If $\mathrm{f}(x)=\frac{\sin \left(\pi \cos ^2 x\right)}{3 x^2}, x \neq 0$ is continuous at $x=0$ then $\mathrm{f}(0)=$

Let $z$ be the complex number with $\operatorname{Im}(z)=10$ and satisfying $\frac{2 \mathrm{z}-\mathrm{n}}{2 \mathrm{z}+\mathrm{n}}=2 \mathrm{i}-1$, where $\mathrm{i}=\sqrt{-1}$, for some natural number ' $n$ ' then

The rate of change of the volume of a sphere with respect to its surface area, when the radius is 5 m is

The maximum value of the function $a \sin x+b \cos x$ is