A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 $$\mu$$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $$\mu$$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

The equivalent resistance between points A and B in the given network is :

A bar magnet having a magnetic moment of 2.0 $$\times$$ 10⁵ JT^$$-$$1, is placed along the direction of uniform magnetic field of magnitude B = 14 $$\times$$ 10^$$-$$5 T. The work done in rotating the magnet slowly through 60$$^\circ$$ from the direction of field is :