If two different numbers are taken from the set {0, 1, 2, 3, ......, 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is :

Two parallel chords of a cycle of radius 2 are at a distance √(3+1) part . If the chords subtend at the center , angles of π/k and 2 π/k where k>0. then value of [k] is {Note []k denotes the largest integer less than or equal to k ]

Let S = { 1,2,3,4,}. The total number of unordered pairs of disjoint subsets of S is equal to

If, for a positive integer n, the quadratic equation, x(x + 1) + (x + 1) (x + 2) + …..+ (x+ n-1)(x+n)=10n has two consecutive integral solutions, then n is equal to :