An edge of a variable cube is increasing at the rate of $3 \, cm/s$. How fast is the volume of the cube increasing when the edge is $10 \, cm$ long?

If the distance $s$ traveled by a particle in time $t$ is $s = a \sin t + b \cos 2t$,then the acceleration at $t = 0$ is

$A$ spherical iron ball of radius $10 \, cm$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \, cm^3/min$. When the thickness of the ice is $5 \, cm$,then the rate at which the thickness (in $cm/min$) of ice decreases is

If the side of a cube is increased by $5 \%$,then the surface area of a cube is increased by (in $\%$)

$A$ man of height $2 \ m$ walks at a uniform speed of $7 \ m/min$ away from a lamp post of height $9 \ m$. The rate (in $m/min$) at which the length of his shadow increases is

Water is being filled at the rate of $1 \, cm^3/sec$ in a right circular conical vessel (vertex downwards) of height $35 \, cm$ and diameter $14 \, cm$. When the height of the water level is $10 \, cm$,the rate (in $cm^2/sec$) at which the wet conical surface area of the vessel increases is