Stability of a molecule is related with bond order as:
Stability \(\propto\) Bond order
Bond order of \(\mathrm{N}_2, \mathrm{~N}_2^{-}\)and \(\mathrm{N}_2^{-2}\) are 3, 2.5 and 2 respectively. Therefore, the bond stability order is \(\mathrm{N}_2^{-2} < \mathrm{N}_2^{-} < \mathrm{N}_2\).
Hence, the correct option is (c).