Mukul Jain, enrolled in IGNOU's Life Sciences course, had been missing since January 8.
Jain returned today and told police that he had gone to Patna to take a holy dip in the Ganga river.
A senior police officer said that Jain was depressed after a break-up with his girlfriend. He left for Patna from the Jawaharlal Nehru University (JNU) campus, leaving behind his mobile phone and ATM card in the JNU lab, the officer added.