Identify the order of following reaction?

$$ 2 \mathrm{NO}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})} $$

Rate of the reaction $\mathrm{A}+\mathrm{B} \longrightarrow$ product is $3.6 \times 10^{-2} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$ and rate law is $\mathrm{r}=\mathrm{k}[\mathrm{A}][\mathrm{B}]^2$. What is rate constant of the reaction if $[\mathrm{A}]=0.2 \mathrm{M}$ and $[\mathrm{B}]=0.1 \mathrm{M}$ ?

Calculate rate constant of a first order reaction having pre exponential factor $1.6 \times 10^{13} \mathrm{~s}^{-1}$.

$$ \left(\mathrm{E}_{\mathrm{a}} / 2.303 \mathrm{RT}=21\right) $$