Concept:
This is a standard
Grignard reagent + CO$_2$ carboxylation sequence.
General steps:
\[
R-Br \xrightarrow[\text{dry ether}]{Mg} R-MgBr
\]
\[
R-MgBr + CO_2 \rightarrow RCOOMgBr
\]
\[
\text{Hydrolysis} \rightarrow RCOOH
\]
Thus bromine is replaced ultimately by:
$$-COOH$$
Step 1: Interpret molecular formula.
Given:
$$C_6H_4NO_2Br$$
This is bromonitrobenzene.
So compound A must be a nitrobromobenzene isomer.
Step 2: Effect of Grignard formation.
When aryl bromide reacts with Mg:
$$ArBr \rightarrow ArMgBr$$
Then with CO$_2$ and hydrolysis:
$$ArMgBr \rightarrow ArCOOH$$
So bromine position becomes carboxylic acid position.
Nitro group remains unchanged.
Step 3: Check positional isomer.
If A is:
$$3\text{-nitrobromobenzene}$$
Then replacing Br by COOH gives:
$$3\text{-nitrobenzoic acid}$$
This matches option (C).
Step 4: Reject others.
- Aniline formula does not match.
- Terephthalic acid needs two substituents COOH.
- Bromobenzoic acid means Br remains, impossible here.
- Wrong positional isomer in option (E).
Step 5: Final answer.
Thus:
$$A = 3\text{-nitrobromobenzene}$$
$$C = 3\text{-nitrobenzoic acid}$$
Hence correct option is:
$$\boxed{\text{(C)}}$$
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