Step 1: Understanding the contact process.
The contact process is used to manufacture sulfuric acid from sulfur dioxide and oxygen. The catalyst used in this process is vanadium pentoxide (V$_2$O$_5$), which speeds up the reaction without being consumed. Step 2: Analyzing the options. (A) Ni: Nickel is not used in the contact process for sulfuric acid production. (B) Fe with Mo: This combination is not used in the contact process. (C) V$_2$O$_5$: This is the correct catalyst used in the contact process for manufacturing sulfuric acid. (D) MnO$_2$: Manganese dioxide is not used in this process. Step 3: Conclusion.
The correct catalyst used in the contact process is (C) V$_2$O$_5$.