Vaishnavi, an 11th standard student from Bhagalpur district in Bihar, allegedly slit the veins of her wrist and throat in her room in Rajiv Gandhi Nagar here yesterday, they said, adding the victim did not leave any suicide note.
Police said she was taken to a hospital but the doctors declared her dead.
The girl had taken admission in a coaching institute here on April 4 to prepare for the entrance exam of IIT-JEE.
Ruling out stress of studies as a reason, Harish Bharti, circle in-charge of Jawharnagar police station said home sickness could be the cause.
A case has been registered under section 174 of Cr.P.C (police to inquire and report on suicide) and the matter is under investigation, they said.
This is the fourth case of suicide by students of coaching centres here this year. Last year, 20 students had committed suicide here.