The correct answer is: A. Sheohar
Sheohar is a district in the Indian state of Bihar. It is located in the north-central part of the state, and is bordered by the districts of Sitamarhi to the north, East Champaran to the east, Muzaffarpur to the south, and Darbhanga to the west. The district has a population of over 1.5 million people, and its headquarters is the town of Sheohar.
Sheohar is a relatively small district, with an area of just over 1,000 square kilometers. It is a predominantly rural district, with agriculture being the main source of livelihood for most of the population. The main crops grown in the district are rice, wheat, maize, and sugarcane.
Sheohar is also home to a number of small industries, including the manufacture of textiles, carpets, and leather goods. The district is also a major producer of milk and dairy products.
Sheohar is a beautiful district with a rich history and culture. It is a popular tourist destination, and is home to a number of historical monuments, including the ruins of the ancient city of Sheohargarh.
The other options are incorrect because they are not the smallest districts in Bihar. Gaya is the largest district in Bihar, with an area of over 4,000 square kilometers. Sheikhpura is the second largest district in Bihar, with an area of over 2,000 square kilometers. West Champaran is the third largest district in Bihar, with an area of over 3,000 square kilometers.