Gas is being pumped into a spherical balloon at the rate of $30 \, ft^3/min$. The rate at which the radius increases when it reaches the value $15 \, ft$ is:

If the displacement of a particle at a point is given by $s = 3t^{2} - 12t + 14$, then the displacement of the particle when its velocity becomes zero is (in $\text{ units}$)

The radius of a sphere is measured to be $20 \, cm$ with a possible error of $0.02 \, cm$. The consequent error in the surface area of the sphere is ....... $sq \, cm$.

The rate of change of the surface area of a sphere of radius $r$ when the radius is increasing at the rate of $2 \text{ cm/sec}$ is proportional to

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

If a particle is moving in a straight line so that after $t$ seconds its distance $S$ (in $cm$) from a fixed point on the line is given by $S = f(t) = t^3 - 5t^2 + 8t$, then the acceleration of the particle at $t = 5 \text{ sec}$ is (in $cm/sec^2$).