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KVPY Exam Pattern, KVPY Questions with Answers Page 37

(#M40026960) KVPY QUESTION Mental Ability Keep an EYE

Let a, b, c, d be numbers in the set {1, 2, 3, 4, 5, 6} such that the curves y = 2x^3 + ax + b and y = 2x^3 + cx + d have no point in common. The maximum possible value of (a - c)^2 + b d is

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(#M40026959) KVPY QUESTION Mental Ability Keep an EYE

Suppose two perpendicular tangents can be drawn from the origin to the circle x2 + y2 – 6x –2py + 17 = 0, for
some real p. then |p| =

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(#M40026958) KVPY QUESTION Mental Ability Keep an EYE

The maximum value M of 3^x + 5^x – 9^x + 15^x –25^x, as x varies over reals, satisfies –
(A) 3 < M < 5 (B) 0 < M < 2 (C) 9 < M < 25 (D) 5 < M < 9

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(#M40026957) KVPY QUESTION Mental Ability Keep an EYE

In the real number system, the equation sqrt(x + 3− 4 x −1) + sqrt(x + 8 − 6 x −1) = 1 has
option
(A) No solution
(B) Exactly two distinct solutions
(C) Exactly four distinct solutions
(D) Infinitely may solutions

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(#M40026956) KVPY QUESTION Mental Ability Keep an EYE

Three children, each accompanied by a guardian, seek admission in a school. The principal want to interview all
the 6 persons one after the other subject to the condition that no child is interviewed before its guardian. In how
many ways can this be done –

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