Manjiri Mahajan has made a list of external exams (olympiads, scholarships, talent searches) that are available for students in Maharashtra from 1st to 10th standards.
Should be useful for parents who’re looking for challenges for their children.
(Interestingly, my kids’ school Vidya Valley discourages parents from making the kids appear for these competitive exams. I personally haven’t formed a strong view on this topic.)