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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 17

(#M40027315) KVPY QUESTION Mental Ability-2010 Keep an EYE

Two identical particles of mass 'm' and charge q are shot at each other from a very great distance with an
initial speed v. The distance of closest approach of these charges is

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(#M40027314) KVPY QUESTION Mental Ability-2010 Keep an EYE

An ideal gas with heat capacity at constant volume CV undergoes a quasistatic process described by PVα in a
P-V diagram, where α is a constant. The heat capacity of the gas during this process is given by-

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(#M40027313) KVPY QUESTION Mental Ability-2010 Keep an EYE

A particle of mass m undergoes oscillations about x = 0 in a potential given by V(x) =
2
1 kx2 – V0cos 




a
x ,
where V0, k, a are constants. If the amplitude of oscillation is much smaller than a, the time period is given
by-

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(#M40027312) KVPY QUESTION Mental Ability-2010 Keep an EYE

A narrow parallel beam of light falls on a glass sphere of radius R and refractive index μ at normal incidence.
The distance of the image from the outer edge is given by

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(#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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