If $f(x) = \sin \log x$, then the value of $f(xy) + f\left( {\frac{x}{y}} \right) - 2f(x).\cos \log y$ is equal to

Prove that the Greatest Integer Function $f: R \rightarrow R ,$ given by $f(x)=[x]$, is neither one-one nor onto, where $[x]$ denotes the greatest integer less than or equal to $x$.

The number of points, where the curve $f(x)=e^{8 x}-e^{6 x}-3 e^{4 x}-e^{2 x}+1, x \in R$ cuts $x$-axis, is equal to

If $f(x)$ be a polynomial function satisfying $f(x).f (\frac{1}{x}) = f(x) + f (\frac{1}{x})$  and $f(4) = 65$ then value of $f(6)$ is

Function ${\sin ^{ - 1}}\sqrt x $ is defined in the interval

The number of one-one function $f :\{ a , b , c , d \} \rightarrow$ $\{0,1,2, \ldots ., 10\}$ such that $2 f(a)-f(b)+3 f(c)+$ $f ( d )=0$ is