Give equations of the following reactions:
$(i)$ Oxidation of propan$-1-$ol with alkaline $KMnO_4$ solution.
$(ii)$ Bromine in $CS_2$ with phenol.
$(iii)$ Dilute $HNO_3$ with phenol.
$(iv)$ Treating phenol with chloroform in presence of aqueous $NaOH$.

(N/A) $(i)$ $CH_3CH_2CH_2OH \xrightarrow{\text{alk. } KMnO_4} CH_3CH_2COOH$ (Propanoic acid)
$(ii)$ Phenol reacts with $Br_2$ in $CS_2$ at $273 \ K$ to give a mixture of $o$-bromophenol (minor) and $p$-bromophenol (major).
$(iii)$ Phenol reacts with dilute $HNO_3$ at low temperature to give a mixture of $o$-nitrophenol and $p$-nitrophenol.
$(iv)$ Phenol reacts with $CHCl_3$ in the presence of aqueous $NaOH$ (Reimer-Tiemann reaction) to form salicylaldehyde.