In energy band diagram of insulators, a band gap and the conduction band is respectively

Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5 , the force experienced by each is (All other parameters are unchanged.)

A string fixed at both the ends forms standing wave with node separation of $$5 \mathrm{~cm}$$. If the velocity of the wave on the string is $$2 \mathrm{~m} / \mathrm{s}$$, then the frequency of vibration of the string is

A ball of mass '$$\mathrm{m}$$' is attached to the free end of a string of length '$$l$$'. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram.

The angular velocity '$$\omega$$' of the ball will be [ $$\mathrm{T}=$$ Tension in the string.]