This reaction is known as Friedel-Craft’s alkylation of benzene.

very stable carbocation.

$$nC{H}_2=C{H}_2\underset{\text{pressure,}\text{catalyst}}{\overset{\text{high temp}\text{.}}{\to }}{\sout{(}C{H}_2-C{H}_2\sout{)}}_n$$
A linear polyethene polymer is formed when ethene polymerises.

No explanation is given for this question. Let's discuss the answer together.

is antiaromatic, hence less stable.

More is the stability, lower is the heat of combustion ( See Baeyer’s strain theory ). Cyclohexane is more stable.

$$Conc.$$  $${H_2}S{O_4}$$  and $$conc.$$  $$HN{O_3}$$  react in the following manner
\[\begin{align} & \underset{\text{Base}}{\mathop{HN{{O}_{3}}}}\,+\underset{\text{Acid}}{\mathop{{{H}_{2}}S{{O}_{4}}}}\,\to {{H}_{2}}NO_{3}^{+}+HSO_{4}^{-} \\ & {{H}_{2}}NO_{3}^{+}\to \underset{\begin{align} & \,\,\,\,\,\,\,\,\text{Nitronium}\text{.} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{ion}\text{.} \\ & \text{Attacking species} \\ & \,\,\,\,\,\,\text{(electrophile)} \\ \end{align}}{\mathop{NO_{2}^{+}}}\,+{{H}_{2}}O \\ \end{align}\]
Hence, in this reaction $$HN{O_3}$$  acts as a base and $${H_2}S{O_4}$$  as an acid.

$$\eqalign{ & C - C\,bond\,energy = 348\,kj/mol = \frac{{348}}{{4.2}}kcal/mol \cr & = 82.85\,kcal/mol \approx 100\,kcal/mol. \cr} $$

Formation of carbocation is $$r.d.s.$$

3-Methylhexane can yield seven different monochlorinated products on chlorination.
\[{{H}_{3}}C-C{{H}_{2}}-C{{H}_{2}}\overset{\begin{smallmatrix} \,\,\,C{{H}_{3}} \\ |\,\,\,\, \end{smallmatrix}}{\mathop{-CH-}}\,C{{H}_{2}}-C{{H}_{3}}\]
Each carbon atom on chlorination givesa different product.