KVPY Government Jobs Exams

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

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KVPY Other Question

The number of ordered pairs (m, n), where m, n ∈{1, 2, 3, …… ,50}, such that 6^m + 9^n is a multiple of 5 is –
(A) 1250 (B) 2500 (C) 625 (D) 500
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