Step 1: Functional group tests.
2,4-DNP test $(+\!)$ $\Rightarrow$ (A) contains a carbonyl group (aldehyde/ketone).
Tollens/Fehling tests $(-)$ $\Rightarrow$ not an aldehyde $\Rightarrow$ (A) is a ketone.
Iodoform test $(+\!)$ with I$_2$/NaOH $\Rightarrow$ methyl ketone fragment \(\;{-}\text{COCH}_3\).
Step 2: Unsaturation test.
No decolourisation of Br$_2$-water/alkaline KMnO$_4$ $\Rightarrow$ no reactive \(\mathrm{C=C}\) in the side chain (an aromatic ring does not respond to these).
Step 3: Use formulas to infer the skeleton.
Given molecular formula C$_8$H$_8$O with a methyl-ketone group suggests \(\mathrm{C_6H_5COCH_3}\) (acetophenone, phenyl methyl ketone).
Step 4: Check with oxidation product.
Strong oxidation of an aryl side chain (including aryl methyl ketones) with chromic acid gives benzoic acid, C$_7$H$_6$O$_2$, which matches (B).
\[
\underbrace{\text{C}_6\text{H}_5\text{COCH}_3}_{\text{(A) acetophenone}}
\;\xrightarrow[\;]{\text{CrO}_3/\text{H}^+}\;
\underbrace{\text{C}_6\text{H}_5\text{COOH}}_{\text{(B) benzoic acid}}
\]
(Consistency check: iodoform reaction of (A): \(\text{C}_6\text{H}_5\text{COCH}_3 \xrightarrow{\text{I}_2/\text{NaOH}} \text{CHI}_3 \downarrow + \text{C}_6\text{H}_5\text{COO}^- \) )
\[
\boxed{\text{(A) } \text{C}_6\text{H}_5\text{COCH}_3 \; \text{(acetophenone)}},
\boxed{\text{(B) } \text{C}_6\text{H}_5\text{COOH} \; \text{(benzoic acid)}}
\]