Range of $f(x) = sin^{-1} (\sqrt {x^2 + x +1})$ is -

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

Let $f\left( n \right) = \left[ {\frac{1}{3} + \frac{{3n}}{{100}}} \right]n$ , where $[n]$ denotes the greatest integer less than or equal to $n$. Then $\sum\limits_{n = 1}^{56} {f\left( n \right)} $ is equal to

Let $x$ be a non-zero rational number and $y$ be an irrational number. Then $xy$ is

Which one of the following is not bounded on the intervals as indicated

The domain of the definition of the function $f\left( x \right) = \frac{1}{{4 - {x^2}}} + \log \,\left( {{x^3} - x} \right)$ is