The graph of the function $y = f(x)$ is symmetrical about the line $x = 2$, then

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by

$f(x)=\frac{2 x}{\sqrt{1+9 x^2}}$. If the composition of $f, \underbrace{(f \circ f \circ f \circ \ldots \circ f)}_{10 \text { times }}(x)=\frac{2^{10} x}{\sqrt{1+9 \alpha x^2}}$, then the value of $\sqrt{3 \alpha+1}$ is equal to....................

If $\mathrm{R}=\left\{(\mathrm{x}, \mathrm{y}): \mathrm{x}, \mathrm{y} \in \mathrm{Z}, \mathrm{x}^{2}+3 \mathrm{y}^{2} \leq 8\right\}$ is a relation on the set of integers $\mathrm{Z},$ then the domain of $\mathrm{R}^{-1}$ is 

If $f(x) = \cos (\log x)$, then $f({x^2})f({y^2}) - \frac{1}{2}\left[ {f\,\left( {\frac{{{x^2}}}{2}} \right) + f\left( {\frac{{{x^2}}}{{{y^2}}}} \right)} \right]$ has the value

Which of the following is correct

Let $A = \left\{ {{x_1},{x_2},{x_3},.....,{x_7}} \right\}$ and $B = \left\{ {{y_1},{y_2},{y_3}} \right\}$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f:A \to B$ which are onto, if there exist exactly three elements $x$ in $A$ such that $f(x) = {y_2}$ , is equal to