The correct answer is (a).
Lord Ellenborough was the Governor-General of India from 1842 to 1844. He was responsible for the conquest of Sindh, which was completed in 1843.
Lord Hardinge was the Governor-General of India from 1844 to 1848. He was responsible for the First Anglo-Sikh War, which was fought from 1845 to 1846.
Lord Auckland was the Governor-General of India from 1836 to 1842. He was responsible for the First Anglo-Afghan War, which was fought from 1839 to 1842.
Lord Amherst was the Governor-General of India from 1823 to 1828. He was responsible for the Burmese War, which was fought from 1824 to 1826.
The conquest of Sindh was a major turning point in the history of British India. It marked the beginning of the British Raj, which lasted for nearly 100 years. The conquest also had a significant impact on the history of Sindh, as it led to the decline of the Talpur dynasty and the establishment of British rule in the region.