(i) ${S}_{{N}} 2$ reaction occurs more quickly in primary alkyl halides than in secondary and tertiary alkyl halides. (a) is primary alkyl halide and (b) is secondary alkyl halide. So, (a) undergoes ${S}_{{N}} 2$ reaction faster than (b). (ii) Out of ${S}_{{N}} 1$ and ${S}_{{N}} 2$, which reaction occurs with: (a) Inversion of configuration: ${S}_{{N}} 2$, because the incoming nucleophile attacks from the backside resulting in inversion of configuration. (b) Racemisation: ${S}_{{N}} 1$, in this first carbocation is formed. The incoming nucleophile can attack from either side resulting in racemic mixture.