If water is being poured at the rate of $36 \text{ } m^3/sec$ into a cylindrical vessel with a base radius of $3 \text{ } m$,then the rate at which the water level is rising is:

$A$ particle is moving on a straight line,where its position $s$ (in metre) is a function of time $t$ (in seconds) given by $s = at^2 + bt + 6, t \ge 0$. If it is known that the particle comes to rest after $4 \, s$ at a distance of $16 \, m$ from the starting position $(t = 0)$,then the retardation in its motion is

If the rate of increase of the area of a circle is not constant but the rate of increase of the perimeter is constant,then the rate of increase of the area varies:

$A$ kind of bacteria grows by $t^3$ in $t \ s$. The time taken for the rate of growth of the bacteria to become $1200 \ \text{per } s$ is: (in $s$)

$A$ point $P$ is moving on the curve $x^3 y^4 = 2^7$. The $x$-coordinate of $P$ is decreasing at the rate of $8 \text{ units per second}$. When the point $P$ is at $(2, 2)$, the $y$-coordinate of $P$:

$A$ 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 $m/sec$)