A nitrogen compound containing four carbon atoms dissolves in water on adding dil. HCl. It forms a coloured compound with \(\mathrm{HNO}_{2}\). If nitrogen does not show chiral properties, the compound may be (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCN}\) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NHCH}_{3}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NHCH}_{2} \mathrm{CH}_{3}\)

We need to analyze if adding dilute HCl helps the compound to dissolve in water. Compounds that dissolve in water upon adding dilute HCl are most likely to be basic compounds, i.e., they have a lone pair on the nitrogen atom that is ready to accept a proton (H+) to form an ammonium ion. (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\): The nitrogen atom here has a lone pair; hence, it will dissolve in water by adding dilute HCl. (b) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CHCN}\): The nitrogen here is the part of nitrile (CN) group, which does not have a lone pair on the nitrogen atom, so it cannot dissolve in water. (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NHCH}_{3}\): Nitrogen in this compound has a lone pair, so it will dissolve in water and accept a proton from HCl. (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NHCH}_{2} \mathrm{CH}_{3}\): Nitrogen atom has a lone pair, so it can dissolve in water after adding dilute HCl.

Now let's check which of the remaining options forms a coloured compound with \(\mathrm{HNO}_{2}\) and has no chiral properties. (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\): Coloured compound formation with \(\mathrm{HNO}_{2}\) requires a nitrogen with a lone pair, so this compound will form a coloured compound with \(\mathrm{HNO}_{2}\). However, as every nitrogen's attached groups are the same, there is no chiral centre. (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NHCH}_{3}\): Nitrogen's lone pair allows it to form a coloured compound with \(\mathrm{HNO}_{2}\). The nitrogen atom, however, has two different groups attached and therefore possesses chiral properties. (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NHCH}_{2} \mathrm{CH}_{3}\): Nitrogen's lone pair allows it to form a coloured compound with \(\mathrm{HNO}_{2}\). The nitrogen atom also has two different groups attached and therefore possesses chiral properties.

Based on the previous steps, the correct option that meets all the criteria is: (a) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\)