Relations and Functions (Class 12)

Let f be a polynomial function such that 2(f(x))= ( 2 (2+ 23+ 29+ ) ) 3 (1+ f(x)f ( 1x ) ), x>0 and f(6)=37. Then n=110f(n) is equal to .

Let R= \(x, y) N N : e(x+y) 2 \. Then the minimum number of elements, required to be added in R to make it a transitive relation, is .

Let A=\1, 2, 3, 4, 5, 6\. The number of one-one functions f : A A such that f(1) 3, f(3) 4 and f(2)+f(3)=5, is .

The number of relations on the set A = \1, 2, 3\, containing at most 6 elements including (1, 2), which are reflexive and transitive but not symmetric, is .