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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 18

(#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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(#M40027301) KVPY QUESTION Mental Ability-2010 Keep an EYE

Suppose a, b are real numbers such that ab ≠ 0. Which of the following four figures represents the curve
(y – ax – b)(bx^2 + ay^2 – ab) = 0

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(#M40027300) KVPY QUESTION Mental Ability-2010 Keep an EYE

Let r be a real number and n ∈ N be such that the polynomial 2x^2 + 2x + 1 divides the polynomial (x + 1)^n – r.
Then (n, r) can be-

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(#M40027299) KVPY QUESTION Mental Ability-2010 Keep an EYE

Arrange the expansion of
n
1/ 4
1/ 2
2x
1 x 



 + in decreasing powers of x. Suppose the coefficient of the first
three terms form an arithmetic progression. Then the number of terms in the expansion having integer
powers of x is-
(A) 1 (B) 2 (C) 3 (D) more than 3

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(#M40027298) KVPY QUESTION Mental Ability-2010 Keep an EYE

Estimate the order of the speed of propagation of an action potential or nerve impulse -
(A) nm/s (B) micron/s (C) cm/s (D) m/s

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(#M40027296) KVPY QUESTION Mental Ability-2010 Keep an EYE

The fluid part of blood flows in and out of capillaries in tissue to exchange nutrients and waste materials.
Under which of the following conditions will fluid flow out from the capillaries into the surrounding tissue ?
(A) When arterial blood pressure exceeds blood osmotic pressure
(B) When arterial blood pressure is less than blood osmotic pressure
(C) When arterial blood pressure is equal to blood osmotic pressure
(D) Arterial blood pressure and blood osmotic pressure have nothing to do with the outflow of fluid from
capilleries

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(#M40027295) KVPY QUESTION Mental Ability-2010 Keep an EYE

Restriction endonucleases are enzymes that cleave DNA molecules into smaller fragments. Which type of
bond do they act on ?
(A) N-glycosidic Bond (B) Hydrogen bond
(C) Phosphodiester bond (D) Disulfide bond

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