Final Answer:
Katie appeared infallible in math class because she had never gotten a problem wrong. The correct choice to replace "infallible" is (c) wrong.
Step-by-step explanation:
In this context, "infallible" means incapable of making mistakes. The sentence conveys that Katie seemed perfect in math because she had never made an error. Therefore, the appropriate synonym for "infallible" in this sentence is "wrong" (option c). This choice maintains the intended meaning of the sentence, emphasizing Katie's flawless performance in math class.
It's crucial to note that "mistaken" (option b) could also be a synonym for "infallible," but it doesn't fit the context of the sentence as well as "wrong" does. "Mistaken" generally implies a specific error or misunderstanding, whereas "wrong" encompasses a broader sense of inaccuracies or mistakes, aligning better with the idea that Katie had never gotten any math problem incorrect.
In conclusion, the most fitting choice to replace "infallible" in the given sentence is "wrong" (option c), as it accurately captures the meaning that Katie never made mistakes in her math class.