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KVPY Exam Pattern, KVPY Questions with Answers Page 9

(#M40027250) KVPY QUESTION General Ability Test -2010 Keep an EYE

A pen of mass 'm' is lying on a piece of paper of mass M placed on a rough table. If the coefficient of
friction between the pen and paper, and, the paper and table are μ1 and μ2, respectively, then the minimum
horizontal force with which the paper has to be pulled for the pen to start slipping is given by-
(A) (m + M) (μ1 + μ2) g (B) (mμ1 + Mμ2)g
(C) {mμ1 + (m + M) μ2} g (D) m(μ1 + μ2) g

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(#M40027249) KVPY QUESTION Mental Ability -2010 Keep an EYE

Let a0 = 0 and ax = 3an–1 + 1 for n ≥ 1. Then the remainder obtained dividing a2010 by 11 is-
(A) 0 (B) 7 (C) 3 (D) 4

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(#M40027248) KVPY QUESTION Mental Ability -2010 Keep an EYE

The number of natural numbers n in the interval [1005, 2010] for which the polynomial 1 + x + x^2 + x^3 + …. x^n–1
divides the polynomial 1 + x^2 + x^3 + x^4 + …. + x^2010 is-
(A) 0 (B) 100 (C) 503 (D) 1006

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(#M40027247) KVPY QUESTION Mental Ability -2010 Keep an EYE

How many six-digit numbers are there in which no digit is repeated, even digits appear at even places, odd
digits appear at odd places and the number is divisible by 4 ?
(A) 3600 (B) 2700 (C) 2160 (D) 1440

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(#M40027246) KVPY QUESTION Mental Ability -2010 Keep an EYE

Let kˆ jˆ iˆ u = 2 − + r , kˆ v = −3ˆj + 2 r be vectors in R3 and w r be a unit vector in the xy-plane. Then the maximum
possible value of | (u r × v r ) .w r | is-

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(#M40027245) KVPY QUESTION Mental Ability -2010 Keep an EYE

Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability
that they form the vertices of an isosceles triangle is-

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(#M40027244) KVPY QUESTION Mental Ability -2010 Keep an EYE

Consider the regions A = {(x, y) | x^2 + y^2 ≤ 100} and = {(x, y) | sin (x + y) > 0} in the plane. Then the area
of the region A ∩ B is-
(A) 10 π (B) 100 (C) 100 π (D) 50 π

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(#M40027243) KVPY QUESTION Mental Ability -2010 Keep an EYE

The roots of (x – 41)^49 + (x – 49)^41 + (x – 2009)^2009 = 0 are -
(A) all necessarily real
(B) non-real except one positive real root
(C) non-real except three positive real roots
(D) non-real except for three real roots of which exactly one is positive

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(#M40027242) KVPY QUESTION Mental Ability -2010 Keep an EYE

Let f : R → R be a differentiable function such that f (a) = 0 = f (b) and f ′(a) f ′(b) > 0 for some a < b. Then
the minimum number of roots of f ′(x = 0 in the interval (a, b) is-
(A) 3 (B) 2 (C) 1 (D) 0

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(#M40027241) KVPY QUESTION Mental Ability -2010 Keep an EYE

The product (1 + tan 1º) (1 + tan 2º) (1 + tan 3º) …. (1 + tan 45º) equals-

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