Step 1: Basic idea of acidity in phenols.
The acidity of phenols depends on the stability of the phenoxide ion formed after removal of the hydrogen ion from the \(-OH\) group. If the phenoxide ion is more stable, the phenol is more acidic. Electron-withdrawing groups increase acidity, while electron-donating groups decrease acidity.
Step 2: Effect of nitro group.
The \(-NO_2\) group is a strong electron-withdrawing group. It withdraws electrons by \(-I\) effect and \(-R\) effect. Due to this, it stabilizes the phenoxide ion and increases acidic strength. Therefore, nitrophenols are more acidic than phenol.
Step 3: Compare \(o\)-nitrophenol and \(m\)-nitrophenol.
In \(o\)-nitrophenol, the \(-NO_2\) group is present at the ortho position. It shows both \(-I\) and \(-R\) effects, which stabilize the phenoxide ion strongly.
In \(m\)-nitrophenol, the \(-NO_2\) group mainly shows the \(-I\) effect because resonance interaction with the phenoxide ion is not as effective at the meta position.
Hence,
\[
o\text{-nitrophenol} > m\text{-nitrophenol}
\]
in acidic strength.
Step 4: Effect of methyl group.
The \(-CH_3\) group is an electron-donating group due to \(+I\) effect and hyperconjugation. It increases electron density on the benzene ring and destabilizes the phenoxide ion. Therefore, \(p\)-cresol is less acidic than phenol.
Step 5: Arrange all compounds.
The given compounds are:
\[
\text{(i) } m\text{-nitrophenol}
\]
\[
\text{(ii) } p\text{-cresol}
\]
\[
\text{(iii) } o\text{-nitrophenol}
\]
\[
\text{(iv) phenol}
\]
Thus, the decreasing order of acidic strength is:
\[
\text{(iii)} > \text{(i)} > \text{(iv)} > \text{(ii)}
\]
Step 6: Final conclusion.
\[
\boxed{\text{(iii)} > \text{(i)} > \text{(iv)} > \text{(ii)}}
\]
Hence, option (3) is correct.