Upvote:2
As stated in a comment by @Thomas Cruise, a residence card from a Schengen country acts as a C category short stay visa for other Schengen countries. So you can travel to other Schengen countries as a visitor for a maximum of 90 days in a 180 day period. You are not generally tracked as such, but like most other laws, there are consequences if caught violating the rules.
Possibly stating the obvious, but while your residence card allows you to enter Schengen, to actually board a flight from India you’ll also need a travel document acceptable to the airline eg passport.