KVPY Government Jobs Exams

A man tosses a coin 10 times, scoring 1 point for each head and 2 points for each tail. Let P(K) be the probability
of scoring at least K points. The largest value of K such that P(K) > ½ is

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KVPY Other Question

A polynomial P(x) with real coefficients has the property that P''(x) ≠ 0 for all x. Suppose P(0) = 1 and P'(0) = –1.
What can you say about P(1) Let
x 1
f (x) x 1
−
+
= for all x ≠ 1. Let
f 1(x) = f (x),f 2 (x) = f (f (x)) and generally
f n (x) = f (f n−1(x)) for n > 1
Let P = f1(2)f2(3)f3(4)f4(5)
Which of the following is a multiple of P –
(A) 125 (B) 375 (C) 250 (D) 147