$\frac{3\sqrt{2}}{\sqrt{6} + \sqrt{3}} - \frac{4\sqrt{3}}{\sqrt{6} + \sqrt{2}} + \frac{\sqrt{6}}{\sqrt{3} + \sqrt{2}} = $

If $x^y=y^x$, then $x(x-y \log x) \frac{d y}{d x}$ is equal to :

Which of the following is the most effective in causing the coagulation of a ferric hydroxide sol?

The number of tetrahedral voids present in $0.5 \text{ mole}$ of an $hcp$ crystal structure is:

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$, the rise in temperature of the gas in $B$ is (in $~K$)

Half-life of a radioactive substance is $20 \ minutes$. The time between $20\%$ and $80\%$ decay will be ........... $minutes$.