Explanation
$$Cis-3-Hexane \quad\underrightarrow{Cold\quad KMnO_4}\quad Meso-3-4-hexaanediol$$
This is because syn addition to a cis molecule results in a meso compound and cold $${ KMnO }_{ 4 }$$ is a syn reagent.
$$Trans-3-hexane\quad\underrightarrow {RCO_3H/H_3O^+}\quad Meso-3-4-hexanediol$$
Similarly anti addition to trans molecule forms meso compound
Carbocation rearrangement in acidic medium takes as shown
refer to image
order of stability of carbocation – teritiary>secondary>primary
More substituted alkene will formed as major product.
Option B is correct.
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