The pressure ' P ', volume ' V ' and temperature ' T ' of a gas in a jar ' $A$ ' and the gas in other jar ' $B$ ' is at pressure ' 2 P ', volume ' V ' and temperature ' $\frac{T}{4}$ '. Then the ratio of the number of molecules in jar A and jar B will be

Let the current ' $I$ ' be associated with an electron of charge ' $e$ ' moving in a circular orbit of radius ' $r$ ' with speed ' $v$ ' around the positively charged nucleus. The ratio $\frac{r}{v}$ is

Figure shows the combination of inductances and capacitances. Resonant frequency of the $\mathrm{L}-\mathrm{C}$ circuit is

Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between ' $\mathrm{q}_1$ ' and ' $\mathrm{q}_2$ ' is ' $\mathrm{F}_{12}$ ' and that between ' $\mathrm{q}_1$ ' and ' $\mathrm{q}_3$ ' is $\mathrm{F}_{13}$, then the ratio of $F_{13}$ to $F_{12}$ is