In the question being asked, the correct answer is Option 1: Akbar at the time of capture of Khandesh in 1601. Let`s analyze each option for better understanding.

Option 1 talks about the kingdom of Akbar when he captured Khandesh in 1601. Khandesh was an important territory that he acquired, thus expanding his empire. This is the correct answer as the given map actually references the Mughal Empire during the reign of Akbar at this specific time.

Option 2 suggests that the map shows Akbar`s kingdom at the time of his death in 1605. While the period is close to the previous one, there could have been territorial changes in the empire between 1601 and 1605, making this option less accurate.

Option 3 and 4 refer to the kingdom of Aurangzeb at different stages. Aurangzeb ruled much later than Akbar, from 1658 to 1707, and the territorial extent of his rule was different from that of Akbar`s. Hence, they are not right choices according to the given map.