In the Battle of Buxar, which took place in 1764, several Indian rulers formed a coalition to fight against the English East India Company. The question asks which of the following was not a part of this coalition.

Option 1: Mir Kasim - Mir Kasim was the Nawab of Bengal and was indeed a part of the coalition. He was one of the key figures in the battle.

Option 2: Mir Jafar - The correct answer is option 2, Mir Jafar. He was not a part of the coalition that fought against the English. Mir Jafar was the predecessor of Mir Kasim and had earlier collaborated with the English against Nawab Siraj-ud-Daulah in the Battle of Plassey. He later became the Nawab of Bengal, but he did not join the coalition against the English in the Battle of Buxar.

Option 3: Shuja-ud-daulah - Shuja-ud-daulah, the Nawab of Awadh, was part of the coalition. He played a significant role and commanded a large number of troops in the battle.

Option 4: Shah Alam II - Shah Alam II, the Mughal Emperor, was also a part of the coalition