The circuit shown here is used to compare the emf of two cells $E_1$ and $E_2$ $(E_1 > E_2)$. The null point is at $C$ when the galvanometer is connected to $E_1$. When the galvanometer is connected to $E_2$,the null point will be

Two liquids $A$ and $B$ have $P_A^o$ and $P_B^o$ in the ratio of $1 : 3$ and the ratio of number of moles of $A$ and $B$ in the liquid phase are $1 : 3$. The mole fraction of $A$ in the vapour phase in equilibrium with the solution is equal to:

Rearrange the following ($I$ to $IV$) in the order of increasing masses:
$I$. $0.5$ mole of $O_3$
$II$. $0.5$ g-atoms of oxygen
$III$. $3.011 \times 10^{23}$ molecules of $O_2$
$IV$. $5.6$ $L$ of $CO_2$ at $STP$

Which one of the following equations is correct for the reaction $N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$?

If $\frac{1}{2} \leq x \leq 1$,then $\cos ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{1}{2} \sqrt{3-3 x^2}\right)$ is equal to

$A$ parallel plate capacitor has plates with area $A$ and separation $d$. $A$ battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d$ is introduced. The ratio of energy stored in the capacitor before and after the slab is introduced is: