If carbon has electronic configuration $1s^6$, it would have lower energy than that of the normal ground state configuration $1s^{2}2s^{2}2p^2$, because the electrons would be closer to the nucleus. Yet $1s^6$ is not observed, since it violates

The correct option is C Pauli's exclusion principle
According to Pauli's exclusion principle, no two electrons can have all the four quantum number same. They should have different spins to exist. Since only two spin quantum numbers are possible, the electronic configuration would violate this rule.