The correct answer is: Bhagalpur.
The Kharagpur Raj was a feudal state in the Indian subcontinent that existed from the 16th to the 19th centuries. It was founded by Raja Man Singh, a Rajput warrior who served the Mughal Empire. The Kharagpur Raj controlled territories in a region that is now part of the modern district of Bhagalpur in the Indian state of Bihar.
The Kharagpur Raj was a powerful and influential state during its time. It had a strong military and a well-developed economy. The state was also known for its culture and education.
The Kharagpur Raj came to an end in the 19th century when it was annexed by the British East India Company. However, the legacy of the Kharagpur Raj continues to this day. The region that was once part of the Kharagpur Raj is now home to a number of important historical and cultural sites.
The other options are incorrect because they do not correspond to the region that was once part of the Kharagpur Raj. Munger, Lakhisarai, and Banka are all districts in the Indian state of Bihar, but they are not located in the region that was once part of the Kharagpur Raj.