Specify the hybridisations of the central atoms in $N_3^{-},NOCl$ and $N_{2}O$.

The correct option is A $sp,s{p}^2,sp$
a. The structure of $N_3^{-}$ is:

The steric number of the central nitrogen atom is 2 (two sigma bond).
Thus, it is $sp$ hybridised.

b. The structure of $NOCl$ is:



So the steric number of the central nitrogen atom is 3 (two sigma bonds and one lone pair of electrons). Thus, it is $s{p}^2$ hybridised.

c. The possible structure of $N_{2}O$ is:



In this structure, the steric number of the central $N$ atom is 2 (two sigma bonds). Thus, the central $N$ atom is $sp$ hybridised.