The forward reaction rate for the nitric oxide-oxygen reaction

$2\mathrm{NO}+{\mathrm{O}}_2⟶2{\mathrm{NO}}_2$ has the rate law as:

$\text{ Rate }=\mathrm{k}[\mathrm{NO}{]}^2\left[{\mathrm{O}}_2\right]$

If the mechanism is assumed to be:

$2\mathrm{NO}\underset{\mathrm{eeg}}{\rightleftharpoons }{\mathrm{N}}_2{\mathrm{O}}_2$ (rapid equilibration)

${\mathrm{N}}_2{\mathrm{O}}_2+{\mathrm{O}}_2\stackrel{k_2}{⟶}2{\mathrm{NO}}_2\text{ (slow step) }$

then which of the following is(are) correct?

I. Rate constant = k_eq k₂

II. $\left[{\mathrm{N}}_2{\mathrm{O}}_2\right]=k_{\mathrm{eq}}[\mathrm{NO}{]}^2$

III. $\left[{\mathrm{N}}_2{\mathrm{O}}_2\right]=k_{\mathrm{eq}}\left[\mathrm{NO}\right]$

IV. $\text{ Rate constant }=k_2$

The correct option is