The domain of definition of the function $f (x) = {\log _{\left[ {x + \frac{1}{x}} \right]}}|{x^2} – x – 6|+ ^{16-x}C_{2x-1} + ^{20-3x}P_{2x-5}$  is

Where $[x]$ denotes greatest integer function.

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 …………….

Least integer in the range of $f(x)$=$\sqrt {(x + 4)(1 – x)}  – {\log _2}x$ is

If $f(x) = \frac{{\alpha \,x}}{{x + 1}},\;x \ne – 1$. Then, for what value of $\alpha $ is $f(f(x)) = x$

Domain of $log\,log\,log\,  ….(x)$ is 

                        $ \leftarrow \,n\,\,times\, \to $