The correct answer is: Munger.
The Kharagpur Raj was a feudal state in the modern-day Indian state of Bihar. It was founded in the 16th century by Raja Man Singh, a Rajput warrior from the Kachwaha clan. The capital of the Kharagpur Raj was the town of Kharagpur, which is now located in the Munger district of Bihar.
The Kharagpur Raj was a powerful state and its rulers were known for their military prowess. They fought many battles against the Mughal Empire and other rival states. The Kharagpur Raj was also a major center of learning and culture.
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 town of Kharagpur is still a major center of education and culture, and the region is home to many historical monuments from the Kharagpur Raj era.
The other options are incorrect because they do not correspond to the area that was ruled by the Kharagpur Raj. Munger is the only district that is located in the area that was ruled by the Kharagpur Raj. Jamui, Banka, and Lakhisarai are all located in different parts of Bihar.