$A$ flask of volume $10^3 \text{ cc}$ is completely filled with mercury at $0 \ ^\circ\text{C}$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^\circ\text{C}$ and that of glass is $40 \times 10^{-6} / ^\circ\text{C}$. If the flask is now placed in boiling water at $100 \ ^\circ\text{C}$,how much mercury (in $\text{cc}$) will overflow?

Which one of the following is more readily hydrolysed by $S_{N}1$ mechanism?

An increase in equivalent conductance of a strong electrolyte with dilution is mainly due to

The molecular formula of diphenylmethane is $C_{13}H_{12}$. How many structural isomers are possible when one of the hydrogen atoms is replaced by a chlorine atom?

$A$ projectile is fired from the surface of the earth with a velocity of $5\, ms^{-1}$ at an angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\, ms^{-1}$ at the same angle follows a trajectory which is identical to the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $ms^{-2}$) (given $g = 9.8\, ms^{-2}$):

Two capillaries of the same material but of different radii are dipped in a liquid. In one of the capillaries,the liquid rises to a height of $22 \ cm$ and in the other to $66 \ cm$. The ratio of their radii is