Hmm .. that journey is surely more than just a weekend trip ?
There are direct trains but no direct flights for this journey. Hyderabad (Andhra Pradesh) to Ajmer (Rajasthan) distance is 1343 km and you can get there by flight + train in just over 7 hours and 20 minutes or by train fares starting from ₹ 553.
It's gonna be warm and sunny, and did I mention warm ?