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

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} - {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} - x}\\
1&{2{a_3} - x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is

Let $R =\{ a , b , c , d , e \}$ and $S =\{1,2,3,4\}$. Total number of onto function $f: R \rightarrow S$ such that $f(a) \neq$ 1 , is equal to $.............$.

Greatest value of the function, $f(x) =  - 1 + \frac{2}{{{2^x}^2 + 1}}$ is 

Range of ${\sin ^{ - 1\,}}\left( {\frac{{1 + {x^2}}}{{2 + {x^2}}}} \right)$ is 

Numerical value of the expression $\left| {\;\frac{{3{x^3} + 1}}{{2{x^2} + 2}}\;} \right|$ for $x = - 3$ is