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(C) The reaction of $n$-butyl alcohol $(CH_3CH_2CH_2CH_2OH)$ with $HBr$ involves the formation of a primary carbocation, which undergoes a $1,2$-hydri

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(C) The reaction of $n$-butyl alcohol $(CH_3CH_2CH_2CH_2OH)$ with $HBr$ involves the formation of a primary carbocation, which undergoes a $1,2$-hydride shift to form a more stable secondary carbocation, leading to a rearranged product ($2$-bromobutane).
In the reaction with conc. $H_2SO_4$ at $413 \ K$, the primary carbocation intermediate can undergo rearrangement before elimination to form the alkene.
In the reaction with $PCl_5$ or $SOCl_2$ (in the presence of pyridine), the reaction proceeds via an $S_N2$ mechanism. In an $S_N2$ mechanism, the nucleophile attacks the carbon atom from the backside, and the leaving group departs simultaneously. Since there is no carbocation intermediate formed in an $S_N2$ reaction, no rearrangement can occur.
Therefore, the reaction of $n$-butyl alcohol with $PCl_5$ or $SOCl_2$ (in the presence of pyridine) does not involve a rearrangement reaction.

The major product of which of the following reactions is not obtained by a rearrangement reaction?

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