Positive and positive charge Repel then why are the protons inside nucleus of atoms held tightly together?

Very good question! Looking at the electromagnetic forces, it would seem like two positive protons so close to each other should not be able to remain close together. However, electromagnetic forces are not the only forces at play!

The strong nuclear force is responsible for holding together the nucleus. At the distance scale of a proton (about 1 femtometer, or 10^(−15) meters), the strong nuclear force is about 137 times stronger than the electromagnetic force. Therefore, the repulsive force due to both the protons being electrically positive is not strong enough to break the nucleus apart.