Let's identify the catalysts commonly used for each of the given reactions:
I.
\( CO + 3H_2 \rightarrow CH_4 + H_2O \)
This reaction is the **hydrogenation of carbon monoxide to methane**, also known as the **Sabatier reaction**.
Nickel (Ni) is a common catalyst used for this reaction, often supported on materials like alumina or silica.
II.
\( CO + 2H_2 \rightarrow CH_3OH \)
This reaction is the **synthesis of methanol from carbon monoxide and hydrogen**.
A mixture of zinc oxide (ZnO) and chromium(III) oxide (\( Cr_2O_3 \)) is a widely used catalyst for this process, especially at high pressures.
Copper-based catalysts are also used in modern low-pressure methanol synthesis.
However, among the given options, ZnO-\( Cr_2O_3 \) is the most fitting catalyst for this reaction under typical conditions implied.
III.
\( O_2 + 2H_2 \rightarrow 2H_2O \)
This is the **reaction of hydrogen and oxygen to form water**.
Platinum (Pt) is a highly effective catalyst for this exothermic reaction, even at room temperature.
Other noble metals like palladium (Pd) can also catalyze this reaction.
Based on these common catalysts for each reaction:
- Catalyst A (for reaction I) is Nickel (Ni).
- Catalyst B (for reaction II) is Zinc oxide-Chromium(III) oxide (ZnO-\( Cr_2O_3 \)).
- Catalyst C (for reaction III) is Platinum (Pt).
Therefore, the catalysts A, B, and C are Ni, ZnO-\( Cr_2O_3 \), and Pt, respectively.
This corresponds to option (A).