A sample of gas at temperature $T$ is adiabatically expanded to double its volume The work done by the gas in the process is (given, \(\gamma=\frac{3}{2}\))
Among the relations $S=\left\{(a, b): a, b \in R -\{0\}, 2+\frac{a}{b}>\right\}$ and $T=\left\{(a, b): a, b \in R , a^2-b^2 \in Z\right\}$,
Let the mean and standard deviation of marks of class A of $100$ students be respectively $40$ and $\alpha$ (> 0 ), and the mean and standard deviation of marks of class B of $n$ students be respectively $55$ and 30 $-\alpha$. If the mean and variance of the marks of the combined class of $100+ n$ students are respectively $50$ and $350$ , then the sum of variances of classes $A$ and $B$ is :