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Option 1 states that the Portuguese had a monopoly over the Eastern trade in the 16th Century. This is correct. During the 16th Century, the Portuguese established control over the lucrative spice trade in the Eastern seas, gaining a monopoly over the trade routes.
Option 2 states that the Portuguese possessed Mumbai in the beginning. This is incorrect. The Portuguese did not possess Mumbai (then known as Bombay) in the beginning. They gained control over Mumbai in 1534, which was several years after their arrival in India.
Option 3 states that the Portuguese had trading settlements at Cochin, Diu, and Daman. This is correct. The Portuguese established trading settlements in these locations. Cochin was an important center for the spice trade, while Diu and Daman were strategic ports for trade and defense.
Option 4 states that the Mughals denied them any trading concessions. This is incorrect. While the Mughals did challenge Portuguese influence in India, they did not completely deny them trading concessions. The Mughals allowed the Portuguese to continue their trade, although they imposed restrictions and demanded tribute.
In conclusion, options I, II, and III are correct, making option 1 the correct answer.