I think the numbers are somewhat disputed. The People's Linguistic Survey of India says there are at least 780, with ~220 having died out in the last half century.[1] The Anthropological Survey of India reported 325 languages.[2]
The discrepancies are made particularly tricky because of the somewhat ambiguous distinction between languages and dialects.
[1] http://blogs.reuters.com/india/2013/09/07/india-speaks-780-l...