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KVPY Exam Pattern, KVPY Questions with Answers Page 26

(#M40027073) KVPY QUESTION Mental Ability Keep an EYE

A certain 12-hour digital clock displays the hour and the minute of a day. Due to a defect in the clock whenever the digit 1 is supposed to be displayed it displays 7. What fraction of the day will the clock show the correct time ?

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(#M40027072) KVPY QUESTION Mental Ability Keep an EYE

A frog is presently located at the origin (0, 0) in the xy-plane. It always jumps from a point with integer coordinates to a point with integer coordinates moving a distance of 5 units in each jump. What is the minimum number of jumps required for the frog to go from (0, 0) to (0, 1)?
option
(A) 2
(B) 3
(C) 4
(D) 9

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(#M40027071) KVPY QUESTION Mental Ability Keep an EYE

A man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of traveling in mud , in water, on tar road is in the ratio 3 : 4 : 5. The ratio of the durations he requires to cross the patch of mud, stream and tar road is

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(#M40027070) KVPY QUESTION Mental Ability Keep an EYE

Consider an incomplete pyramid of balls on a square base having 18 layers; and having 13 balls on each side of the top layer. Then the total number N of balls in that pyramid satisfies
option
(A) 9000 < N < 10000
(B) 8000 < N < 9000
(C) 7000 < N < 8000
(D) 10000 < N < 12000

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(#M40027066) KVPY QUESTION Mental Ability Keep an EYE

The number of distinct prime divisors of the number 512^3 - 253^3 - 259^3 is

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(#M40027065) KVPY QUESTION Mental Ability Keep an EYE

Three circles each of radius 1, touch one another externally and they lie between two parallel lines. The minimum possible distance between the lines is

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(#M40027064) KVPY QUESTION Mental Ability Keep an EYE

Let ABC be a triangle with Angle B = 90. Let AD be the bisector of Angle A with D on BC. Suppose AC = 6 cm and the area of the triangle ADC is 10 cm2. Then the length of BD in cm is equal to

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(#M40027063) KVPY QUESTION Mental Ability Keep an EYE

Below are four equations in x. Assume that 0 < r < 4. Which of the following has the largest solution for x ?

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(#M40027062) KVPY QUESTION Mental Ability Keep an EYE

Let a, b, c, d be real numbers such that |a - b| = 2, |b - c| = 3, |c -d| = 4. Then the sum of all possible values of |a - d| is

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(#M40027061) KVPY QUESTION Mental Ability Keep an EYE

Let a, b, x, y be real numbers such that a^2 + b^2 = 81, x^2 + y^2 = 121 and ax + by = 99. Then the set of all possible values of ay - bx is

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