$A$ square plate is contracting at the uniform rate $3 \,cm^2 / sec$. The rate at which the perimeter is decreasing, when the side of the square is $15 \,cm$, is

The side of an equilateral triangle expands at the rate of $2 \, cm/s$. The rate of increase of its area when each side is $10 \, cm$ is:

If by dropping a stone in a quiet lake a wave moves in a circle at a speed of $3.5 \, cm/sec$,then the rate of increase of the enclosed circular region when the radius of the circular wave is $10 \, cm$ is ......... $cm^2/sec$. $\left( \pi = \frac{22}{7} \right)$

$A$ firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ with respect to the additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs $25$ more workers,then the new level of production of items is:

The distance travelled $s$ (in $cm$) by a particle in $t$ seconds is given by $s = t^3 + 2t^2 + t$. The speed of the particle after $1$ second will be ......... $cm/sec$.

$A$ particle is moving along a line according to the law $S = t^3 - 3t^2 + 4t - 2$,where $S$ is measured in meters and $t$ is measured in seconds. Then the velocity (in $m/s$) of the particle when its acceleration is zero is: