Domain of function $f(x) = log|5{x} - 2x|$ is $x \in R - A$, then $n(A)$ is (where $\{.\}$ denotes fractional part function)

The range of $f(x) = \cos (x/3)$ is

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 :

Let $A = \left\{ {{x_1},{x_2},{x_3},.....,{x_7}} \right\}$ and $B = \left\{ {{y_1},{y_2},{y_3}} \right\}$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f:A \to B$ which are onto, if there exist exactly three elements $x$ in $A$ such that $f(x) = {y_2}$ , is equal to

Domain of the function $f(x) = {\sin ^{ - 1}}(1 + 3x + 2{x^2})$ is

If the domain of the function $f(x)=\sec ^{-1}\left(\frac{2 x}{5 x+3}\right)$ is $[\alpha, \beta) \cup(\gamma, \delta]$, then $|3 \alpha+10(\beta+\gamma)+21 \delta|$ is equal to $.......$.