Correct Option (B)
Jahangir
Emperor Jahangir granted permission to the English East India Company (EIC) in 1613 to establish its first factory in Surat. This decision followed initial diplomatic overtures by Captain William Hawkins in 1609 and was further solidified by the efforts of Sir Thomas Roe, who served as an ambassador from King James I of England to the Mughal court from 1615 to 1619. The Mughal administration permitted this establishment to encourage foreign trade, which brought revenue and access to European goods, and to potentially counter the existing dominance of the Portuguese in maritime trade.
Incorrect Options
Akbar: Emperor Akbar's reign concluded in 1605, prior to the significant English diplomatic missions and the formal establishment of their first factory in Surat in 1613. While initial English interest in trade with India emerged during his rule, the permission for the Surat factory was not granted by him.
Shahjahan: Emperor Shahjahan ascended to the throne in 1628, well after the English East India Company had already secured permission and established its first factory in Surat under Jahangir's rule.
Aurangzeb: Emperor Aurangzeb's reign began in 1658. By this period, the English East India Company had already solidified its presence in Surat and expanded its trading operations to other regions of India, making it impossible for him to have granted permission for the 'first' factory.