When did the first train run in British India?
1853
1853 is correct.
The first passenger train in British India ran on 16 April 1853 from Bori Bunder (Bombay) to Thane, covering about 34 km with 14 carriages hauled by three locomotives named Sahib, Sultan and Sindh.
The line was built by the Great Indian Peninsula Railway during the time of Governor-General Lord Dalhousie, who is regarded as the father of Indian Railways.