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

Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then Domain of $f (x)$ is

Let $f(\theta)$ is distance of the line $( \sqrt {\sin \theta } )x + (  \sqrt {\cos  \theta })y +1 = 0$ from origin. Then the range of $f(\theta)$ is -

Let $E = \{ 1,2,3,4\} $ and $F = \{ 1,2\} $.Then the number of onto functions from $E$ to $F$ is

The domain of ${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$ is

Let $f: R \rightarrow R$ be a function defined $f(x)=\frac{2 e^{2 x}}{e^{2 x}+\varepsilon}$. Then $f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+f\left(\frac{3}{100}\right)+\ldots .+f\left(\frac{99}{100}\right)$ is equal to