Consider the above sequence of reactions. $151 \ g$ of $2-$bromopentane is made to react. The yield of the major product $P$ is $80 \%$ whereas the yield of $Q$ is $100 \%$. The mass of product $Q$ obtained is $........ \ g$. (Given molar mass in $g \ mol^{-1}$: $H: 1, C: 12, Br: 80$)

Write the structure of the major organic product in each of the following reactions:
$(i)$ $CH_3-CH_2-CH_2-Cl + NaI \xrightarrow[\text{heat}]{\text{acetone}}$
$(ii)$ $CH_3-C(CH_3)_2-Br + KOH \xrightarrow[\text{heat}]{\text{ethanol}}$
$(iii)$ $CH_3-CH(Br)-CH_2-CH_3 + NaOH \xrightarrow{\text{water}}$
$(iv)$ $CH_3-CH_2-Br + KCN \xrightarrow{\text{aq. ethanol}}$
$(v)$ $C_6H_5-ONa + C_2H_5-Cl \longrightarrow$
$(vi)$ $CH_3-CH_2-CH_2-OH + SOCl_2 \longrightarrow$
$(vii)$ $CH_3-CH_2-CH=CH_2 + HBr \xrightarrow{\text{peroxide}}$
$(viii)$ $CH_3-CH=C(CH_3)_2 + HBr \longrightarrow$

The products obtained in the above reactions $(1)$,$(2)$,and $(3)$ are:

What is the major product obtained in the following reaction?

Consider the following statements:
$(1)$ Bridgehead halides are inert towards both $S_{N^1}$ and $S_{N^2}$ reactions (until one of the ring size is an eight-membered ring).
$(2)$ The first step in both $S_{N^1}$ and $E_1$ reactions is the same.
$(3)$ $S_{N^2}$ reactions proceed with total retention of configuration.
$(4)$ $E_2$ eliminations are favored by the use of a solvent of low polarity and a high concentration of a strong base.
Which of the above statements are correct?

The given product cannot be obtained in the above reaction. Identify the correct product obtained.