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 :

A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ flow through resistance of $$3\, \Omega$$ and $$2\,\Omega$$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :