Diazonium salt decomposes as 

${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{N}}_2^{+}{\mathrm{Cl}}^{-}\to {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{Cl}+{\mathrm{N}}_2.{\text{ At 0}}^{\mathrm{o}}\mathrm{C}$, the evolution of ${\mathrm{N}}_2$ becomes two times faster when the initial concentration of the salt is doubled. Therefore, it is 

For reaction ${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{N}}_2^{+}{\mathrm{Cl}}^{-}\to {\mathrm{C}}_6{\mathrm{H}}_5\mathrm{Cl}+{\mathrm{N}}_2$

Let the rate law be     $\mathrm{r}=\frac{\mathrm{d}\left[{\mathrm{N}}_2\right]}{\mathrm{dt}}=\mathrm{k}{\left[{\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{N}}_2^{+}\mathrm{Cl}\right]}^{\mathrm{x}}$

                                   $=\mathrm{k}{\left[\text{Salt}\right]}^{\mathrm{x}} ..... \left(\mathrm{i}\right)$

From given,        if  $2\mathrm{r}=\frac{2\mathrm{d}\left[{\mathrm{N}}_2\right]}{\mathrm{dt}}=\mathrm{k}{\left[2\left[\text{salt}\right]\right]}^{\mathrm{x}}.....\left(\mathrm{ii}\right)$

Then, on dividing (i) by (ii), we get 

$\frac{1}{2}={\left(\frac{1}{2}\right)}^{\mathrm{x}}\Rightarrow \mathrm{x}=1$

$\therefore$ Reaction is of 1st order.