The correct answer is C. Rohtas.
Rohtas is a district in the Indian state of Bihar. It is located in the northwestern part of the state and is bordered by the districts of Aurangabad to the north, Buxar to the east, Kaimur to the south, and Jehanabad to the west. The district headquarters is the town of Rohtasgarh.
The climate of Rohtas is tropical, with hot summers and mild winters. The average temperature in the summer is around 35 degrees Celsius, while the average temperature in the winter is around 15 degrees Celsius. The district receives an average annual rainfall of around 1,000 mm.
The lowest temperature in Bihar is found in Rohtas. This is because the district is located in the northwestern part of the state, which is the coldest part of Bihar. The district is also located in the foothills of the Himalayas, which further contributes to the cold weather.
The other options are incorrect because they are not located in the northwestern part of Bihar. Gaya is located in the central part of Bihar, Buxar is located in the eastern part of Bihar, and Darbhanga is located in the northeastern part of Bihar.