Step 1: Aldol condensation of ethanal.
Two molecules of ethanal undergo aldol condensation in presence of dilute NaOH.
\[
2CH_3CHO \xrightarrow{dil.\ NaOH} CH_3CH(OH)CH_2CHO
\]
This product is aldol (3-hydroxybutanal).
Step 2: Dehydration using HCl.
The aldol undergoes dehydration in acidic medium to form an \(\alpha,\beta\)-unsaturated aldehyde.
\[
CH_3CH(OH)CH_2CHO \xrightarrow{HCl} CH_3CH=CHCHO
\]
This compound is crotonaldehyde (but-2-enal).
Step 3: Reduction using NaBH\(_4\).
NaBH\(_4\) reduces aldehyde group to alcohol without affecting the double bond.
\[
CH_3CH=CHCHO \xrightarrow{NaBH_4} CH_3CH=CHCH_2OH
\]
The product formed is but-2-en-1-ol.
Step 4: Oxidation using \(Cr_2O_7^{2-}/H^+\).
Primary alcohol gets oxidized to carboxylic acid using strong oxidizing agent.
\[
CH_3CH=CHCH_2OH \xrightarrow{Cr_2O_7^{2-}/H^+} CH_3CH=CHCOOH
\]
The product formed is but-2-enoic acid.
Step 5: Checking structure of final product.
The final compound contains:
- Four carbon atoms
- A double bond between C2 and C3
- A carboxylic acid group
Thus, it is but-2-enoic acid.
Step 6: Matching with options.
Among the given options, but-2-enoic acid corresponds to option (B).
Step 7: Final Answer.
\[
\boxed{\text{But-2-enoic acid}}
\]
Hence, the correct answer is option (B).