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Question:

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My attempt:

After getting the carbocation after protonation, in order to form a more stable alkene, it rearranged the methyl group on the adjacent carbon so as to get the alkene in the option (b). I am confused that whether it should be "1,2 hydride shift" or should it be "1,2 methyl shift" because the migratory aptitude of $\ce{H-}$ group is more than $\ce{CH3-}$ but here if carbocation formation is the RDS (considering E1) should we not rearrange it to a more stable species?

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