The conjunction yet indicates a contrast between the student’s tiredness (a challenge) and an unexpected or positive outcome.
Option (B) managed fits perfectly, as it means the student succeeded in completing the assignment despite the difficulty, aligning with the contrast implied by yet.
Option (A) failed contradicts the expected positive outcome, as it suggests the student did not complete the assignment.
Option (C) refused implies a deliberate choice not to do the work, which doesn’t fit the context of effort.
Option (D) ignored suggests neglecting the assignment entirely, which also contradicts the idea of completion. The complete sentence, The student was very tired, yet he managed to complete the assignment on time, conveys determination and success.