The correct answer is: A) Bengaluru Urban.
Bengaluru Urban is the most populous district in Karnataka, with a population of 11,181,015 as of 2021. It is the capital of the state of Karnataka and is also the third most populous city in India. The district is located in the southern part of the state and is bordered by the districts of Ramanagara, Chikkaballapur, Kolar, Tumkur, and Hassan. The city of Bengaluru is the administrative headquarters of the district.
The district is home to a number of important industries, including information technology, biotechnology, and manufacturing. It is also a major tourist destination, with a number of historical and cultural attractions.
The other options are incorrect because they are not the most populous districts in Karnataka. Belagavi is the second most populous district in the state, with a population of 5,061,000. Mysuru is the third most populous district, with a population of 3,541,000. Ballari is the fourth most populous district, with a population of 2,371,000.