The correct answer is option 3: Both 1 and 2.

Statement 1 is correct because the Battle of Buxar, which took place in 1764, was a major turning point in the British conquest of India. The British East India Company`s victory in the battle allowed them to establish their dominance over the Mughal Empire and other Indian powers, solidifying their control over vast territories.

Statement 2 is also correct. The Treaty of Allahabad, signed in 1765, gave the British East India Company the diwani rights, which allowed them to collect revenue and administer the region of Bengal. This treaty was a crucial step in the British expansion in India, providing a legal framework for their rule in Bengal.

Both of these statements highlight key events that contributed to the establishment of British rule in India. The Battle of Buxar provided military success, while the Treaty of Allahabad granted the British legal and administrative authority. Together, these events played a significant role in the British colonization of India.