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Frequently Asked KVPY Exam Pattern, KVPY Questions with Answers Page 32

(#M40027037) KVPY QUESTION Mental Ability Keep an EYE

Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is 360 degree. At 6:15 the difference between these two angles is
option
(A) 165 degree
(B) 170 degree
(C) 175 degree
(D) 180 degree

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(#M40027036) KVPY QUESTION Mental Ability Keep an EYE

Suppose Q is a point on the circle with centre P and radius 1, as shown in the figure ; R is a point outside the circle such that QR = 1 and QRP = 2 degree. Let S be the point where the segment RP intersects the given circle. Then measure of RQS equals

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(#M40027034) KVPY QUESTION Mental Ability Keep an EYE

A regular octagon is formed by cutting congruent isosceles right- angled triangles from the corners of a square. If
the square has side- length 1, the side - length of the octagon is

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(#M40027032) KVPY QUESTION Mental Ability Keep an EYE

If a, b, c, d are positive real numbers such that
6
a b c d
5
a b c
4
a b
3
a + + +
=
+ +
=
+
= , then
b 2c 3d
a
+ +
is

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(#M40027031) KVPY QUESTION Mental Ability Keep an EYE

Let f(x) be a quadratic polynomial with f(2) = 10 and f(2) = – 2. Then the coefficient of x in f(x) is–
(A) 1 (B) 2 (C) 3 (D) 4

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(#M40027029) KVPY QUESTION Mental Ability Keep an EYE

The sum of (1^2 – 1 + 1)(1!) + (2^2 – 2 + 1)(2!) + …. + (n^2 – n + 1)(n!) is

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(#M40027028) KVPY QUESTION Mental Ability Keep an EYE

Let a b cr r r , , be three vectors in the xyz space such that a ×b = b × c = c × a ≠ 0 r r r r r r If A, B, C are points with
position vectors a b cr r r , , respectively, then the number of possible positions of the centroid of triangle ABC is

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(#M40027027) KVPY QUESTION Mental Ability Keep an EYE

Two players play the following game : A writes 3, 5, 6 on three different cards ; B writes 8, 9, 10 on three
different cards. Both draw randomly two cards from their collections. Then A computes the product of two
numbers he/she has drawn, and B computes the sum of two numbers he/she has drawn. The player getting the
larger number wins. What is the probability that A wins ?

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(#M40027025) KVPY QUESTION Mental Ability Keep an EYE

Which of the following intervals is a possible domain of the function f (x) = log{x} [x] + log[x] {x}, where [x]
is the greatest integer not exceeding x and {x} = x – [x] ?
(A) (0, 1) (B) (1, 2) (C) (2, 3) (D) (3, 5)

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(#M40027024) KVPY QUESTION Mental Ability Keep an EYE

In triangle ABC, we are given that 3 sin A + 4 cos B = 6 and 4 sin B + 3 cos A = 1. Then the measure of the
angle C is -
(A) 30º (B) 150º (C) 60º (D) 75º

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