Question

If neutrons exerts only attractive forces then why dont we have any nucleus containing only neutrons?

Answer 1

This is because in the absence of protons, neutrons decay into protons, electrons and anti-neutrinos due to the weak interaction.

But in the presence of protons, the lower energy states in the nucleus are already occupied, into which the protons born from neutronic decay cannot fall into (due to the half integer spins of protons, two protons can't be in the same state).

As a result, we don't see any nuclei comprised exclusively of neutrons; because they will ultimately decay into protons and form a normal nucleus!