You didn't mentioned your stream for intermediate. If you are in science then you can apply for KVPY examination in 11th. Rather than this you can also apply for Olympiads like Pre-RMO etc.

If you are from any other stream then you should come back to career360.com (//career360.com) with proper specifics so that we can help you out.

I hope my answer helps. All the very best for your future endeavors!