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KVPY Exam Pattern, KVPY Questions with Answers Page 30

(#M40027030) KVPY QUESTION General Ability Keep an EYE

A narrow but tall cabin is falling freely near the earth's surface. Inside the cabin, two small stones A and B
are released from rest (relative to the cabin). Initially A is much above the centre of mass and B much below
the centre of mass of the cabin. A close observation of the motion of A and B will reveal that -
(A) both A and B continue to be exactly at rest relative to the cabin
(B) A moves slowly upward and B moves slowly downward relative to the cabin
(C) both A and B fall to the bottom of the cabin with constant acceleration due to gravity
(D) A and B move slightly towards each other vertically

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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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(#M40027026) KVPY QUESTION Mental Ability Keep an EYE

The minimum distance between a point on the curve y = e^x and a point on the curve y = logex is

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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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(#M40027023) KVPY QUESTION Mental Ability Keep an EYE

In the xy-plane, three distinct lines l1, l2, l3 concur at a point (λ, 0). Further the lines l1, l2, l3 are normals to the
parabola y^2 = 6x at the points A = (x1, y1), B = (x2, y2), C = (x3, y3) respectively. Then find λ

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(#M40027022) KVPY QUESTION Mental Ability Keep an EYE

In a rectangle ABCD, the coordinates of A and B are (1, 2) and (3, 6) respectively and some diameter of the
circumscribing circle of ABCD has equation 2x – y + 4 = 0. Then the area of the rectangle is

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(#M40027021) KVPY QUESTION Mental Ability Keep an EYE

Let A = (4, 0), B = (0, 12) be two points in the plane. The locus of a point C such that the area of triangle
ABC is 18 sq. units is

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