The correct answer is D. After being driven to the museum, Professor Kumar was dropped at his hotel.
The other options are incorrect because they do not accurately reflect the order of events in the sentence. In option A, it is stated that Professor Kumar was dropping himself off at his hotel, which is not possible. In option B, it is stated that Professor Kumar was dropped off at his hotel before he was driven to the museum, which is also not possible. In option C, it is stated that Professor Kumar was being driven to the museum and then being dropped off at his hotel, but this does not specify the order of these events.
The sentence “After driving Professor Kumar to the museum she dropped him at his hotel” clearly states that Professor Kumar was driven to the museum first and then dropped off at his hotel. This is the only option that accurately reflects the order of events in the sentence.