correct option is C .
A.Methoxy methyl cation is more stable than n-ethyl cation.
It is because the + mesomeric effect of the methoxy group stabilizes the positive charge more than the +inductive effect of the ethyl group as in n-ethyl cation.
Mesomeric effect stabilizes more than inductive effect because of +mesomeric effect.
All alkyl groups show + inductive effect.
B.Stability of carbocation
The stability of carbocation follows the order : 3° > 2° > 1°> methyl
Reason:
Inductive effect:
An alkyl group has a +I effect . When an alkyl group is attached to a positively charged carbon atom of a carbocation, it tends to release electrons towards that carbon. In doing so, it reduces the positive charge on the carbon. In other words, the positive charge gets
dispersed and the alkyl group becomes somewhat positively charged. This dispersal of the
positive charge stabilizes the carbocation.
The more the number of alkyl groups on the carbon atom carrying the +ve charge, the greater would be the dispersal of the charge, and hence more stable would be the carbonation. Thus Stability decreases as the +I effect of the alkyl group decrease.
C. The true structure of the conjugated allyl carbocation is a hybrid of the two resonance structure so the positive charge is delocalized over the two terminal carbons. This delocalization stablizes the allyl carbocation making it more stable than a normal primary carbocation.
D.Tertiary carbocation with three alkyl groups is more stabilized than secondary carbocation and primary carbocation. In vinyl, carbocation is a primary carbon and thereby hardly any hyperconjugation structures can be possible as well. This is why vinyl cation is highly unstable.