A poly-atomic molecule $\left(C_V=3 R, C_P=4 R\right.$, where $R$ is gas constant) goes from phase space point $\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)$ to point $\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.$ $\mathrm{Pa}, \mathrm{V}_C=8 \times 10^{-6} \mathrm{~m}^3$ ). A to $B$ is an adiabatic path and $B$ to $C$ is an isothermal path.

The net heat absorbed per unit mole by the system is :

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L₁, L₂ by AB plane and L₃, L₄ by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L₁ and L₃ is

A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :

(Given $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

A capacitor, $C_1 = 6 \mu F$ is charged to a potential difference of $V_0 = 5V$ using a 5V battery. The battery is removed and another capacitor, $C_2 = 12 \mu F$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached.