Three complexes,
[CoCl(NH$$_3$$)$$_5$$]$$^{2+}$$(I), [Co(NH$$_3$$)$$_5$$H$$_2$$O]$$^{3+}$$(II) and [Co(NH$$_3$$)$$_6$$]$$^{3+}$$(III)
absorb light in the visible region. The correct order of the wavelength of light absorbed by them is:

The colour shown by any coordination complex arises because an incident photon of suitable energy is absorbed to promote an electron from the lower $$t_{2g}$$ set of $$d$$-orbitals to the higher $$e_g$$ set. The energy difference between these two sets is called the crystal-field splitting energy and is denoted by $$\Delta$$.

According to the relation between energy and wavelength,

$$E = h\nu = \dfrac{hc}{\lambda} \qquad\Longrightarrow\qquad \Delta = \dfrac{hc}{\lambda}$$

We see that $$\lambda \propto \dfrac1{\Delta}$$ - a larger splitting energy corresponds to a smaller wavelength (higher-energy light) absorbed, and vice-versa.

Now, the magnitude of $$\Delta$$ depends on the position of the ligands in the spectrochemical series (weak-field ligands give small $$\Delta$$, strong-field ligands give large $$\Delta$$). The relevant part of the series is

$$\text{Cl}^- \;\lt \; H_2O \;\lt \; NH_3$$

Let us examine each complex, keeping in mind that every complex contains the same metal centre, cobalt in the +3 oxidation state ($$d^6$$ configuration):

1. Complex (I): $$[{\rm CoCl}(NH_3)_5]^{2+}$$ contains one weak-field ligand $$\text{Cl}^-$$ and five stronger ligands $$NH_3$$.

2. Complex (II): $$[{\rm Co}(NH_3)_5H_2O]^{3+}$$ contains one ligand $$H_2O$$, which is stronger than $$\text{Cl}^-$$ but weaker than $$NH_3$$.

3. Complex (III): $$[{\rm Co}(NH_3)_6]^{3+}$$ is bound exclusively to the stronger ligand $$NH_3$$.

Because a single weak ligand lowers the overall field strength of the entire octahedral set, the net order of crystal-field splitting is

$$\Delta_{\text{III}} \;\gt \; \Delta_{\text{II}} \;\gt \; \Delta_{\text{I}}$$

Applying $$\lambda \propto \dfrac1{\Delta}$$, we invert this order to obtain the wavelengths of light absorbed:

$$\lambda_{\text{I}} \;\gt \; \lambda_{\text{II}} \;\gt \; \lambda_{\text{III}}$$

Written in the language of the question,

$$(I) \;\gt \; (II) \;\gt \; (III)$$

Hence, the correct answer is Option C.