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(A) Compounds that are soluble in aqueous $NaOH$ are those that are sufficiently acidic to react with the base to form water-soluble salts. These incl

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$5$

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(A) Compounds that are soluble in aqueous $NaOH$ are those that are sufficiently acidic to react with the base to form water-soluble salts. These include carboxylic acids and phenols.Let us analyze each compound:$(I)$ Benzaldehyde: Not acidic enough to dissolve in $NaOH$.$(II)$ $1$-Naphthol: $A$ phenol, acidic, soluble in $NaOH$.$(III)$ $4$-(Dimethylamino)phenol: $A$ phenol, acidic, soluble in $NaOH$.$(IV)$ $4$-Methylphenol: $A$ phenol, acidic, soluble in $NaOH$.$(V)$ Benzoic acid: $A$ carboxylic acid, acidic, soluble in $NaOH$.$(VI)$ $N,N$-Dimethylcyclohexanamine: $A$ base, not soluble in $NaOH$.$(VII)$ $1$-Naphthoic acid: $A$ carboxylic acid, acidic, soluble in $NaOH$.$(VIII)$ $1,4$-Di-tert-butylbenzene: $A$ hydrocarbon, not soluble in $NaOH$.$(IX)$ $1$-Naphthylmethanol: An aliphatic alcohol, not acidic enough to dissolve in $NaOH$.The compounds that are soluble in $NaOH$ are $(II)$, $(III)$, $(IV)$, $(V)$, and $(VII)$. Therefore, the total number of such compounds is $5$.

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