KVPY Government Jobs Exams

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

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KVPY Other Question
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 The total energy of a black body radiation source is collected for five minutes and used to heat water. The
temperature of the water increases from 10.0º C to 11.0ºC. The absolute temperature of the black body is doubled
and its surface area halved and the experiment repeated for the same time. Which of the following statements
would be most nearly correct ?
(A) The temperature of the water would increase from 10.0º C to a final temperature of 12º C
(B) The temperature of the water would increase from 10.0º C to a final temperature of 18º C
(C) The temperature of the water would increase from 10.0º C to a final temperature of 14ºC
(D) The temperature of the water would increases from 10.0º C to a final temperature of 11º C