Which of the following cannot undergo $E_2$ reaction?

What is the major product $Z$ in the given reaction sequence?
$(CH_3)_2 C=O \xrightarrow[(2) H_3O^{+}]{\text{(1) } C_2H_5MgBr} X$
$i) SOCl_2$ $\xrightarrow[\Delta]{\text{ii) } CH_3ONa} Y$ $\xrightarrow[\text{Peroxide}]{HBr} Z$

In the $S_{N}2$ substitution reaction $R-Br + Cl^- \xrightarrow{DMF} R-Cl + Br^-$,which of the following will have the highest rate?

Consider the following reaction:
$CH_3-CH_2-CH(Br)-CH_3 \xrightarrow{alc. KOH, \Delta} CH_3-CH_2-CH=CH_2 (I) + CH_3-CH=CH-CH_3 (II)$
Which of the following statements are correct?
$a.$ $I$ is the major product of the reaction
$b.$ $II$ is the major product of the reaction
$c.$ Formation of $I$ is in accordance with Saytzeff's rule
$d.$ $II$ is more stable because it is more substituted

Which of the following compounds will undergo $S_{N^1}$ reaction most easily?

The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is: $CH_{3}Br + Nu^{\ominus} \longrightarrow CH_{3}Nu + Br^{\ominus}$