Let's analyze the given reaction sequence and determine the structure of compound 'P'.
- Compound 'P' first reacts with \(NH_3\), and then under the influence of heat \((\Delta)\) forms compound 'Q'. This indicates that 'P' undergoes partial conversion with ammonia, likely forming an amide.
- Next, 'Q' is treated with \(KOH\) and \(Br_2\), followed by \(CHCl_3\) and alcoholic \(KOH\) with heat. This sequence suggests a Hoffman degradation, which produces a primary amine with a reduced carbon chain (loss of one carbon from the amide carbon).
- The final product is NC-CH3. This implies that the amide initially involved in the reaction must have had a methylene adjacent to the carbonyl group, which may have originally been a carboxylic acid.
Based on this reasoning, the initial structure of 'P' should be a carboxylic acid. Examining the given options:
- Option 1: An amide - not likely since it cannot form an amide with ammonia.
- Option 2: An aldehyde - does not fit the reaction sequence.
- Option 3: A ketone - unsuitable for forming an amide.
- Option 4: A carboxylic acid - fits the criteria.
Therefore, the correct answer is Option 4.
Thus, the compound 'P' is a carboxylic acid, which successfully undergoes a series of reactions to eventually form an alkyl cyanide.