Among the triatomic molecules/ions,${\mathrm{BeCl}}_2,{\mathrm{N}}_3^{-},{\mathrm{N}}_2\mathrm{O},{\mathrm{NO}}_2^{+},{\mathrm{O}}_3,{\mathrm{SCl}}_2,{\mathrm{ICl}}_2^{-},{\mathrm{I}}_3^{-}\text{and }{\mathrm{XeF}}_2$ the total number of linear molecule(s)/ion(s) where the hybridization of the central atom does not have contribution from the d-orbital(s) is :

$\text{ [Atomic number }:\mathrm{S}=16,\mathrm{Cl}=17,\mathrm{I}=53\text{ and }\mathrm{Xe}=54\text{ ] }$

${\mathrm{BeCl}}_2,{\mathrm{N}}_3^{-},{\mathrm{N}}_2\mathrm{O},{\mathrm{NO}}_2^{+},{\mathrm{O}}_3,{\mathrm{SCl}}_2,{\mathrm{ICl}}_2^{-},{\mathrm{I}}_3^{-},{\mathrm{XeF}}_2$

$\begin{array}{l}{\mathrm{BeCl}}_2⟶\mathrm{sp}⟶\text{ linear; }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} {\mathrm{N}}_3^{-}⟶\mathrm{sp}⟶\text{ linear }\\ {\mathrm{N}}_2\mathrm{O}⟶\mathrm{sp}⟶\text{ linear; }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} {\mathrm{NO}}_2⟶\mathrm{sp}⟶\text{ linear }\\ {\mathrm{O}}_3⟶{\mathrm{sp}}^2⟶\text{ bent; }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{ \mathrm{SCl}}_2⟶{\mathrm{sp}}^3⟶\text{ bent }\\ {\mathrm{I}}_3^{-}⟶{\mathrm{sp}}^3\mathrm{d}⟶\text{ linear; }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}{ \mathrm{ICl}}_2^{-}⟶{\mathrm{sp}}^3\mathrm{d}⟶\text{ linear }\\ {\mathrm{XeF}}_2⟶{\mathrm{sp}}^3\mathrm{d}⟶\text{ linear }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\end{array}$

There are four (4) linear molecules/ions and no d- orbital is involved in hybridization.