Relations and Functions (Class 12)

Let N denote the set of all positive integers. Consider the sets A=\1,2,3,4,5\ and B=\1,2,3,4,5,6,7\. Let S be the set of all functions f:A B such that f(2) 2 and f(4) 4. Consider the set T=\f S: there exists a function g:B N such that g(f(x))=2x for all x A\. Then the number of elements in the set T is .

Let the set of all relations R on the set \a, b, c, d, e, f\, such that R is reflexive and symmetric, and R contains exactly 10 elements, be denoted by S. Then the number of elements in S is .

If n(X)=mC6, then the value of m is .

If the value of n(Y)+n(Z) is k2, then |k| is .