The $P-V$ diagram of $2\,g$ of helium gas for a certain process $A \to B$ is shown in the figure. What is the heat given to the gas during the process $A \to B$ (in $P_0V_0$)?

If $\bar{M}_w$ is the weight average molecular weight and $\bar{M}_n$ is the number average molecular weight of a polymer,the poly dispersity index $(PDI)$ of the polymer is given by

Let $a, b, c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax + 2ay + c = 0$ and $5bx + 2by + d = 0$ lies in the fourth quadrant and is equidistant from the two coordinate axes,then

The number of ways of choosing $10$ objects out of $31$ objects,of which $10$ are identical and the remaining $21$ are distinct,is

The Bhopal gas tragedy of $1984$ was caused by:

Two rigid bodies $A$ and $B$ rotate with rotational kinetic energies $E_A$ and $E_B$ respectively. The moments of inertia of $A$ and $B$ about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A = \frac{I_B}{4}$ and $E_A = 100E_B$,then the ratio of the angular momentum of $A$ $(L_A)$ to the angular momentum of $B$ $(L_B)$ is: