An organic compound ($C_3H_9N$) (A), when treated with nitrous acid, gave an alcohol, and $N_2$ gas was evolved. (A) on warming with $CHCl_3$ and caustic potash gave (C) which on reduction gave isopropylmethylamine. The structure of (A) is:

Let us deduce the structure of compound A step-by-step:

1. Reaction with Nitrous Acid ($HNO_2$): Compound A ($C_3H_9N$) reacts with $HNO_2$ to yield an alcohol and $N_2$ gas. This is a characteristic reaction of primary aliphatic amines. Secondary and tertiary amines do not release nitrogen gas with $HNO_2$.
2. Carbylamine Reaction: Compound A warms with $CHCl_3$ and caustic potash (KOH) to give compound C. This is the Carbylamine test, which is exclusively given by primary amines to form foul-smelling isocyanides (carbylamines). Thus, C is an alkyl isocyanide ($R-NC$).
3. Reduction of C: Isocyanide C ($R-NC$) on reduction gives isopropylmethylamine, which is a secondary amine with the structure $(CH_3)_2CH-NH-CH_3$. Reduction of an isocyanide always yields a secondary amine with one methyl group: $R-NC + 4[H] \rightarrow R-NH-CH_3$. Comparing $R-NH-CH_3$ with the product $(CH_3)_2CH-NH-CH_3$, we can identify the alkyl group '$R$' as the isopropyl group $(CH_3)_2CH-$.
4. Conclusion: Since the alkyl group is isopropyl, the original primary amine 'A' must be isopropylamine, $(CH_3)_2CH-NH_2$.