Amines are classified as primary, secondary, or tertiary depending on whether one, two, or three hydrogen atoms of ammonia are replaced by alkyl or aryl groups. The Hinsberg test uses benzenesulphonyl chloride to distinguish these classes by the acidity of the nitrogen-bound hydrogen. A primary amine has an N–H left after sulphonamide formation, making the product acidic and soluble in alkali (KOH). A secondary amine forms a sulphonamide with no N–H remaining, so the product is a solid insoluble in alkali. A tertiary amine has no N–H to react and gives no sulphonamide at all. Since C3H9N with an alkali-insoluble Hinsberg product must retain no acidic N–H yet still react, it is a secondary amine such as N-methylethanamine. The tertiary amine option is wrong because it would not react with the reagent; the primary amine option is wrong because its product would dissolve in alkali; the quaternary salt cannot form here as the formula corresponds to a neutral amine. This matches the NCERT treatment of amine identification. A final consistency check: C3H9N satisfies the general formula CnH2n+3N for a saturated amine, confirming a valid acyclic amine structure.