Which of the following compounds reacts with $HBr$ to form $1$-Bromo-$1$-methylcyclohexane?

Consider the following reaction:
$Alkene (A) \xrightarrow{KMnO_4, \Delta} CH_3CH_2COCH_3 + CH_3CH_2CH_2CH_2COOH$
$A$ is:

The final product $B$ of the below reaction sequence is:
$CH_3-CH(Br)-CH_3$ $\xrightarrow{KOH/C_2H_5OH} A$ $\xrightarrow{(C_6H_5CO)_2O_2, HBr} B$

The product of acid catalyzed hydration of $2-$phenylpropene is

Identify the correct statements with respect to $cis/trans$-but$-2$-ene from the following:
$I$. $cis$-but$-2$-ene is more polar than $trans$-but$-2$-ene
$II$. Melting point of $cis$-but$-2$-ene is greater than that of $trans$-but$-2$-ene
$III$. Boiling point of $cis$-but$-2$-ene is greater than that of $trans$-but$-2$-ene
Correct answer is

Which of the following compounds is obtained when cyclohexene is oxidized using $KMnO_4$ in dilute $H_2SO_4$?