(a)(i) Only $\mathrm{S}_{\mathrm{N}} 2$ mechanism is operating here because. ${ }_{\mathrm{CN}}^{\Theta}$ is a strong nucleophilic. $\mathrm{CH}_{3} \mathrm{OH}$ is a weak nucleophile.
(b)DMF is an aprotic polar solvent in which nucleophilic does not get solvated. $\mathrm{CH}_{3} \mathrm{OH}$ is a protic polar solvent which stablises the carbocation formed in $\mathrm{S}_{\mathrm{N}} 1$ mechanism.
(c)Alkyl halide is primary, so steric hinderence is less. Alkyl halide is tertiary,
(d)Allylic group increases the electropositive character (because, $\mathrm{sp}^{2}$ carbon is more electronegative than $\mathrm{sp}^{3}$ carbon), so nucleophile can attach faster. (ii) here $\mathrm{S}_{\mathrm{N}} 1$ mechanism is operative because: In $\mathrm{S}_{\mathrm{N}} 1$ mechanism, carbocation formed is stablished by resonance with double bond. - -л. 3