What is the product of the following $S_N2$ reaction?

Identify the major product $C$ in the given sequence of reactions.
$(CH_3)_2C=O$ $\xrightarrow[(ii) H^+/H_2O]{(i) CH_3MgBr/Ether} A$ $\xrightarrow[\Delta]{SOCl_2} B$ $\xrightarrow[\Delta]{CH_3ONa} C$

The main product of the following reaction will be:

Consider the nucleophilic attacks given below. Select the reaction in each pair that shows the greater $S_N2$ reaction rate.

$A$ compound $A$ $(C_5H_{10}Cl_2)$ on hydrolysis gives $C_5H_{10}O$ which reacts with $NH_2OH$,forms iodoform,but does not give Fehling's test. $A$ is:

The increasing order of the reactivity of the following halides for the $S_N1$ reaction is:
$(I)$ $CH_3-CHCl-CH_2-CH_3$
$(II)$ $CH_3-CH_2-CH_2-Cl$
$(III)$ $p-CH_3O-C_6H_4-CH_2Cl$