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KVPY Exam Pattern, KVPY Questions with Answers Page 3

(#M40027311) KVPY QUESTION Mental Ability-2010 Keep an EYE

Three equal charges +q are placed at the three vertices of an equilateral triangle centered at the origin. They
are held in equilibrium by a restoring force of magnitude F(r) = kr directed towards the origin, where k is a
constant. What is the distance of the three charges from the origin ?

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(#M40027310) KVPY QUESTION Mental Ability-2010 Keep an EYE

certain planet completes one rotation about its axis in time T. The weight of an object placed at the equator
on the planet's surface is a fraction f (f is close to unity) of its weight recorded at a latitude of 60º. The
density of the planet (assumed to be a uniform perfect sphere is given by-

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(#M40027309) KVPY QUESTION Mental Ability-2010 Keep an EYE

Suppose m, n are positive integers such that 6^m + 2^m+n 3^w + 2^n = 332. The value of the expression
m^2 + mn + n^2 is-

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(#M40027308) KVPY QUESTION Mental Ability-2010 Keep an EYE

A ball is dropped vertically from a height of h onto a hard surface. If the ball rebounds from the surface with
a fraction r of the speed with which it strikes the latter on each impact, what is the net distance traveled by
the ball up to the 10th impact

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(#M40027307) KVPY QUESTION Mental Ability-2010 Keep an EYE

Suppose m, n are positive integers such that 6m + 2m+n 3w + 2n = 332. The value of the expression
m2 + mn + n2 is-

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(#M40027306) KVPY QUESTION Mental Ability-2010 Keep an EYE

Let ABC be a triangle and P be a point inside ABC such that PA 2PB 3PC 0
r
+ + = . The ratio of the area of
triangle ABC to that of APC is-
(A) 2 (B)
2
3 (C)
3
5 (D) 3

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(#M40027305) KVPY QUESTION Mental Ability-2010 Keep an EYE

The value of ∫
π
− π −
2
0
min{| x |, cos 1(cos x)} dx is

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(#M40027304) KVPY QUESTION Mental Ability-2010 Keep an EYE

Let f : R → R be a continuous function satisfying f(x) = x + ∫
x
0
f (t) dt , for all x ∈ R. Then the number of
elements in the set S = {x ∈ R ; f(x) = 0} is-

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(#M40027303) KVPY QUESTION Mental Ability-2010 Keep an EYE

Let V1 be the volume of a given right circular cone with O as the centre of the base and A as its apex. Let V2
be the maximum volume of the right circular cone inscribed in the given cone whose apex is O and whose
base is parallel to the base of the given cone. Then the ratio V2/V1 is-

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(#M40027302) KVPY QUESTION Mental Ability-2010 Keep an EYE

Among all cyclic quadrilaterals inscribed in a circle of radius R with one of its angles equal to 120º.
Consider the one with maximum possible area. Its area is

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