The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is

Let $A=\{(x, y): 2 x+3 y=23, x, y \in N\}$ and $B=\{x:(x, y) \in A\}$. Then the number of one-one functions from $\mathrm{A}$ to $\mathrm{B}$ is equal to ................

Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then Range of the function f (x) is

If $f(x) = \frac{{{{\cos }^2}x + {{\sin }^4}x}}{{{{\sin }^2}x + {{\cos }^4}x}}$ for $x \in R$, then $f(2002) = $

Let $f : R \rightarrow R$ be a function such that $f(x)=\frac{x^2+2 x+1}{x^2+1}$. Then

Let $S=\{1,2,3,4\}$. Then the number of elements in the set $\{f: S \times S \rightarrow S: f$ is onto and $f(a, b)=f(b, a)$ $\geq a; \forall(a, b) \in S \times S\}$ is