Whoa - that's a really nice trip with interesting options.
There are direct flights but no direct trains for this journey. New Delhi (Delhi) to Srinagar (Jammu And Kashmir) distance is 832 km and you can get there by flight in just over 1 hour and 15 minutes or by train + flight fares starting from ₹ 1690.
Beautiful weather for sightseeing and other outdoor activity.