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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 36

(#M40026986) KVPY QUESTION General Ability Test Keep an EYE

A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be
the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about
its equilibrium shape. By dimensional analysis the ratio
3
v
σ / ρR
can be (Here σ is surface tension, ρ is density,
g is acceleration due to gravity, and k is arbitrary dimensionless constant)

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(#M40026983) KVPY QUESTION Mental Ability Keep an EYE

Let S = {1, 2, 3, …..,n} and A = {(a, b) |1< a, b < n} = S x S. A subset B of A is said to be a good subset if
(x, x) ∈ B for every x ∈ S. Then the number of good subsets of A is

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(#M40026982) KVPY QUESTION Mental Ability Keep an EYE

Suppose a1, a2, a3, …….,a2012 are integers arranged on a circle. Each number is equal to the average of its two
adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers ?
(A) 0 (B) 1509 (C) 3018 (D) 6036

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(#M40026978) KVPY QUESTION Mental Ability Keep an EYE

Let Σ=
=
n
k 1
Sn k denote the sum of the first n positive integers. The numbers S1, S2, S3,…S99 are written on 99
cards. The probability of drawing a card with an even number written on it is

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(#M40026977) KVPY QUESTION Mental Ability Keep an EYE

Let [x] and {x} be the integer part and fractional part of a real number x respectively. The value of the integral [x]{x}dx is

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(#M40026976) KVPY QUESTION Mental Ability Keep an EYE

Let f : R → R be the function f(x) = (x – a1)(x–a2)+(x–a2)(x–a3) + (x– a3) (x–a1) with a1, a2, a3 ∈ R. Then f(x) > 0 if
and only if –
(A) At least two of a1, a2, a3 are equal (B) a1 = a2 = a3
(C) a1, a2, a3 are all distinct (D) a1, a2, a3 , are all positive and distinct

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(#M40026974) KVPY QUESTION Mental Ability Keep an EYE

The mid- point of the domain of the function f (x) =sqrt( 4 − 2x + 5) for real x is

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(#M40026973) KVPY QUESTION Mental Ability Keep an EYE

The value of sec9° – sec27° – sec63° + sec81° is

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(#M40026972) KVPY QUESTION Mental Ability Keep an EYE

The value of sec81° – sec63° – sec27° + sec9° is

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(#M40026971) KVPY QUESTION Mental Ability Keep an EYE

The value of cosec9° – cosec27° – cosec63° + cosec81° is

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