The smallest district in Andhra Pradesh by population is:

Vizianagaram
Srikakulam
West Godavari
East Godavari

The correct answer is: a) Vizianagaram.

Vizianagaram is the smallest district in Andhra Pradesh by population. It has a population of 2,764,538 as of 2011. The district is located in the northern part of the state and is bounded by the states of Odisha and Chhattisgarh to the north, the district of Srikakulam to the east, the district of East Godavari to the south, and the district of Visakhapatnam to the west. The district headquarters is the city of Vizianagaram.

The district is divided into 10 revenue mandals: Vizianagaram, Bobbili, Gajapatinagaram, Kurupam, Sattenapalle, Nellimarla, Parvathipuram, Salur, Eturunagaram, and Dumbriguda.

The district is home to a number of historical and cultural sites, including the Vizianagaram Fort, the Bobbili Fort, and the Nellimarla Caves. The district is also known for its scenic beauty, with a number of hill stations and waterfalls.

The district is a major producer of rice, cotton, and tobacco. The district is also home to a number of industries, including steel, cement, and power generation.

The district is well-connected by road and rail. The nearest airport is the Visakhapatnam Airport.

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