Read the following statements :

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies $$P$$ and $$Q$$ having equal surface areas are maintained at temperature $$10^{\circ} \mathrm{C}$$ and $$20^{\circ} \mathrm{C}$$. The thermal radiation emitted in a given time by $$\mathrm{P}$$ and $$\mathrm{Q}$$ are in the ratio $$1: 1.15$$.

C. A Carnot Engine working between $$100 \mathrm{~K}$$ and $$400 \mathrm{~K}$$ has an efficiency of $$75 \%$$.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1: 4$$, then

A. The r.m.s. velocity of gas molecules in two vessels will be the same.

B. The ratio of pressure in these vessels will be $$1: 4$$.

C. The ratio of pressure will be $$1: 1$$.

D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $$1: 4$$.

Choose the correct answer from the options given below :

Two identical positive charges $$Q$$ each are fixed at a distance of '2a' apart from each other. Another point charge $$q_{0}$$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $$\mathrm{q}_{0}$$ executes $$\mathrm{SHM}$$. The time period of oscillation of charge $$\mathrm{q}_{0}$$ will be :

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are $$r_{1}$$ and $$r_{2}$$ $$\left(r_{1}>r_{2}\right)$$. If the potential difference across the source of internal resistance $$r_{1}$$ is zero, then the value of R will be :