Step 1: Identify the first reaction.
Toluene reacts with acetyl chloride \(\mathrm{CH_3COCl}\) in the presence of anhydrous \(\mathrm{AlCl_3}\).
This is Friedel-Crafts acylation.
Since \(-\mathrm{CH_3}\) group is ortho-para directing, the major product is para-methyl acetophenone.
\[
\mathrm{C_6H_5CH_3 \rightarrow p\text{-}CH_3C_6H_4COCH_3}
\]
Step 2: Oxidation with alkaline \(\mathrm{KMnO_4}\).
Strong oxidizing agent \(\mathrm{KMnO_4/KOH}\) oxidizes benzylic side chains to carboxylic acid groups.
Thus, both side chains are converted into \(-\mathrm{COOH}\) groups.
\[
p\text{-}\mathrm{CH_3C_6H_4COCH_3}
\rightarrow
p\text{-}\mathrm{HOOC-C_6H_4-COOH}
\]
Step 3: Acidification.
Dilute \(\mathrm{H_2SO_4}\) acidifies the reaction mixture and gives the final dicarboxylic acid.
The product is benzene-1,4-dicarboxylic acid, commonly called terephthalic acid.
Step 4: Final conclusion.
Hence, the major product formed is
\[
\boxed{\text{Terephthalic acid}}
\]