The correct option is B 2-methylpropan-2-ol
The reaction of alcohol with Lucas reagent (conc. HCl+anhyd. ZnCl2) is mostly SN1 reaction and the rate of reaction is directly proportional to the stability fo carbocation formed in the reaction.
Since, 3o alcohol forms 3o carbocation (most stable) hence, it will react fastest by SN1 reaction.
The rates of reaction with Lucas reagent (conc. HCl+anhyd. ZnCl2) follows follows the order 3∘ alcohol > 2∘ alcohol > 1∘ alcohol.
2-methylpropan-2-ol is 3o alcohol thus it will react fastest as compared to others.