The district formed by the bifurcation of the erstwhile North Arcot district is:

Vellore
Tiruvannamalai
Ranipet
Krishnagiri

The correct answer is: Vellore.

Vellore district is one of the 32 districts of Tamil Nadu, India. It is located in the northern part of the state and is bordered by Andhra Pradesh to the north, Tiruvannamalai district to the east, Krishnagiri district to the south, and Kanchipuram district to the west. The district has a population of over 4 million people and its headquarters is the city of Vellore.

Vellore district was formed in 1997 by the bifurcation of the erstwhile North Arcot district. The district is divided into 10 taluks: Vellore, Arcot, Vaniyambadi, Gudiyatham, Tirupattur, Kanakapura, Hosur, Krishnagiri, and Dharmapuri.

Vellore district is a major industrial and agricultural district. The district is home to a number of industries, including textiles, engineering, and pharmaceuticals. The district is also a major producer of rice, sugarcane, and cotton.

Vellore district is a popular tourist destination. The district is home to a number of historical and religious sites, including the Vellore Fort, the Arulmigu Andal Temple, and the Sri Venkateswara Temple.

The other options are incorrect because they are not districts that were formed by the bifurcation of the erstwhile North Arcot district.