$A$ balloon,which always remains spherical,is being inflated by pumping in $900 \ cm^3/sec$ of gas. Find the rate at which the radius of the balloon is increasing when the radius is $15 \ cm$.

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).

$A$ stone is dropped into a quiet lake and waves move in circles at a speed of $4 \text{ cm/s}$. At the instant when the radius of the circular wave is $10 \text{ cm}$,how fast is the enclosed area increasing?

$A$ particle starts moving from rest from a fixed point in a fixed direction. The distance $s$ from the fixed point at a time $t$ is given by $s = t^{2} + at - b + 17$, where $a$ and $b$ are real numbers. If the particle comes to rest after $5 \ s$ at a distance of $s = 25$ units from the fixed point, then the values of $a$ and $b$ are respectively:

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then,the rate at which the area increases,is

$A$ particle moves such that $S = 6 + 48t - t^3$. The direction of motion reverses after moving a distance of