They should have been registered with the British authorities in India - there were separate lists for military birth and civilian ones. I can't get my free access to overseas records on familyrelatives.com working at the moment.

I hope they haven't sneakily done something to it, they're still claiming they're free.
"C & M Station" was a muncipality of Bangalore, so that's referring to the location in which he took the exam, not which exam he took.
J. Harrington Trott apparently was the author of 'Trott's Coloured Map of Railways in India' and related works. (re: Google Books). So he was probably working for the railways.
Also on fibis: In 1841 James Henry Trott married Margaret Harrington. Could these be James Harrington Trott's parents (grandparents?).