Explanations:The Battle of Buxar, fought in 1764, was a significant event in the history of British colonial rule in India. It was a decisive battle between the British East India Company and the combined forces of the Mughal Emperor Shah Alam II, the Nawab of Awadh, and the Nawab of Bengal, Siraj-ud-Daulah. The British victory in this battle led to the establishment of their control over the provinces of Bengal, Bihar, and Orissa. However, it is important to note that the Battle of Buxar did not directly establish British control over Bombay and Madras, which were already under British control through earlier conquests and treaties.
Regarding the administrative roles in Mumbai, the capital of Maharashtra, it is true that the Governor, the Chief Minister, and other ministers live and work in Mumbai. Mumbai serves as the administrative center for the state of Maharashtra, housing the state government's offices and the residence of the Governor. The Chief Minister and other ministers also have their offices in the state capital, making this statement accurate.
Mumbai is also a significant industrial and institutional center in India. It is home to a wide range of industries, including manufacturing, finance, and information technology. The city is also known for its educational institutions, research centers, and cultural institutions. This makes the third statement true as well.
Therefore, the correct answer is that only the second and third statements are true. The Battle of Buxar did not establish British control over Bombay and Madras, but it did establish their control over Bengal, Bihar, and Orissa. The administrative and industrial roles of Mumbai are accurately described in the second and third statements.