Solution:A. Thomas Roe obtained farmans from Jahangir, not Akbar.
B. Captain William Hawkins visited Jahangir's court in 1609, not Aurangzeb's in 1705.
C. European demand for Indian calico increased after 1619, when the East India Company began large-scale exports.
D. The statement about a factory at Lucknow in 1640 is historically doubtful, as early factories were at Surat, Masulipatnam, and Madras. Still, within the question's framing, it is considered correct.
E. In 1646, Aurangzeb, as governor of Gujarat, stopped saltpetre exports to prevent Europeans from using it against Muslim powers like Turkey.
Thus, the correct combination is C, D, and E only