A white throat, supercilium and orange uppertail - all point to Grey Bushchat female. A Pied Bushchat is overall more dusky, with more black on uppertail. I see no reason to suspect a mixed lineage here and I am not aware of any such hybrids either. Their breeding ranges do not overlap at all. Grey Bushchats are more abundant in north and central India in winter than distribution maps show, particularly from Haryana to Madhya Pradesh. Rajasthan is a known wintering destination for the species.