$A$ tank in the shape of a rectangular parallelepiped has a volume of $27 \ m^3$. This tank is filled with water such that the rate of change of the water level is thrice the rate of change of the water quantity falling into the tank. The height of the tank (in meters) is:

If $r$ is the radius of a spherical balloon at time $t$ and the surface area of the balloon changes at a constant rate $K,$ then ....

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/sec}$. When the radius is $12 \text{ cm}$,the rate at which the area increases is:

$A$ ladder of length $13 \ m$ has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \ m/min$, then the speed (in $m/min$) at which the upper end falls when the bottom is $5 \ m$ away from the wall is

$A$ stone,thrown vertically upward from the surface of the moon at a velocity of $24 \ m/s$,reaches a height of $s = 24t - 0.8t^2$ meters after $t$ seconds. The acceleration due to gravity in $m/s^2$ at the surface of the moon is:

$A$ water tank has the shape of an inverted right circular cone whose semi-vertical angle is $\tan^{-1}\left(\frac{1}{2}\right)$. Water is poured into it at a constant rate of $5 \text{ m}^3/\text{min}$. The rate at which the level of water is rising in $\text{m/min}$ at the instant when the depth of water in the tank is $10 \text{ m}$ is: