Step 1: Examine the time expression used in the sentence. The phrase “by the time” followed by a future reference typically tests whether an action will be in progress or completed at the moment of another future event, especially at the point of arrival.
Step 2: Since the question focuses on an action that will be ongoing at that future moment, the appropriate tense is the future continuous. In the interrogative form, this tense is constructed as:
will + be + verb–ing.
Step 3: Among the given options, only option (C) correctly follows this structure. The other options either use passive constructions or mix tenses incorrectly. Therefore, (C) is the correct answer.