The answer is D.
The target, \((\text{CH}_3)_2\text{CHCH}_2\text{CO}_2\text{H}\), is 3-methylbutanoic acid, with 5 carbon atoms.
• D is correct: 3-methylbutan-1-ol, \((\text{CH}_3)_2\text{CHCH}_2\text{CH}_2\text{OH}\), is a primary alcohol. Heating with acidified \(\text{Cr}_2\text{O}_7^{2-}\) oxidises it to the carboxylic acid \((\text{CH}_3)_2\text{CHCH}_2\text{CO}_2\text{H}\).
• A is wrong: concentrated \(\text{H}_2\text{SO}_4\) dehydrates 2-methylbutan-1-ol to an alkene, 2-methylbut-1-ene, not an acid.
• B is wrong: 3-methylbutan-2-ol is a secondary alcohol, so acidified \(\text{MnO}_4^-\) oxidises it to a ketone, 3-methylbutan-2-one.
• C is wrong: 2-methylpropanenitrile, \((\text{CH}_3)_2\text{CHCN}\), has only 4 carbon atoms. Hydrolysis with sodium hydroxide gives the salt sodium 2-methylpropanoate, \((\text{CH}_3)_2\text{CHCO}_2^-\text{Na}^+\) (and \(\text{NH}_3\)): it has one carbon too few and is a carboxylate salt, not the acid.

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