After driving professor Kumar to the museum she dropped him at his hotel.

After being driven to the museum, Professor Kumar was dropped at his hotel.
Professor Kumar was being driven dropped at his hotel.
After she had driven Professor Kumar to the museum she had dropped him at his hotel.
After she was driven Professor Kumar to the museum she had dropped him at his hotel.

The correct answer is A. After being driven to the museum, Professor Kumar was dropped at his hotel.

The other options are incorrect because they do not correctly reflect the order of events. In option B, Professor Kumar is being driven and dropped at the same time, which is not possible. In option C, Professor Kumar is dropped at the museum before he is driven to the museum, which is also not possible. In option D, Professor Kumar is driven to the museum by someone else, which is not mentioned in the original sentence.

The original sentence states that Professor Kumar was driven to the museum by the speaker, and then dropped off at his hotel. This means that the speaker drove Professor Kumar to the museum, and then drove him to his hotel. The order of events is as follows:

  1. The speaker drove Professor Kumar to the museum.
  2. The speaker dropped Professor Kumar off at his hotel.

Option A correctly reflects this order of events.

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