Step 1: Identify compound \(X\).
The compound gives both
\[
\text{Iodoform test}
\]
and
\[
\text{2,4-DNP test},
\]
therefore \(X\) must be a methyl ketone.
The aromatic compound with molecular formula
\[
\mathrm{C_8H_8O}
\]
is
\[
\boxed{\mathrm{C_6H_5COCH_3}}
\]
(acetophenone).
Step 2: Check Set-II.
Oxidation of acetophenone with alkaline
\[
\mathrm{KMnO_4}
\]
followed by acidification converts the side chain into
\[
\boxed{\mathrm{C_6H_5COOH}}
\]
(benzoic acid), which liberates
\[
\mathrm{CO_2}
\]
with
\[
\mathrm{NaHCO_3}.
\]
Hence,
\[
\boxed{\text{Set-II is correct}.}
\]
Step 3: Check Set-I.
Clemmensen reduction first converts acetophenone into ethylbenzene.
Subsequent oxidation with
\[
\mathrm{KMnO_4/OH^-}
\]
followed by acidification again gives
\[
\boxed{\mathrm{Benzoic\ acid}.}
\]
Hence,
\[
\boxed{\text{Set-I is also correct}.}
\]
Step 4: Check Set-III.
Reduction with
\[
\mathrm{LiAlH_4}
\]
produces a secondary alcohol,
which does not react with
\[
\mathrm{NaHCO_3}
\]
to evolve
\[
\mathrm{CO_2}.
\]
Hence,
\[
\boxed{\text{Set-III is incorrect}.}
\]
Therefore,
\[
\boxed{\text{I and II only}}
\]
are correct.
Thus,
\[
\boxed{(A)}
\]
is the correct answer.