The correct answer is option 'A', the Treaty of Madras.

The First Mysore War (1767-1769) was a conflict between the Kingdom of Mysore, ruled by Hyder Ali, and the British East India Company. It was a significant event in the history of South India and marked the beginning of a series of wars between Mysore and the British.

The Treaty of Madras, signed in 1769, marked the end of the First Mysore War. Let's discuss the details of the treaty and its significance.

1. Treaty of Madras:
- The Treaty of Madras was signed on 4 April 1769 between the British East India Company and Hyder Ali, the ruler of Mysore.
- The treaty was negotiated in Madras (now Chennai), the capital of British Madras Presidency.
- It was signed by Colonel Joseph Smith, the British representative, and Mir Miran, the representative of Hyder Ali.

2. Terms of the Treaty:
- The Treaty of Madras had several significant terms that were advantageous to the British and addressed their concerns.
- Hyder Ali agreed to restore all the territories he had captured from the British during the war.
- He also agreed to pay a large sum of money as war indemnity to the British.
- The treaty established a mutual defensive alliance between Mysore and the British East India Company, ensuring peace and preventing future conflicts.

3. Significance of the Treaty:
- The Treaty of Madras brought an end to the hostilities between Mysore and the British, providing a temporary period of peace.
- It allowed the British to consolidate their position in South India and focus on their other colonial interests.
- The treaty also recognized the military strength of Hyder Ali and his Kingdom of Mysore, making him an important player in the regional politics of South India.
- However, the treaty did not resolve the underlying issues and conflicts between Mysore and the British, leading to further wars in the future.

In conclusion, the Treaty of Madras was the agreement that ended the First Mysore War in 1769. It provided temporary peace between Mysore and the British East India Company and established a defensive alliance. However, it did not resolve the deeper conflicts, leading to subsequent wars between the two powers.