The city of Lahore, once a major cultural center of Punjab, became part of:

The correct answer is: b) Pakistan.

Lahore is a city in Pakistan, located in the Punjab province. It is the capital of Punjab and the second-largest city in Pakistan after Karachi. Lahore is one of the oldest cities in the world, with a history dating back to the 16th century. It was once the capital of the Mughal Empire and a major cultural center of Punjab. After the partition of India in 1947, Lahore became part of Pakistan.

The other options are incorrect. India is a country in South Asia. Bangladesh is a country in South Asia. An independent princely state is a state that is not part of any country.