The newly appointed professor found it hard to_________the students who were_________ and_________to the topics discussed during lectures.

encourage withdrawn and indifferent students — the verb fits *trying to motivate* uninterested students.

withdrawn (= shy, uncommunicative) and indifferent (= apathetic) — coherent pair describing students who neither engage nor care.

Why other options fail:

• Option 1: "enthuse" is fine, but "difficult" is vague and "undisciplined" doesn't pair naturally with "hard to enthuse."
• Option 2: "engage" works, but "deficient and diffident" describes students as inadequate + shy — an odd combination.
• Option 3: "belligerent" (= hostile) and "uninstructed" don't pair — hostile students aren't simply uninstructed.