From what I've read, the Citizenship Act of India specifies that any citizen of India who obtains citizenship of any other country immediately ceases to be a citizen of India. At that point, it is his or her duty to surrender their passport to the nearest Indian mission abroad.
I guess that one could ignore this and keep on using their Indian passport - but doing so would be fraud and criminal misrepresentation.
WARNING
If holder acquires Nationality
of another country, he should
Surrender This Passport
forthwith to the nearest Indian
Mission/Post Abroad. Un-
authorized possession of this
Document shall Constitute an
Offence Punishable under
the Indian Passport Act 1967
I guess that one could ignore this and keep on using their Indian passport - but doing so would be fraud and criminal misrepresentation.