Recall what Hinsberg's reagent is

Hinsberg's reagent is benzenesulphonyl chloride $\left(\mathrm{C_6H_5SO_2Cl}\right)$.

It reacts with primary and secondary amines:

• Primary amine $\rightarrow$ forms sulphonamide having one acidic H on nitrogen, hence soluble in alkali.
• Secondary amine $\rightarrow$ forms sulphonamide without N-H, hence insoluble in alkali.
• Tertiary amine $\rightarrow$ does not react.

Identify the given species

From the question text, the visible compounds are:

• $\textbf{C} = \mathrm{CH_3NH_2}$, which is a primary amine.
• $\textbf{D} = \mathrm{N(CH_3)_3}$, which is a tertiary amine.

Therefore:

• $\textbf{C}$ reacts with Hinsberg's reagent.
• $\textbf{D}$ does not react with Hinsberg's reagent.

Use the options to infer A, B, E

Since $\textbf{C}$ reacts and $\textbf{D}$ does not react:

• Any correct option must include C.
• Any correct option must exclude D.

Check options:

• Option A: A, C and E only
  Includes C, excludes D.
• Option B: A, B and E only
  Does not include C, so impossible.
• Option C: C and D only
  Includes D, so impossible.
• Option D: B and D only
  Includes D and excludes C, so impossible.

Hence only Option A can be correct.

Conclusion

The compounds reacting with Hinsberg's reagent are A, C and E only.

So the correct choice is:

$\boxed{\text{A}}$