Correct Option (A):
The first quarter of the seventeenth century spans the years 1601 to 1625. During this period, the English East India Company (EIC) initiated its presence in India by establishing trading posts. The EIC's first factory was set up in Surat in 1613. Following this, factories were established in other significant trading centres in Gujarat, including Broach (present-day Bharuch) and Ahmedabad. These early establishments were crucial for the EIC's trade operations in Western India.
Incorrect Options:
Chicacole (present-day Srikakulam, Andhra Pradesh) was part of the Golconda Sultanate during the first quarter of the seventeenth century. The British East India Company did not establish a factory here during this period. Chicacole, along with the other Northern Circars, came under British control much later, specifically in 1766, when they were acquired from the Nizam of Hyderabad.
Trichinopoly (present-day Tiruchirappalli) was under the control of local Carnatic rulers in the early seventeenth century. The English East India Company did not have a factory or significant influence in Trichinopoly during the 1601-1625 period. British involvement and the establishment of their presence in this region expanded considerably in the mid-eighteenth century, particularly during the Carnatic Wars, which is significantly later than the timeframe specified in the question.