The hybridization of central atoms in ${\mathrm{N}}_3^{-},\mathrm{NOCl}$ and ${\mathrm{N}}_2\mathrm{O}$ respectively are :

The hybridization of central atoms in ${\mathrm{N}}_3^{-},\mathrm{NOCl}$ and ${\mathrm{N}}_2\mathrm{O}$ respectively are $sp, s{p}^2, sp$.

The hybridization of central atoms in ${\mathrm{N}}_3^{-},\mathrm{NOCl}$ and ${\mathrm{N}}_2\mathrm{O}$respectively are $\mathrm{sp}, {\mathrm{sp}}^2, \mathrm{sp}$

The central N atom in azide ion contains two bonding domains and zero lone pairs of electrons.
The central O atom in $\mathrm{NOCl}$contains 2 bonding domains and 1 lone pair of electrons. The central N atom in ${\mathrm{N}}_2\mathrm{O}$ contains two bonding domains and zero lone pair of electrons.

Hence, the option A is correct.