Relations and F...

Let $$A = \left \{x, y, z\right \}$$ and $$B = \left \{p, q, r, s\right \}$$. What is the number of distinct relations from $$B$$ to $$A$$?

Let $$ f(x)=1+2x^2+ 2^2x^4 +..... + 2^{10}x^{20}$$. Then f(x) has

Let $$A=\left\{ u,v,w,z \right\} ;B=\left\{ 3,5 \right\} $$, then the number of relations from $$A$$ to $$B$$ is

Consider two sets $$A=\{a, b, c\}, B=\{e, f\}$$. If maximum numbers of total relations from A to B; symmetric relation from A to A and from B to B are $$l, m, n$$ respectively, then the value of $$2l+m-n$$ is

Let R be a relation from a set A to a set B then 

If $$f:R-\left\{ 2 \right\} \rightarrow R$$ is a function defined by $$f(x)=\cfrac { { x }^{ 2 }-4 }{ x-2 } $$, then its range is

If $$n(A) = 2, n(B) = m$$ and the number of relation from $$A$$ to $$B$$ is $$64$$, then the value of $$m$$ is

If $$f(x)=\dfrac{1-x}{1+x}$$ then the value of $$(fof)(x)$$.

If $$f(x)=\dfrac {2^{x}+2^{-x}}{2}$$, then $$f(x+y).f(x-y)$$ is equal to ?

If $$f:{R}^{+}\rightarrow {R}^{+},f(x)={x}^{2}+2$$ and $$g:{R}^{+}\rightarrow {R}^{+},g(x)=\sqrt{x+1}$$
then $$(f+g)(x)$$ equals