The correct answer is option 'A' - 1605.

The Dutch East India Company, also known as the Vereenigde Oostindische Compagnie (VOC), established its base in Masulipatnam in the year 1605. Masulipatnam, also known as Machilipatnam, is located in the present-day Indian state of Andhra Pradesh. The Dutch set up their base in Masulipatnam as part of their efforts to establish trade and dominance in the Indian Ocean region.

The Dutch in the Indian Ocean Region:
In the early 17th century, various European powers, including the Dutch, were vying for control of the lucrative spice trade in the Indian Ocean region. The Dutch East India Company, being one of the major players, had already established trading posts and bases in other parts of Asia, such as the Indonesian archipelago, Sri Lanka, and the Malabar Coast of India.

Establishment of the Dutch Base in Masulipatnam:
The Dutch recognized the strategic importance of Masulipatnam due to its location on the eastern coast of India. It provided access to the rich textile markets of the Coromandel Coast and served as a gateway to the Golconda Sultanate, known for its diamond mines. Moreover, Masulipatnam had a well-developed port and was a center of trade and commerce.

The Dutch established a fortified trading post in Masulipatnam in 1605. They constructed a factory, warehouses, and residential quarters within the fortifications. The Dutch base in Masulipatnam served as a hub for their trade activities in the region, including the export of textiles, indigo, and spices, as well as the import of European goods.

Trade and Conflict:
The Dutch initially had cordial relations with the local rulers and enjoyed a profitable trade in Masulipatnam. However, conflicts arose with the growing influence of the British East India Company and the competition for trade revenues. Over time, the Dutch faced challenges from the British and other European powers, leading to a decline in their dominance in the region.

In the late 17th century, the Dutch base in Masulipatnam was captured by the British, who emerged as the dominant colonial power in India. The Dutch influence in the region gradually diminished, and Masulipatnam lost its significance as a major trading center.

In conclusion, the Dutch established their base in Masulipatnam in the year 1605 as part of their efforts to expand their trade and influence in the Indian Ocean region. This base played a crucial role in their trade activities, particularly in the textile markets of the Coromandel Coast, until it was eventually captured by the British.