According to the Valence Shell Electron Pair Repulsion (VSEPR) theory and the concept of hybridisation, the geometry of a molecule is determined by the number of bonding and lone pairs around the central atom:

1. $N_{2}O$ (Nitrous Oxide): The central nitrogen atom in $N_{2}O$ ($N \equiv N ightarrow O$) is bonded to two atoms and possesses no lone pairs. This results in $sp$ hybridisation and a linear structure with a bond angle of 180°, similar to other $AB_{2}$ type molecules like $BeCl_{2}$ .
2. $NO_{2}$ (Nitrogen Dioxide): This is an odd-electron molecule where nitrogen has one lone electron (or effectively one lone pair). This results in a bent or angular geometry due to electron-pair repulsion .
3. $O_{3}$ (Ozone): The central oxygen atom is bonded to two other oxygen atoms and has one lone pair. According to VSEPR theory ($AB_{2}E$ type), it adopts a bent geometry with an approximate bond angle of 117° .
4. $HOCl$ (Hypochlorous Acid): In this molecule, the central oxygen atom is bonded to H and Cl and has two lone pairs ($AB_{2}E_{2}$ type). Like water, this results in a bent (V-shaped) geometry .

Therefore, only $N_{2}O$ exhibits a linear structure.