KVPY Government Jobs Exams

The diameter of one of the bases of a truncated cone is 100 mm. If the diameter of this base is increased by
21% such that it still remains a truncated cone with the height and the other base unchanged, the volume also
increases by 21%. The radius of the other base (in mm) is-
(A) 65 (B) 55 (C) 45 (D) 35

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KVPY Other Question

Let f(x) = ax^2 + bx + c, where a, b, c are integers. Suppose f(1) = 0, 40 < f(6) < 50, 60 < f(7) < 70, and
1000t < f(50) < 1000 (t + 1) for some integer t. Then the value of t is
(A) 2 (B) 3 (C) 4 (D) 5 or more Two friends A and B are 30 km apart and they start simultaneously on motorcycles to meet each other. The speed of A is 3 times that of B. The distance between them decreases at the rate of 2 km per minute. Ten minutes after they start, A's vehicle breaks down and A stops and waits for B to arrive. After how much time (in minutes) A started riding, does B meet A?
option
(A) 15
(B) 20
(C) 25
(D) 30