If a function $f(x)$ is such that $f\left( {x + \frac{1}{x}} \right) = {x^2} + \frac{1}{{{x^2}}};$ then  $(fof )$ $\sqrt {11} )$ =

The period of the function $f(x) = e^{x -[x]+|cos\, \pi x|+|cos\, 2\pi x|+....+|cos\, n\pi x|}$ (where $[.]$ denotes greatest integer function); is:-

Let $f : R -\{0,1\} \rightarrow R$ be a function such that $f(x)+f\left(\frac{1}{1-x}\right)=1+x$. Then $f(2)$ is equal to :

Consider the function $f (x) = x^3 - 8x^2 + 20x -13$
Number of positive integers $x$ for which $f (x)$ is a prime number, is

If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 +  .... + \infty } } } } \right)$ 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