The correct option is C Phenol < p-ethoxyphenol < methanol
In methanol, there is no resonance. In phenol, there is resonance. In p-Ethoxyphenol, there is resonance involved but the involvement of lone pair of oxygen in OH group is poor as compared with phenol due to the presence of lone pair oxygen in OCH3 group which are also involved in resonance.
So, partial double bond character develops in C—OH bond of phenol and p-ethoxyphenol but in case of p-ethoxyphenol, resonance is poor as compared to phenol. So, bond length follows the order: methanol > p-ethoxyphenol > phenol