A) f is one-one
(B) f has a real root
(C) f ′ never vanishes
(D) f takes only positive values

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(#M40027211) KVPY QUESTION Mental Ability Keep an EYE

The smallest possible positive slope of a line whose y-intercept is 5 and which has a common point with the
ellipse 9x^2 + 16y^2 = 144 is-

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(#M40027210) KVPY QUESTION Mental Ability Keep an EYE

Let A and B be any two n × n matrices such that the following conditions hold : AB = BA and there exist
positive integers k and l such that Ak = I (the identity matrix) and Bl = 0 (the zero matrix). Then-
(A) A + B = I (B) det (AB) = 0
(C) det (A + B) ≠ 0 (D) (A + B)m = 0 for some integer m

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(#M40027209) KVPY QUESTION General Ability Test Keep an EYE

The locus of the point P = (a, b) where a, b are real numbers such that the roots of x^3 + ax^2 + bx + a = 0 are in
arithmetic progression is-
(A) an ellipse
(B) a circle
(C) a parabola whose vertex in on the y-axis
(D) a parabola whose vertex is on the x-axis

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