With reference to Indian history, consider the following statements:

1. The Dutch established their factories/warehouses on the east coast on lands granted to them by Gajapati rulers.
2. Alfonso de Albuquerque captured Goa from the Bijapur Sultanate.
3. The English East India. Company established a factory at Madras on a plot of land leased from a representative of the Vijayanagara empire.

Which of the statements given above are correct?

The correct answer is 2 and 3 only.

Let us analyze each statement step-by-step to understand why this option is correct:

Statement 1 is incorrect:
The Gajapati dynasty ruled parts of Kalinga (modern Odisha and northern Andhra Pradesh) from 1434 to 1541 CE. The Dutch East India Company (Vereenigde Oostindische Compagnie or VOC) was established much later in 1602 CE, and they set up their factories on the east coast (such as in Masulipatnam and Pulicat) in the early 17th century. By the time the Dutch established these factories, the Gajapati rulers were no longer in power. Therefore, the lands were not granted to the Dutch by Gajapati rulers.

Statement 2 is correct:
Alfonso de Albuquerque, the Portuguese governor of India, captured Goa from the Sultan of Bijapur, Yusuf Adil Shah, in 1510 CE. This event marked the beginning of Portuguese rule in Goa, establishing a permanent territorial foothold in India.

Statement 3 is correct:
In 1639 CE, the English East India Company obtained a lease for a strip of land on the Coromandel Coast (which became Madras/Chennai) from Damarla Venkatadri Nayaka, a local chieftain and representative of the Aravidu dynasty of the Vijayanagara Empire (ruling from Chandragiri). Here, they constructed Fort St. George, which became the headquarters of the English on the east coast.

Therefore, since statements 2 and 3 are correct and statement 1 is incorrect, the correct option is 2 and 3 only.