$A$ gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and its volume is reduced by $10\%$. How much percentage of the gas will leak out?

$z=\tan (y+a x)+\sqrt{y-a x} \Rightarrow z_{x x}-a^2 z_{y y}$ is equal to

An insect crawls up a hemispherical surface very slowly (see figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by

The venous system of a frog differs from that of a mammal due to the presence of:

The time period of a vibration magnetometer is $T_0$. Its magnet is replaced by another magnet whose moment of inertia is $3$ times and magnetic moment is $1/3$ of the initial magnet. The new time period will be:

$A$ committee of $12$ members is to be formed from $9$ women and $8$ men. The number of committees in which the women are in majority is