$CH_2 = CH_2 \xrightarrow[KOH/H_2O]{KMnO_4} X = ......$

The carbon-carbon bond length in an ethylene molecule is:

Identify the relationship between $A$ and $B$ in the following reactions:
$CH_3-CH=CH_2 \xrightarrow[(2)H_2O_2, OH^-]{(1)BH_3-THF} A$
$CH_3-CH=CH_2 \xrightarrow[(2)NaBH_4]{(1)(AcO)_2Hg, H_2O} B$

For the given reaction sequence,identify $C$ and $D$:
$3\text{-methylbut-1-ene}$ $\xrightarrow[(ii) NaBH_4]{(i) Hg(OAc)_2/H_2O} A$ $\xrightarrow{H^\oplus/\Delta} B$ $\xrightarrow{O_3/Zn/H_2O} C + D$

Following are the four molecules $P$,$Q$,$R$ and $S$. Which one among the four molecules will react with $HBr_{(aq)}$ at the fastest rate?

In the given reaction sequence,identify the final product $C$:
$CH_2=CH-CH=CH_2$ $\xrightarrow{HCl, 40^{\circ}C} A$ $\xrightarrow{HI} C$
(Note: The reaction proceeds via electrophilic addition to a conjugated diene.)