Let $A=\{a, b, c\}$ and $B=\{1,2,3,4\}$ Then the number of elements in the set $C =\{ f : A \rightarrow B \mid 2 \in f ( A )$ and $f$ is not one-one $\}$ is

Let function $f(x) = {x^2} + x + \sin x - \cos x + \log (1 + |x|)$ be defined over the interval $[0, 1]$. The odd extensions of $f(x)$ to interval $[-1, 1]$ is

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

Range of the function $f(x) = \frac{{{x^2}}}{{{x^2} + 1}}$ is

The total number of functions,$f:\{1,2,3,4\} \cdot\{1,2,3,4,5,6\}$   such that $f (1)+ f (2)= f (3)$, is equal to .

Let $f : R \rightarrow R$ be a function such that $f(x)=\frac{x^2+2 x+1}{x^2+1}$. Then