Arrange the following set of compounds in order of their decreasing relative reactivity with an electrophile,$E^{+}$:
$(a)$ Chlorobenzene,$2,4-$dinitrochlorobenzene,$p-$nitrochlorobenzene
$(b)$ Toluene,$p-CH_3-C_6H_4-NO_2$,$p-O_2N-C_6H_4-NO_2$

(A) Electrophiles are reagents that participate in a reaction by accepting an electron pair to bond with nucleophiles.
The higher the electron density on a benzene ring,the more reactive the compound is towards an electrophile,$E^{+}$ (Electrophilic aromatic substitution).
$(a)$ The presence of electron-withdrawing groups $(EWG)$ deactivates the aromatic ring by decreasing electron density. Since the $-NO_2$ group is a stronger $EWG$ (via $-I$ and $-M$ effects) than the $-Cl$ group (which is weakly deactivating via $-I$ effect but activating via $+M$ effect),the reactivity decreases as the number of $-NO_2$ groups increases.
Order: $\text{Chlorobenzene} > p-\text{nitrochlorobenzene} > 2,4-\text{dinitrochlorobenzene}$.
$(b)$ The $-CH_3$ group is electron-donating ($+I$ and hyperconjugation),while the $-NO_2$ group is strongly electron-withdrawing. Toluene has the highest electron density. As the number of $-NO_2$ groups increases,the electron density on the ring decreases.
Order: $\text{Toluene} > p-CH_3-C_6H_4-NO_2 > p-O_2N-C_6H_4-NO_2$.