The capital of Bihar is located in:

Patna
Ranchi
Muzaffarpur
Gaya

The correct answer is Patna.

Patna is the capital and most populous city of the Indian state of Bihar. It is the 19th largest city in India and the 13th largest city in the Indian subcontinent. Patna is the seat of the Patna High Court and the headquarters of the Patna division and Patna district. The city is located on the southern bank of the Ganges River in the northern part of the state, 120 kilometers (75 mi) east of the Indo-Nepal border and 100 kilometers (62 mi) west of the state capital of Ranchi.

Patna was founded in 490 BCE by the king of Magadha, Ajatshatru. It was the capital of the Magadha Empire, which was one of the largest and most powerful empires in the world at that time. Patna was also the capital of the Gupta Empire, which was another major empire in Indian history.

Patna is a major center of education and culture. It is home to several universities, including the Patna University, the Nalanda University, and the Indian Institute of Technology Patna. The city is also home to several museums, including the Patna Museum, the Gandhi Smriti, and the Mahabodhi Temple.

Patna is a major transportation hub. It is connected to other major cities in India by air, rail, and road. The city is also home to the Patna Junction railway station, which is one of the busiest railway stations in India.

Patna is a major tourist destination. The city is home to several historical monuments, including the Patna Fort, the Golghar, and the Kumhrar archaeological site. The city is also home to several temples, including the Mahabodhi Temple, which is a UNESCO World Heritage Site.