If $f(x)$ satisfies the relation $f\left( \frac{5x - 3y}{2} \right) = \frac{5f(x) - 3f(y)}{2}$ for all $x, y \in R$ and $f(0)=1, f'(0)=2$,then the period of $\sin(f(x))$ is:

In a $500 \ mL$ flask,the degree of dissociation of $PCl_5$ at equilibrium is $40 \%$ and the initial amount is $5 \ moles$. The value of equilibrium constant in $mol \ L^{-1}$ for the decomposition of $PCl_5$ is

Which of the following is a biodegradable polymer?

If $f:[-6,6] \rightarrow R$ is defined by $f(x)=x^2-3$ for $x \in R$,then $(f \circ f \circ f)(-1)+(f \circ f \circ f)(0)+(f \circ f \circ f)(1)$ is equal to

Let $f$ be a non-zero real-valued continuous function satisfying $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$. If $f(2)=9$,then $f(6)$ is equal to

The number of nodal planes in a $p_x$ orbital is