When was the capital of Magadha shifted from Rajagaha to Pataliputra?

Fourth century BCE

The correct answer is Option (3) → Fourth century BCE

Note: The given answer is as per NTA. However, there is a contradiction in NCERT in relation to shifting of capital to Pataliputra. As mentioned below at one place, it is mentioned that the capital was shifted in 4th BC, at the other it is mentioned as 5th BC.

NCERT:

"...Initially, Rajagaha (the Prakrit name for present-day Rajgir in Bihar) was the capital of Magadha. Interestingly, the old name means “house of the king”. Rajagaha was a fortified settlement, located amongst hills. Later, in the fourth century BCE, the capital was shifted to Pataliputra, present-day Patna, commanding routes of communication along the Ganga."

"History of Pataliputra: Each city had a history of its own. Pataliputra, for instance, began as a village known as Pataligrama. Then, in the fifth century BCE, the Magadhan rulers decided to shift their capital from Rajagaha to this settlement and renamed it. By the fourth century BCE, it was the capital of the Mauryan Empire and one of the largest cities in Asia. Subsequently, its importance apparently declined. When the Chinese pilgrim Xuan Zang visited the city in the seventh century CE, he found it in ruins, and with a very small population."