Identify what “polar molecular solids” means

Molecular solids are solids in which the constituent particles are molecules.

These may be:

• non-polar molecular solids: made of non-polar molecules
• polar molecular solids: made of polar molecules

So, we need the pair in which both substances are molecular solids and both molecules are polar.

Check each option

Option A: $\mathrm{HCl}(s), \mathrm{AlN}(s)$

• $\mathrm{HCl}$ is a polar molecule, so solid HCl is a polar molecular solid.
• $\mathrm{AlN}$ is not a molecular solid; it is a giant covalent/ionic-type solid.

Hence, A is not correct.

Option B: $\mathrm{MgO}(s), \mathrm{SO_2}(s)$

• $\mathrm{MgO}$ is an ionic solid, not a molecular solid.
• $\mathrm{SO_2}$ is a polar molecule and forms a molecular solid.

Since both are not polar molecular solids, B is not correct.

Option C: $\mathrm{SO_2}(s), \mathrm{NH_3}(s)$

• $\mathrm{SO_2}$ has a bent structure, so its bond dipoles do not cancel. It is polar.
• $\mathrm{NH_3}$ has a trigonal pyramidal structure, so it is also polar.
• Both exist as molecular solids in solid state.

Therefore, C is correct.

Option D: $\mathrm{SO_2}(s), \mathrm{CO_2}(s)$

• $\mathrm{SO_2}$ is polar.
• $\mathrm{CO_2}$ is linear, so dipoles cancel and it is non-polar.

Hence, D is not correct.

Final Answer

The correct pair of polar molecular solids is:

$\boxed{\mathrm{SO_2}(s),\ \mathrm{NH_3}(s)}$

So, the correct option is C.