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

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 $……………$.

If a function $g(x)$ is defined in $[-1, 1]$ and two vertices of an equilateral triangle are $(0, 0)$ and $(x, g(x))$ and its area is $\frac{\sqrt 3}{4}$ , then $g(x)$ equals :-

The domain of the function $f(x) =\frac{{\,\cot^{-1} \,x}}{{\sqrt {{x^2}\,\, – \,\,\left[ {{x^2}} \right]} }}$ , where $[x]$ denotes the greatest integer not greater than $x$, is :

Let a function $f : R \rightarrow  R$ is defined such that $3f(2x^2 -3x + 5) + 2f(3x^2 -2x + 4) = x^2 -7x + 9\ \ \  \forall  x \in R$, then the value of $f(5)$ is-