The correct answer is option 2, the Battle of Plassey. This battle, which took place on June 23, 1757, is seen as a significant event in the establishment of British colonial rule in India. The battle was fought between the forces of the British East India Company, led by Robert Clive, and the army of the Nawab of Bengal, Siraj ud-Daulah.

The British victory in this battle gave them control over the Bengal region, which was a major center of trade and wealth in India. The battle allowed the British East India Company to consolidate its power and set the stage for further expansion and domination of the Indian subcontinent. It marked the beginning of British political control and the start of the process that led to the establishment of the British Raj in India.

Option 1, the Third Battle of Panipat, which took place in 1761, was a major battle between the Maratha Empire and the Durrani Empire, but it did not directly contribute to the establishment of the British Raj.

Option 3, the Battle of Buxar, which occurred in 1764, was a decisive battle in which the forces of the British East India Company defeated the combined armies of the Nawabs of Bengal,