Work done in increasing the size of a soap bubble from a radius of $3\, cm$ to $5\, cm$ is nearly (Surface tension of soap solution $= 0.03\, Nm^{-1}$). (in $\pi \,mJ$)

If $z = 3 + 5i$,then $z^3 + \bar{z} + 198$ is equal to

The supportive skeletal structures in the human external ears and in the nose tip are examples of

$A$ wire,which passes through the hole in a small bead,is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$,the force it applies on the wire is

Molten sodium chloride conducts electricity due to the presence of

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth $y$,where the constant of proportionality $k > 0$ depends on the acceleration due to gravity and the geometry of the hole. If $t$ is measured in minutes and $k = \frac{1}{15}$,then the time to drain the tank if the water is $4 \text{ m}$ deep to start with is ......... $\text{min}$.