Concept:
Acid strength depends on the stability of the conjugate base (phenoxide ion).
• Electron-donating groups decrease acidity by destabilizing the phenoxide ion.
• Electron-withdrawing groups increase acidity by stabilizing the phenoxide ion.
• The \(-NO_2\) group exhibits both \(-I\) and \(-R\) effects at para position.
Step 1: Compare \(m\)-cresol and phenol.
The methyl group shows \(+I\) effect and increases electron density on oxygen.
Therefore, \(m\)-cresol is less acidic than phenol.
\[\begin{aligned}
m\text{-Cresol} \lt Phenol
\end{aligned}\]
Step 2: Compare phenol and nitrophenols.
The nitro group is strongly electron withdrawing.
Hence nitrophenols are more acidic than phenol.
\[\begin{aligned}
Phenol \lt m\text{-Nitrophenol}
\end{aligned}\]
Step 3: Compare \(m\)-nitrophenol and \(p\)-nitrophenol.
At meta position, the nitro group exerts mainly the \(-I\) effect.
At para position, both \(-I\) and resonance \((-R)\) effects operate, giving greater stabilization to the phenoxide ion.
Therefore,
\[\begin{aligned}
m\text{-Nitrophenol} \lt p\text{-Nitrophenol}
\end{aligned}\]
Step 4: Arrange the compounds in increasing order of acidity.
Increasing Acid Strength:
\[
m\text{-Cresol}
\;\lt \;
\text{Phenol}
\;\lt \;
m\text{-Nitrophenol}
\;\lt \;
p\text{-Nitrophenol}
\]
\[\begin{aligned}
\boxed{
m\text{-Cresol}
\lt
Phenol
\lt
m\text{-Nitrophenol}
\lt
p\text{-Nitrophenol}
}
\end{aligned}\]
Hence, option \(\mathbf{(A)}\) is correct.