Air capacitor has capacitance of $1 \mu \mathrm{~F}$. Now the space between two plates of capacitor is filled with two dielectrics as shown in figure. The capacitance of the capacitor is [ $\mathrm{d}=$ distance between two plates of capacitor, $\mathrm{K}_1$ and $\mathrm{K}_2$ are dielectric constants of first dielectric and second dielectric respectively]

In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged $(\mathrm{Q})$ is $\left(\gamma=\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}\right)$

A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)^{\text {th }}$ then the new value of magnetic field will be

An astronomical telescope has a large aperture to