Step 1: Understanding the Buddha’s first sermon.
Gautam Buddha delivered his first sermon at Sarnath, near Varanasi, after attaining enlightenment. This sermon, known as the "Dhammacakkappavattana Sutta," marked the beginning of his teachings.
Step 2: Analyzing the options.
(A) Vaishali: Vaishali is a significant city in Buddha's life, but not the location of his first sermon.
(B) Sarnath: Correct — Sarnath is where Buddha delivered his first sermon after enlightenment.
(C) Sanchi: Sanchi is known for its stupas, but Buddha did not deliver his first sermon there.
(D) Pataliputra: Pataliputra was an important city, but Buddha’s first sermon was not given there.
Step 3: Conclusion.
The correct answer is (B) Sarnath, as it is where Buddha delivered his first sermon.