If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?

If the surface area of a sphere of radius $r$ is increasing uniformly at the rate $8 \, cm^2/s$,then the rate of change of its volume is

For the curve $y=5x-2x^3$,if $x$ increases at the rate of $2 \text{ units/sec}$,the rate of change in the slope of the curve at $x=3$ is ......../sec

$A$ particle is moving in a straight line according to the formula $s = t^2 + 8t + 12$. If $s$ is measured in meters and $t$ is measured in seconds,then the average velocity of the particle in the third second is .......... $m/s$.

In a $\triangle ABC$, the sides $b$ and $c$ are fixed. If there is an error of $\delta A$ in measuring angle $A$, then the percentage error in measuring the length of the side $a$ is:

$A$ particle moves in a straight line such that its displacement $S$ (in $m$) at a time $t$ (in $sec$) is given by $S(t) = t^3 - 4t^2 + 7t$. The instantaneous velocity $v$ at $t = 4$ is (in $m/sec$)