An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is: (in $/T$)

Which of the following hydrides has the lowest boiling point?

The number of roots of the equation $(81)^{\sin ^2 x} + (81)^{\cos ^2 x} = 30$ in the interval $[0, \pi]$ is equal to

Two ideal slits $S_1$ and $S_2$ are at a distance $d$ apart and are illuminated by light of wavelength $\lambda$ passing through an ideal source slit $S$ placed on the line through $S_2$ as shown. The distance between the plane of the slits and the source slit is $D$. $A$ screen is held at a distance $D$ from the plane of the slits. The minimum value of $d$ for which there is darkness at $O$ is

One mole of $A_{(g)}$ is heated to $200^{\circ} C$ in a one litre closed flask,till the following equilibrium is reached.
$A_{(g)} \rightleftharpoons B_{(g)}$
The rate of forward reaction at equilibrium is $0.02 \ mol \ L^{-1} \ min^{-1}$. What is the rate (in $mol \ L^{-1} \ min^{-1}$) of the backward reaction at equilibrium?

Select the correct statement: