Despite his pompous style and gestures, the audience failed to evince any interest in his lecture.

The correct answer is A.

To evince means to show or display something, especially an emotion or feeling. In this case, the audience failed to show any interest in the lecture.

The other options are incorrect because they do not accurately describe what the audience did.

• Option B, hide, means to conceal something. The audience did not conceal their lack of interest; they made it clear by their body language and lack of participation.
• Option C, develop, means to grow or become more advanced. The audience did not develop any interest in the lecture; they remained uninterested throughout.
• Option D, take, means to accept or receive something. The audience did not take any interest in the lecture; they did not pay attention and did not seem to care about what the speaker was saying.