Which is the least reactive halide in both ${\text{E}}^{\text{1}}{\text{ and\hspace{0.17em}\hspace{0.17em}S}}_{\text{N}}\text{1}$ reaction?

 In E¹, formation of carbocation is the slowest step. Hence, it is the rate determining step.
Rate of reaction∝stability of carbocation

Carbocation at bridge head carbon of bicyclic compound is highly unstable due to lack of planarity thus, compound (c) is the least reactive alkyl halide for E¹ reaction.

Compound (a), (b) and (d) forms secondary carbocation which is relatively stable than the carbocation at bridge head carbon.