Explanation:

Let’s break it down:

- To make evasive or misleading statement means: twisting the truth, being deliberately vague or dishonest.

- Option 1: Prevaricate—this means to avoid telling the truth by not directly answering a question. Basically, to lie or dodge.

- Option 2: Peroration—that’s the closing part of a speech, nothing to do with lying or dodging.

- Option 3: Sophist—someone who uses clever but false arguments. The word’s origin ties to tricky thinkers, but it’s about argument style, not simply dodging a question.

- Option 4: Ineffable—means something too great or extreme to be described in words. Not related.

- So, the best fit is prevaricate