In the reaction ${C_6}{H_6}\xrightarrow{{C{H_3}Cl/AlC{l_3}}}A\xrightarrow{{KMn{O_4}}}B$, B is :
a.) benzoic acid
b.) benzoyl chloride
c.) benzaldehyde
d.) chlorobenzene

Hint: The first reagent given is the methyl chloride in the presence of aluminium trichloride. It functions in alkylation of the compound while the second reagent functions in oxidation of the compound. The answer to this question is a carboxylic acid with molecular mass 122 g. This is because the ultimate product of oxidation of alkyl is the acid.

Complete step by step solution:
Let us move step by step in the reaction to get the correct product.
We have the initial reactant benzene. We know that benzene is electron rich in nature. It is even highly stable due to resonance and thus it does not let resonance chain break. So, it does not give addition reactions.
It can very easily give aromatic electrophilic substitution reactions.
The first reagent is the methyl chloride in the presence of aluminium trichloride. It is an alkylation reaction where benzene gets converted into toluene and HCl is released as a byproduct. The A product formed is toluene. This reaction is Friedel Crafts alkylation. The reaction can be written as -

This reaction involves following mechanism-
The methyl chloride reacts with aluminium chloride to give $ \oplus C{H_3}$carbocation. This methyl carbocation is an electrophile and this gets attached to benzene.
$C{H_3}Cl + AlC{l_3} \to \oplus C{H_3}$

This carbocation is stabilised by resonance as-

The hydrogen is eliminated restoring resonance.

The second reagent that acts on toluene is potassium permanganate. The potassium permanganate is used for oxidation and here also, it does oxidation of the methyl group of toluene.
The oxidation is the addition of oxygen or removal of hydrogen. Here, the oxygen will get bonded with carbon and result in the formation of Benzoic acid. The benzoic acid is the product B.
The answer can-not be benzaldehyde because the potassium permanganate is a very strong reagent and it converts the benzaldehyde formed into benzoic acid. Firstly, from toluene benzaldehyde is formed which later gets converted into benzoic acid.
The reaction for this is as -


So, the answer is option a.)

Note: It must be noted that alkylation means the addition of alkyl groups. As here, the reagent was methyl chloride; this means the reagent had a methyl group. So, the methylation occurred. If it would have been ethyl chloride along with aluminium trichloride, the ethylation would have occurred.