For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of $3,$ the rate of the reaction increases by a factor of $.....$. (Round off to the Nearest Integer).
As the reaction is elementary, the rate of reaction is $r = K \cdot[ A ]^{2}\left[ B _{2}\right]$
on reducing the volume by a factor of $3,$ the concentrations of $A$ and $B _{2}$ will become $3$ times and hence, the rate becomes $3^{2} \times 3=27$ times of initial rate.
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$ Given\, :\, lna = 2.3\, loga$
(IMAGE)
$[A]$ $I$ and $III$ follow $\mathrm{S}_{\mathrm{N}} 1$ mechanism
$[B]$ $I$ and $II$ follow $\mathrm{S}_{\mathrm{N}} 2$ mechanism
$[C]$ Compound $IV$ undergoes inversion of configuration
$[D]$ The order of reactivity for $I$, $III$ and $IV$ is: $IV$ $>$ $I$ $>$ $III$