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KVPY Exam Pattern, KVPY Questions with Answers Page 29

(#M40027040) KVPY QUESTION Mental Ability Keep an EYE

How many ordered pairs of (m, n) integers satisfy ?
m/12=12/n

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(#M40027039) KVPY QUESTION Mental Ability Keep an EYE

When a bucket is half full, the weight of the bucket and the water is 10 kg. When the bucket is two - thirds full, the total weight is 11kg. What is the total weight, in kg, when the bucket is completely full

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(#M40027038) KVPY QUESTION Mental Ability Keep an EYE

Two workers A and B are engaged to do a piece of work. Working alone, A takes 8 hours more to complete the work than if both worked together. On the other hand, working alone, B would need 2 4 1 hours more to complete
the work than if both worked together. How much time would they take to complete the job working together?
option
(A) 4 Hours
(B) 5 Hours
(C) 6 Hours
(D) 7 Hours

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(#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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(#M40027035) KVPY QUESTION Mental Ability Keep an EYE

A circle is drawn in a sector of a larger circle of radius r, as shown in the adjacent figure. The smaller circle is
tangent to the two bounding radii and the arc of the sector. The radius of the small circle is

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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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(#M40027033) KVPY QUESTION Mental Ability Keep an EYE

In triangle ABC, let AD, BE and CF be the internal angle bisectors with D, E and F on the sides BC, CA and AB
respectively. Suppose AD, BE and CF concur at I and B, D, I, F are concyclic, then ∠IFD has measure

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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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