Which one of the following compounds is inactive towards $S_N1$ reaction?

Two isomers $(A)$ and $(B)$ with molar mass $184 \ g/mol$ and elemental composition $C, 52.2 \ \%; H, 4.9 \ \%$ and $Br, 42.9 \ \%$ give benzoic acid and $p$-bromobenzoic acid,respectively,on oxidation with $KMnO_4$. Isomer '$A$' is optically active and gives a pale yellow precipitate when warmed with alcoholic $AgNO_3$. Isomer '$A$' and '$B$' are,respectively .... .

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

The order of reactivity of alkyl halides for dehydrohalogenation is:

Arrange the following in their correct order of reactivity towards ${S_N}^1$ reaction.

$A$ small amount of alcohol is added to a bottle of $CHCl_3$ because .............