Petroleum refining is:

Relationship between products $(Q)$ and $(S)$ is
$CH_3-CH=CH_2$ $\xrightarrow[H_2O_2, OH^{-}]{BH_3, THF}$ $(P)$ $\xrightarrow[CH_2Cl_2]{PCC}$ $(Q)$
$CH_3-CH=CH_2$ $\xrightarrow[NaBH_4, HO^{-}]{Hg(OAc)_2, H_2O}$ $(R)$ $\xrightarrow[CH_2Cl_2]{PCC}$ $(S)$

The product obtained by heating $(NH_4)_2SO_4$ and $KCNO$ is

$C_3H_6$ $\xrightarrow{X} Y$ $\xrightarrow[C_6H_6]{AlCl_3} Z \text{ (major product)}$
$X$ and $Z$ respectively in the following reaction sequence are

Write the main product of the given reactions:
$(1)$ $C_6H_5CH = CH_2 \xrightarrow{HBr}$
$(2)$ $C_4H_{10} \xrightarrow{\text{air}, \Delta}$

Consider the following reactions:
$(a)$ $CH_3-CH=CH_2 + HBr \rightarrow CH_3-CH(Br)-CH_3$
$(b)$ $CH_3-CH=CH_2 + HBr \xrightarrow{Peroxide} CH_3-CH_2-CH_2Br$
$(c)$ $CH_4 + Cl_2 \xrightarrow{hv} CH_3Cl + HCl$
Which of these reactions proceed via a free radical mechanism?