KVPY Government Jobs Exams

Let S = {1, 2, 3, …..,n} and A = {(a, b) |1< a, b < n} = S x S. A subset B of A is said to be a good subset if
(x, x) ∈ B for every x ∈ S. Then the number of good subsets of A is

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KVPY Other Question

Suppose a1, a2, a3, …….,a2012 are integers arranged on a circle. Each number is equal to the average of its two
adjacent numbers. If the sum of all even indexed numbers is 3018, what is the sum of all numbers ?
(A) 0 (B) 1509 (C) 3018 (D) 6036 An ideal monatomic gas expands to twice its volume. If the process is isothermal, the magnitude of work done by
the gas is W1. If the process is adiabatic, the magnitude of work done by the gas is Wa . Which of the following is
true ?
(A) Wi = Wa > 0 (B) Wi > Wa = 0 (C) Wi >Wa > 0 (D) Wi > Wa > 0