The correct answer is option 2: Madraspatnam. Madraspatnam, also known as Fort St. George, is the place in South India where the British East India Company constructed a trading post in 1639.

Option 1: Cuddalore is not the correct answer. Although Cuddalore is a coastal town in South India, it was not the location where the British East India Company constructed their trading post.

Option 3: Kalahasti is also not the correct answer. Kalahasti is a temple town in the state of Andhra Pradesh, and it is not associated with the British East India Company`s trading post.

Option 4: Karwar is not the correct answer. Karwar is a port city in the state of Karnataka, and it is not the location of the trading post established by the British East India Company.

In summary, the correct answer is option 2: Madraspatnam, where the British East India Company constructed their trading post in 1639.