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

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

If $f: N \rightarrow Z$ is defined by $f(n)=\begin{cases} 2 & \text{if } n=3k, k \in Z \\ 10 & \text{if } n=3k+1, k \in Z \\ 0 & \text{if } n=3k+2, k \in Z \end{cases}$, then $\{n \in N: f(n)>2\}$ is equal to

If $f(x) = |\sin x| + |\cos x|$ and $g(x) = [x]$,then what is the period of $h(x) = g(f(x))$,where $[.]$ denotes the Greatest Integer Function $(G.I.F.)$?

Let $g: N \rightarrow N$ be defined as
$g(3n+1)=3n+2$
$g(3n+2)=3n+3$
$g(3n+3)=3n+1, \text{ for all } n \geq 0$
Then which of the following statements is true?

Let $f(x) = \begin{cases} -a & \text{if } -a \leq x \leq 0 \\ x+a & \text{if } 0 < x \leq a \end{cases}$ where $a > 0$ and $g(x) = \frac{f(|x|) - |f(x)|}{2}$. Then the function $g: [-a, a] \rightarrow [-a, a]$ is