As nucleus is positively charged and electron is negatively charged in an atom , both of them having opposite charges then why they did not attract each other.

Many scientists tried to answer the same question you asked today.I used the word tried because when someone comes up with a theory in physics it may not proove all the experimental facts (all the theories came from the experimental observations) but it satisfies majority of them.

As we all know electrons are the sub atomic particles found outside the nucleus. Now lets check some theories which tried to find a solution for this question.In Bohr’s model ,Bohr said why electrons doesn’t fall into nucleus.

Niels Bohr in his model said that The electrons can only orbit stably, without radiating, in certain orbits (called by Bohr the "stationary orbits") at a certain discrete set of distances from the nucleus. These orbits are associated with definite energies and are also called energy shells or energy levels.In these orbits,the electron’s acceleration does not result in radiation and energy loss as required by classical electromagnetics.

By the 1920's, it became clear that a tiny object such as the electron cannot be treated as a classical particle having a definite position and velocity. The best we can do is specify the probability of its manifesting itself at any point in space. As you know, the potential energy of an electron becomes more negative as it moves toward the attractive field of the nucleus; in fact, it approaches negative infinity. However, because the total energy remains constant (a hydrogen atom, sitting peacefully by itself, will neither lose nor acquire energy), the loss in potential energy is compensated for by an increase in the electron's kinetic energy (sometimes referred to in this context as "confinement" energy) which determines its momentum and its effective velocity.

So as the electron approaches the tiny volume of space occupied by the nucleus, its potential energy dives down toward minus-infinity, and its kinetic energy (momentum and velocity) shoots up toward positive-infinity. This "battle of the infinities" cannot be won by either side, so a compromise is reached in which theory tells us that the fall in potential energy is just twice the kinetic energy, and the electron dances at an average distance that corresponds to the Bohr radius.

There is still one thing wrong with this picture; according to the Heisenberg uncertainity principle , a particle as tiny as the electron cannot be regarded as having either a definite location or momentum. The Heisenberg principle says that either the location or the momentum of a quantum particle such as the electron can be known as precisely as desired, but as one of these quantities is specified more precisely, the value of the other becomes increasingly indeterminate. It is important to understand that this is not simply a matter of observational difficulty, but rather a fundamental property of nature.

What this means is that within the tiny confines of the atom, the electron cannot really be regarded as a "particle" having a definite energy and location, so it is somewhat misleading to talk about the electron "falling into" the nucleus.