In an electrical circuit ' $R$ ', ' $L$ ', ' $C$ ' and an a.c. voltage source are all connected in series. When ' L ' is removed from the circuit, the phase difference between the voltage and the current in the circuit is $\frac{\pi}{3}$. If instead ' $C$ ' is removed from the circuit, the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $\left(\tan \frac{\pi}{3}=\sqrt{3}\right)$

A parallel plate capacitor having plate area ' $A$ ' and separation ' $d$ ' is charged to a potential difference ' $V$ '. The charging battery is disconnected and the plates are pulled apart to four times the initial separation. The work required to increase the distance between the plates is ( $\varepsilon_0=$ permittivity of free space)

The length of the simple pendulum is made 3 times the original length. If ' T ' is its original time period, then the new time period will be

A plano convex lens fits exactly in to a plano concave lens. Their plane surfaces are parallel to each other. Lenses are made up of different materials of refractive indices ' $\mathrm{n}_1$ ' ' $\mathrm{n}_2$ ' and ' R ' is the radius of curvature of the curved surface of lenses. Focal length of the combination is