Step 1: Understanding the Buddhist Councils.
The first Buddhist Council was held shortly after the death of Lord Buddha to preserve and codify his teachings. It was convened by the elder monk Mahakasyapa at Rajagriha (modern-day Rajgir) under the patronage of Emperor Ashoka.
Step 2: Analyzing the options.
(A) Pataliputra: Incorrect. The first Buddhist Council was not held in Pataliputra. It was held in Rajagriha.
(B) Kashi: Incorrect. Kashi (Varanasi) was an important center for Buddhism, but the first Council was not held there.
(C) Rajagriha: Correct. The first Buddhist Council was held in Rajagriha, also known as Rajgir.
(D) Vaishali: Incorrect. Vaishali was an important place for early Buddhism, but the first Council was not held there.
Step 3: Conclusion.
The correct answer is (C) Rajagriha, as it was the site of the first Buddhist Council.