$A$ stone is dropped into a pond. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of $5 \ cm/sec$. The rate at which the area increases after $2 \ seconds$ is:

If a metallic circular plate of radius $50 \, cm$ is heated so that its radius increases at the rate of $1 \, mm$ per hour,then the rate at which the area of the plate increases (in $cm^2/hour$) is (in $\pi$)

$A$ right circular cone has height $9 \text{ cm}$ and radius of base $5 \text{ cm}$. It is inverted and water is poured into it. If at any instant, the water level rises at the rate $\frac{\pi}{A} \text{ cm/sec}$, where $A$ is the area of the water surface at that instant, then the cone is completely filled in: (in $\text{ sec}$)

The total cost $C(x)$ in Rupees,associated with the production of $x$ units of an item is given by $C(x) = 0.05x^3 - 0.2x^2 + 3x + 500$. The marginal cost,where $x = 3$ is $\rule{1cm}{0.15mm}$ (in Rupees).

$A$ balloon,which always remains spherical on inflation,is being inflated by pumping in $900 \, cm^3$ of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15 \, cm$.

$A$ particle moves according to the law $s=t^{3}-6t^{2}+9t+25$. Find the displacement of the particle when its velocity is zero. (in $\text{ units}$)