Presidency cities were the major administrative and commercial centers during the British colonial rule in India. They were called presidency cities because they were the headquarters of the three presidencies established by the East India Company. These presidencies were Bengal Presidency (with Calcutta as its capital), Madras Presidency (with Madras as its capital), and Bombay Presidency (with Bombay as its capital).

The correct group of cities recognized as Presidency cities is option 'c', which includes Bombay, Madras, and Calcutta.

Explanation:
1. Bombay:
- Bombay (now known as Mumbai) was the capital of the Bombay Presidency, one of the three presidencies established by the East India Company. It was an important port city and commercial center.
- Bombay Presidency was located on the western coast of India and included regions such as Gujarat, parts of present-day Maharashtra, and some areas of present-day Pakistan.
- Bombay was a major center for trade, industry, and administration. It played a crucial role in the development of British colonial rule in India.

2. Madras:
- Madras (now known as Chennai) was the capital of the Madras Presidency. It was located on the eastern coast of India.
- Madras Presidency included regions such as Tamil Nadu, parts of present-day Andhra Pradesh, Kerala, and Karnataka.
- Madras was an important administrative and commercial center. It had a significant presence of British colonial institutions and was a hub for trade and industry.

3. Calcutta:
- Calcutta (now known as Kolkata) was the capital of the Bengal Presidency. It was located in the eastern part of India.
- Bengal Presidency included regions such as West Bengal, Bihar, Odisha, and Bangladesh.
- Calcutta was the most important city among the presidency cities. It served as the center of British colonial administration in India and was a major hub for trade, industry, and intellectual activities.
- Calcutta was often referred to as the "Second City of the Empire" after London due to its significance in the British Empire.

Overall, the group of cities recognized as Presidency cities includes Bombay, Madras, and Calcutta. These cities played a crucial role in the British colonial administration and were centers of trade, industry, and governance.