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

Two sources of equal emf $E$ are connected in series to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2$ $(R_2 > R_1)$. If the potential difference across the source having internal resistance $R_2$ is zero,then the value of $R$ is:

In a $\triangle ABC$,if $\frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$,then $B$ is equal to

Which one of the following removes temporary hardness of water?

The centre of mass of a system of particles does not depend on:

If $f(x) = \frac{x^2}{x+a}$, then $f^{\prime \prime}(a)$ is equal to