The etymology of the phrase "3rd world country"[1] is interesting, and isn't directly related to economic strength. According to the original definition, India is indeed a 3rd world country.
A second definition of 3rd world is "developing countries" [2]. India still falls into this definition, but it's rapidly approaching "developed country" status.
[1]: http://en.wikipedia.org/wiki/Third_World#Third_Worldism