The back-side attack on $2$-bromobutane by methoxide $(CH_3O^{-})$ gives the product shown below. Which Fischer projection represents $2$-bromobutane used as the reactant in this reaction?

The rate of the following reaction is influenced by the hyperconjugation of group $R$. The rate of reaction will be maximum when $R$ is:

What is the correct decreasing order of the relative rate of solvolysis for the following alkyl halides in formic acid containing a small amount of water?
$(I) \ CH_2=CH-CH_2Cl$
$(II) \ CH_2=CH-CH(CH_3)Cl$
$(III) \ CH_2=C(CH_3)CH_2Cl$
$(IV) \ CH_3CH=CH-CH_2Cl$

Identify the structure of the major product in the following reaction:
$Ph-CH(Br)-CH(Br)-CHO \xrightarrow[\Delta]{K_2CO_3} ?$

In a nucleophilic substitution reaction $R - Br + Cl^{-} \xrightarrow{DMF} R - Cl + Br^{-}$,which one of the following undergoes complete inversion of configuration?

Identify $A, B, C, D, E, R$ and $R^1$ in the following reactions:
$Cyclohexyl-Br + Mg$ $\xrightarrow{dry\,ether} A$ $\xrightarrow{H_2O} B$
$R-Br + Mg$ $\xrightarrow{dry\,ether} C$ $\xrightarrow{D_2O} CH_3-CH(D)-CH_3$
$CH_3-C(CH_3)_2-C(CH_3)_2-CH_3 \xleftarrow{Na/ether} R^1-X$ $\xrightarrow{Mg} D$ $\xrightarrow{H_2O} E$