Vittal Sharma, a native of Banswara district, who was preparing for IIT in a coaching institute here, was filling water in the cooler last evening in his private hostel when he received electric shock and died, police said.
The student had come to Kota in May for the coaching.
Following the complaint from his parents, a case of carelessness and negligence had been registered against the hostel's manager, Prakesh Vyas.
Investigation into the matter is on, however no arrest has been made so far, police said.