The increasing order of the reactivity of the following halides for the S$$_{N}$$1 reaction is

In an $$S_N1$$ reaction, reactivity depends on the stability of the carbocation formed: $$3^\circ > 2^\circ > 1^\circ$$

(II) is a $$1^\circ$$ alkyl halide, forming an unstable primary carbocation → least reactive.

(I) is a $$2^\circ$$ alkyl halide, forming a more stable secondary carbocation.

(III) is a benzylic halide. The carbocation formed is highly stabilized by resonance and the $$+M$$ effect of the $$-OCH_3$$ group.

Therefore, the increasing order of $$S_N1$$ reactivity is: $$(II)<(I)<(III)$$