In BF $_{3}$ molecule, a number of $\sigma$ bond is $3$ ie, $sp^{2}$ hybridization.
In $\mathrm{NO}_{2}^-$ molecule, the number of $\sigma$ bond is $2$ and the number of lone pairs is $2$ ie, $sp^3$ hybridization.
In $\mathrm{NH}_{2}$ molecule, the number of $\sigma$ bond is $2$ and the number of lone pairs is $2$ ie, $sp^{3}$ hybridization.
In $\mathrm{H}_{2} \mathrm{O}$ molecule, the number of $\sigma$ bond is $2$ and number of the lone pair are $2$ ie, $sp ^{3}$ hybridization.
Thus, in $\mathrm{BF}_{3}$ and $\mathrm{NO}_{2}$ - central atom is $\mathrm{sp}^{2}$ hybridised.