$A$ gas mixture consists of $2$ moles of $O_2$ and $4$ moles of $Ar$ at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is: (in $RT$)

For a sample of a perfect gas,when its pressure is changed isothermally from $p_i$ to $p_f$,the entropy change is given by:

In which of the following molecules is the $N$ atom not $sp^2$ hybridized?

$10 \ g$ of a radioactive element is disintegrated to $1 \ g$ in $2.303 \ \text{minutes}$. What is the half-life (in minutes) of that radioactive element?

Light waves producing interference have their amplitudes in the ratio $3:2$. The intensity ratio of maximum and minimum of interference fringes is

One mole of $N_2H_4$ loses $10$ moles of electrons to form a new compound $Z$. Assuming that all the nitrogen atoms appear in the new compound,what is the oxidation state of nitrogen in $Z$? (There is no change in the oxidation state of hydrogen.)