The correct answer is: B) Mysore and Hubli.
The growth of the textile industry in Karnataka during the British period transformed cities like Mysore and Hubli. Mysore was the capital of the princely state of Mysore, and Hubli was a major commercial center. The textile industry was one of the most important industries in both cities, and its growth led to the development of infrastructure, such as roads, railways, and factories. The textile industry also created jobs and attracted workers from other parts of the country.
The other options are incorrect because they are not cities that were transformed by the growth of the textile industry during the British period. Bangalore and Davangere are both located in the southern part of Karnataka, but they were not major centers of the textile industry. Belgaum and Shimoga are both located in the northern part of Karnataka, and they were also not major centers of the textile industry. Mangalore and Udupi are both located on the coast of Karnataka, and they were not major centers of the textile industry.