A Carnot engine has efficiency of $$50 \%$$. If the temperature of sink is reduced by $$40^{\circ} \mathrm{C}$$, its efficiency increases by $$30 \%$$. The temperature of the source will be:

Given below are two statements :

Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.

Statement II : The rms speed of oxygen molecules in a gas is $$v$$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $$2 v$$.

In the light of the above statements, choose the correct answer from the options given below :

In $$1^{\text {st }}$$ case, Carnot engine operates between temperatures $$300 \mathrm{~K}$$ and $$100 \mathrm{~K}$$. In $$2^{\text {nd }}$$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $$2^{\text {nd }}$$ case) will be :

Which statements are correct about degrees of freedom ?

(A) A molecule with n degrees of freedom has n$$^{2}$$ different ways of storing energy.

(B) Each degree of freedom is associated with $$\frac{1}{2}$$ RT average energy per mole.

(C) A monatomic gas molecule has 1 rotational degree of freedom where as diatomic molecule has 2 rotational degrees of freedom.

(D) $$\mathrm{CH}_{4}$$ has a total of 6 degrees of freedom.

Choose the correct answer from the options given below :