When did the Dual Government of Bengal start?

The correct answer is Option (1) → 1765

After the Battle of Buxar (1764), the Treaty of Allahabad (1765) gave the East India Company the diwani (the right to collect revenue) of Bengal, Bihar and Orissa, while the Nawab kept the nizamat (police and justice). This division of power, set up by Robert Clive in 1765, is called the Dual Government of Bengal: the Company had the money and the Nawab the responsibility. Warren Hastings ended it in 1772.