In which case racemisation takes place?

The correct order of rate of ${\mathrm{S}}_{\mathrm{N}}1$ reaction is:

Which of the following can give($2-$methylbutan$-2-$ol) as major product:

What is the decreasing order for the rate of ${\mathrm{S}}_{\mathrm{N}}2$ reaction of following compounds?

I.  ${\mathrm{CH}}_3-\mathrm{Cl}$

II 

III 

IV 

$\left(\mathrm{X}\right){\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{Cl}}_2\stackrel{\text{ aq. NaOH }}{\to }\text{ Compound}\left(\mathrm{Y}\right)$

The compound $\left(\mathrm{Y}\right)$ can give a yellow precipitate with both $2, 4-$$\mathrm{DNP}$ and  ${\mathrm{l}}_2/\mathrm{NaOH}$. What is the compound $\left(\mathrm{X}\right)$ ?