The correct option that best expresses the sentence in the passive voice is:

Option 1: After being driven to the museum, Professor Mohan was dropped at the airport.

Explanation: In the original sentence, the subject "she" is performing the actions of driving and dropping off Professor Mohan. To convert this sentence into the passive voice, we need to make Professor Mohan the subject of the sentence and show that he is receiving the action.

Option 1 correctly uses the passive voice by starting the sentence with "After being driven to the museum," indicating that Professor Mohan is the one being driven. It then follows with "Professor Mohan was dropped at the airport," showing that he is the one being dropped off.

Option 2 is incorrect because it combines both the passive and active voice in a confusing manner. "Professor Mohan was being driven dropped at the airport" is not a grammatically correct sentence.

Option 3 and Option 4 use the past perfect tense ("had driven" and "had dropped") unnecessarily, suggesting that the actions occurred before another past event. However, the original sentence does not provide any context for this, so the use of the past perfect tense is unnecessary.

Therefore, Option 1 is the correct choice as it effectively expresses the sentence in the passive voice.