Would the carbocation intermediate undergo rearrangement? I have my concerns regarding option (a) in this question.



During the dehydration step, wouldn't the resulting carbocation intermediate formed in option (a) rearrange?
That is, the ring should contract from a $7$-carbon to a $6$-carbon one because the resulting carbocation would be more stable. But the resulting product would have to be an addition product since elimination now becomes impossible. 

I know that this situation can arise because I have tackled it before and the answer was an addition product in that case, but that reasoning contradicts with the official answer key in this question. (The answers are a,b and d).

The shift I called for was the bond between carbon (endocylic with nitrogen) and the carbocation.
Unfortunately, I cannot back this with references at the moment but in my opinion there should be no carbocation formed in the first place and therefore no tendency to undergo any Wagner-Meerwein rearrangements.

Secondary carbocations, while being less unstable than primary ones, are still rather unstable. There are no stabilisation mechanisms that suggest themselves in the reaction conditions (concentrated sulphuric acid) in which the nitrogen will be protonated and therefore unable to stabilise a carbocation in &#x3b1; position. I would assume that the elimination proceeds much more $\mathrm{E2}$-like: likely with no intermediate carbocation at all but if there is one it should be extremely short lived and the neighbouring proton should dissociate practically instantly.