Identify the reaction involved

Treatment with benzene sulphonyl chloride is the Hinsberg test for amines.

Reagent: $C_6H_5SO_2Cl$

Recall Hinsberg test results

• Primary amine $(1^\circ)$: forms sulphonamide having an acidic $N-H$ proton, so it is soluble in dilute NaOH.
• Secondary amine $(2^\circ)$: forms sulphonamide with no acidic hydrogen on nitrogen, so it is insoluble in dilute NaOH.
• Tertiary amine $(3^\circ)$: does not form sulphonamide in the usual way.

Since compound $B$ is soluble in dilute NaOH, compound $A$ must be a primary amine.

Check the options

• Option B: $C_6H_5-NHCH_2CH_3$

  Nitrogen is attached to phenyl and ethyl groups, and has one H. So this is a secondary amine.

• Option C: $C_6H_5-N(CH_3)_2$

  Nitrogen is attached to phenyl and two methyl groups. So this is a tertiary amine.

• Option D: $C_6H_5CH_2NHCH_3$

  Nitrogen is attached to benzyl and methyl groups, and has one H. So this is a secondary amine.

Therefore, the only suitable choice must be Option A, which is the primary amine among the options.

Conclusion

Since only a primary amine gives a benzene sulphonyl derivative soluble in dilute NaOH, compound $A$ is Option A.

Comparison with stored answer

Stored correct answer = A.

Our derived answer also = A.