If $x = {\log _2}\left( {\sqrt {56 + \sqrt {56 + \sqrt {56 +  .... + \infty } } } } \right)$ then 

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

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

For a real number $x,\;[x]$ denotes the integral part of $x$. The value of $\left[ {\frac{1}{2}} \right] + \left[ {\frac{1}{2} + \frac{1}{{100}}} \right] + \left[ {\frac{1}{2} + \frac{2}{{100}}} \right] + .... + \left[ {\frac{1}{2} + \frac{{99}}{{100}}} \right]$ is

Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f : A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to $...............$.

Let $A$ denote the set of all real numbers $x$ such that $x^3-[x]^3=\left(x-[x]^3\right)$, where $[x]$ is the greatest integer less than or equal to $x$. Then,