Final answer:
The correct answer is (b) 2 and 3 only, as the Dutch focus was more on Indonesia rather than the east coast of India, while Alfonso de Albuquerque did capture Goa, and the English established a factory at Madras with land leased from the Raja of Chandragiri of the Vijayanagara Empire.
Step-by-step explanation:
The correct statements with reference to Indian history regarding European engagements are statements 2 and 3 only, which means that the answer is (b) 2 and 3 only. Statement 1 is incorrect as the Dutch were more focused on Indonesia and did not establish their factories on the land granted by Gajapati rulers on the east coast of India.
Statement 2 is correct because Alfonso de Albuquerque indeed captured Goa from the Bijapur Sultanate. This marked the establishment of a lasting European presence in India, with Goa becoming a critical part of the Portuguese Empire in the East.
Statement 3 is also correct. The English East India Company established a factory at Madras, which was indeed leased from a representative, but it was on land given by the Raja of Chandragiri, a remnant part of the disintegrating Vijayanagara Empire.