In the following reactions, P, Q, R , and S are the major products....

Toluene part of the reactant in the first reaction undergoes oxidation with ${KMnO}_{4}$, forms benzoic acid. In this conversion, alkyl part of toluene converts into carboxylic group. So, $P$ is a monocarboxylic acid.

Both ester and acid halides undergo hydrolysis to give carboxylic acid. Hence, the product $Q$ is the dicarboxylic acid. And it is known as isophthalic acid.

In the third reaction, ester undergo hydrolysis in the first step, which results beta keto acid. Beta keto acids are unstable. They liberate carbon dioxide on heating. The alpha methyl ketone formed undergo oxidation with chromic acid give carboxylic acid. Hence, $R$ is also isophthalic acid.

In the fourth reaction, the bromo part reacts with magnesium metal to give Grignard reagent. Grignard reagent give carboxylic acid upon reaction with carbon dioxide. Now during the hydrolysis of previous step acetal cleavage takes place and gives aldehyde functional group. This aldehyde converts to carboxylic acid with Tollen's reagent. This results the terephthalic acid.

The products $RandS$ are dicarboxylic acids and does not undergo Aldol condensation reaction or Cannizzaro's reaction.