Domain of the definition of function 

$f(x) = \sqrt {\frac{{4 - {x^2}}}{{\left[ x \right] + 2}}} $ is      $($ where $[.] \rightarrow G.I.F.)$

Statement $1$ : If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^P$.
Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^q{C_p}$.

The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$

If $f:R \to R$ and $g:R \to R$ are given by $f(x) = \;|x|$ and $g(x) = \;|x|$ for each $x \in R$, then $\{ x \in R\;:g(f(x)) \le f(g(x))\} = $

Let $[t]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of al prime factors of $2310$ and $f: A \rightarrow \mathbb{Z}$ be the function $f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]$. The number of one-to-one functions from $A$ to the range of $f$ is :

The number of points, where the curve $f(x)=e^{8 x}-e^{6 x}-3 e^{4 x}-e^{2 x}+1, x \in R$ cuts $x$-axis, is equal to