(I) 1, 2-dihydroxy benzene (II) 1, 3-dihydroxy benzene (III) 1,...

1, 4-dihydroxy benzene shows the highest boiling point among given compounds because it form strong intermolecular hydrogen bond (It does not form intramolecular $\mathrm{H}$-bonding).
Order of H-bonding in $o, m$ and $p$-isomers of a compound is given below. Intermolecular $\mathrm{H}$-bonding $0 < m < p$-isomers Intramolecular $\mathrm{H}$-bonding $o>m>p$-isomers Hydroxy benzene do not form a chain of $\mathrm{H}$-bonding. Hence, intermolecular $\mathrm{H}$-bond is stronger then intermolecular $\mathrm{H}$-bond, so the stability of 1, 4-dihydroxy benzene is highest. Hence, its boiling point is highest. The increasing order of the boiling points of the given compounds IV $<$ I $<$ II $<$ III.