The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

$A$ ladder $10 \, m$ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3 \, cm/sec$. The height of the upper end while it is descending at the rate of $4 \, cm/sec$ is (in $, m$)

$A$ bulb is placed at the centre of a circular track of radius $10 \ m$. $A$ vertical wall is erected touching the track at a point $P$. $A$ man is running along the track with a speed of $10 \ m/sec$. Starting from $P$, the speed with which his shadow is running along the wall when he is at an angular distance of $60^{\circ}$ from $P$ is: (in $m/sec$)

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

If the rate of increase of the radius of a circle is $5 \text{ cm/sec}$, then the rate of increase of its area, when the radius is $20 \text{ cm}$, will be

If the path of a moving point is the curve $x = at$,$y = b \sin(at)$,then its acceleration at any instant