The capital of the Magadha Kingdom shifted to Pataliputra during the reign of which king:

Ajatashatru
Udayin
Bindusara
Ashoka

The correct answer is: Ajatashatru.

Ajatashatru was the son of Bimbisara, the founder of the Magadha Empire. He ascended to the throne after killing his father and ruling for 24 years. During his reign, he shifted the capital of the Magadha Kingdom from Rajgriha to Pataliputra. Pataliputra was located on the banks of the Ganges River and was a more strategic location for the empire. It was also a more developed city with better infrastructure.

Udayin was the son of Ajatashatru and ruled the Magadha Empire for 25 years. He was a popular king and is credited with expanding the empire. He also built many temples and other public works projects.

Bindusara was the son of Udayin and ruled the Magadha Empire for 28 years. He was a powerful king and is known for his military conquests. He expanded the empire to include much of the Indian subcontinent.

Ashoka was the son of Bindusara and ruled the Magadha Empire for 37 years. He is one of the most famous kings in Indian history. He is known for his military conquests, his Buddhist reforms, and his construction of many stupas and pillars.

Ajatashatru was the first king of the Magadha Empire to shift the capital to Pataliputra. This was a significant event in the history of the empire. Pataliputra became the capital of the empire for centuries and was a major center of power and culture.