The compound that forms a linear polymer due to hydrogen bonding is:

Hydrogen bonding results in the association of molecules into different types of structures based on the number of bonds formed per molecule:

1. Hydrogen Fluoride ($HF$): Due to the high electronegativity of fluorine, $HF$ forms strong intermolecular hydrogen bonds. Each $HF$ molecule typically forms two hydrogen bonds (one through $H$ and one through $F$), resulting in the formation of long, zig-zag chains ($...H-F...H-F...H-F...$). In the context of 1D vs 3D structures, this is often referred to as a linear polymer .
2. Water ($H_{2}O$): Each water molecule can form up to four hydrogen bonds with neighbouring molecules. This leads to an extensive three-dimensional network rather than a linear chain .
3. Ammonia ($NH_{3}$): Like water, ammonia forms a three-dimensional network in its solid state due to hydrogen bonding.
4. $HCl$ and $HBr$: These molecules have very weak dipole-dipole interactions and negligible hydrogen bonding because the electronegativity of $Cl$ and $Br$ is not high enough to facilitate strong H-bonds like $F$, $O$, or $N$ .

Note: This question appears to contain a typo in the options. In the original AIPMT 2000 paper, Option C was $HF$, which is the correct answer. Given the current options, none are scientifically accurate for a linear polymer structure, and $NH_{3}$ (the Probable Answer) is a 3D network.