(c)
As we know that, rate of reaction is directly proportional to concentration of reactant and inversely proportional to the volume of vessel.
$i.e.,$concentration$\alpha \propto \frac{n}{v}$
For a given reaction,
$2NO(g) + O_{2}(g) \rightleftharpoons 2NO_{2}(g)$
Rate of reaction=$k\lbrack NO\rbrack^{2}\lbrack O_{2}\rbrack$
If volume of vessel is reduced by $\frac{1}{3}rd$ of its initial value, then concentration of compound is increase by 3 times. Hence, the rate of reaction will be increased by 27 times.