Step 1: Requirement of the reaction.
Benzoic acid contains
\[
7
\]
carbon atoms. The required primary amine must contain
\[
8
\]
carbon atoms, i.e., one carbon more than benzoic acid.
Step 2: Check Set-I.
\[
\mathrm{C_6H_5COOH}
\xrightarrow{\mathrm{NH_3,\Delta}}
\mathrm{C_6H_5CONH_2}
\xrightarrow{\mathrm{Br_2/OH^-}}
\mathrm{C_6H_5NH_2}
\]
The Hofmann bromamide reaction removes one carbon atom.
Thus, aniline has only
\[
6
\]
carbon atoms.
Hence,
\[
\boxed{\text{Set-I is incorrect}.}
\]
Step 3: Check Set-II.
\[
\mathrm{C_6H_5COOH}
\xrightarrow{\mathrm{LiAlH_4}}
\mathrm{C_6H_5CH_2OH}
\]
Only benzyl alcohol is formed; no amine is obtained.
Hence,
\[
\boxed{\text{Set-II is incorrect}.}
\]
Step 4: Check Set-III.
\[
\mathrm{C_6H_5COOH}
\xrightarrow{\mathrm{LiAlH_4}}
\mathrm{C_6H_5CH_2OH}
\]
\[
\mathrm{C_6H_5CH_2OH}
\xrightarrow{\mathrm{NaBr/H_2SO_4}}
\mathrm{C_6H_5CH_2Br}
\]
\[
\mathrm{C_6H_5CH_2Br}
\xrightarrow{\mathrm{KCN}}
\mathrm{C_6H_5CH_2CN}
\]
\[
\mathrm{C_6H_5CH_2CN}
\xrightarrow{\mathrm{H_2/Ni}}
\mathrm{C_6H_5CH_2CH_2NH_2}
\]
The nitrile introduces one additional carbon atom, and reduction gives a primary amine.
Hence,
\[
\boxed{\text{Set-III is correct}.}
\]
Therefore,
\[
\boxed{\text{III only}}
\]
is the correct answer.
Thus,
\[
\boxed{(C)}
\]
is the correct answer.