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

If $y = x - x^2$,then the rate of change of $y^2$ with respect to $x^2$ at $x = 2$ is

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.

The relation between pressure $p$ and volume $V$ is given by $p V^{1/4} = \text{constant}$. If the percentage decrease in volume is $\frac{1}{2} \%$, then the percentage increase in pressure is:

$A$ particle is moving along the curve $x = at^2 + bt + c$. If $ac = b^2$,then the particle would be moving with uniform

The law of motion of a body moving along a straight line is $x = \frac{1}{2} vt$, where $x$ is its distance from a fixed point on the line at time $t$ and $v$ is its velocity. Then: