Which one of the carbocations from the following is most stable?

Carbocation stability — key factors: Resonance > Hyperconjugation > Inductive effects.

Option (b): $\overset{+}{\text{CH}_2}\text{–CH=CH–OCH}_3$

This is an allylic carbocation where the oxygen of –OCH₃ is directly conjugated with the double bond:

$\overset{+}{\text{CH}_2}\text{–CH=CH–O–CH}_3 \longleftrightarrow \text{CH}_2\text{=CH–CH=}\overset{+}{\text{O}}\text{–CH}_3$

The oxygen lone pair delocalises into the carbocation through the π system → oxocarbenium resonance → maximum stabilisation.

Comparison:

• (a): –OCH₃ is separated by –CH₂– (no direct conjugation with +)
• (c): Ester oxygen is less electron-donating (carbonyl withdraws electrons)
• (d): F is electronegative; –I effect destabilises carbocation

Most stable: (b)