Let $f(x)=x \sqrt{4 a x-x^2}, a>0$ then $f^{\prime}(x)$ at $x=2 a$ is :

If the function $f(x)=\mu \sin x+\frac{1}{3} \sin 3 x$ has its derivative equal to zero at $x=\frac{\pi}{3}$, then the value of ' $\mu$ ' is

A man is moving away from a tower 41.6 m high at a rate of $2 \mathrm{~m} / \mathrm{s}$. If the eyelevel of the man is 1.6 m above the ground, then the rate at which the angle of elevation of the top of the tower changes, when he is at a distance of 30 m from the foot of the tower is :

If a quadratic function in $x$ has the value 19 when $x=1$ and has a maximum value 20 when $x=2$, then the function is