The last major extension of British Indian territory took place during the time of

1. The question asks about the time during which the last major extension of British Indian territory took place. 2. Lord Dalhousie served as Governor-General of India from 1848 to 1856. 3. His tenure is famously associated with the Doctrine of Lapse and outright annexations based on alleged misgovernance or conquest. 4. Major territorial acquisitions during his time included the annexation of Punjab (1849 after the Second Anglo-Sikh War), Lower Burma (Pegu) (1852 after the Second Anglo-Burmese War), and several states through the Doctrine of Lapse (Satara, Jaitpur, Sambalpur, Baghat, Udaipur, Jhansi, Nagpur) and the annexation of Awadh (Oudh) on grounds of misrule (1856). 5. These annexations represented the most significant and geographically extensive expansion of direct British rule in India. 6. While later Governor-Generals/Viceroys like Dufferin (Third Anglo-Burmese War, annexation of Upper Burma, 1885), Lytton, and Curzon consolidated control and dealt with frontier issues, the period under Dalhousie saw the last large-scale additions to the territory directly administered by the British in India. Therefore, the last *major* extension occurred during Dalhousie's time.