The domain of the function $f(x) =\frac{{\,\cot^{-1} \,x}}{{\sqrt {{x^2}\,\, - \,\,\left[ {{x^2}} \right]} }}$ , where $[x]$ denotes the greatest integer not greater than $x$, is :

Domain of function $f(x) = {\sin ^{ - 1}}5x$ is

Let $\mathrm{f}(\mathrm{x})$ be a polynomial of degree $3$ such that $\mathrm{f}(\mathrm{k})=-\frac{2}{\mathrm{k}}$ for $\mathrm{k}=2,3,4,5 .$ Then the value of $52-10 \mathrm{f}(10)$ is equal to :

If $f\left( x \right) = {\left( {\frac{3}{5}} \right)^x} + {\left( {\frac{4}{5}} \right)^x} - 1$ , $x \in R$ , then the equation $f(x) = 0$ has

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

Let $f$ be a function satisfying $f(xy) = \frac{f(x)}{y}$ for all positive real numbers $x$ and $y.$ If $ f(30) = 20,$ then the value of $f(40)$ is-