For the given reaction:
(Cyclohexyl)-$CH$=$CH$-(Cyclohexyl) $\xrightarrow{KMnO_4/H^+}$ '$P$' (major product)
'$P$' is:

Reaction of $HBr$ with propene in the presence of peroxide gives

The correct statement$(s)$ for the following addition reactions is(are):
$(i)$ $trans-but-2-ene \xrightarrow{Br_2/CHCl_3} M \text{ and } N$
(ii) $cis-but-2-ene \xrightarrow{Br_2/CHCl_3} O \text{ and } P$
[$A$] ($M$ and $O$) and ($N$ and $P$) are two pairs of diastereomers
[$B$] Bromination proceeds through trans-addition in both the reactions
[$C$] $O$ and $P$ are identical molecules
[$D$] ($M$ and $O$) and ($N$ and $P$) are two pairs of enantiomers

The product $(B)$ is

Which of the following is the most stable alkene?

Which of the following alkenes reacts fastest with $H_2$ under catalytic hydrogenation conditions?