$A$ spherical balloon is being inflated at the rate of $35 \, cc/min$. The rate of increase of the surface area of the balloon when its diameter is $14 \, cm$ is ....... $sq \, cm/min$.

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 along a straight line according to the law $s=16-2t+3t^{3}$,where $s$ metres is the distance of the particle from a fixed point at the end of $t$ seconds. The acceleration of the particle at the end of $2 \ s$ is

$A$ $10 \, cm$ long rod $AB$ moves with its ends on two mutually perpendicular straight lines $OX$ and $OY$. If the end $A$ is moving at the rate of $2 \, cm/sec$,then when the distance of $A$ from $O$ is $8 \, cm$,the rate at which the end $B$ is moving is:

Let $x$ and $y$ be the sides of two squares such that $y = x - x^2$. The rate of change of the area of the second square with respect to the area of the first square is

The surface area of a cube increases at a rate of $2 \ cm^2/sec$. The rate at which its volume increases when the length of its edge is $90 \ cm$ is ..... $cm^3/sec$.