The girl was sleeping when Firoz Shamsher (20), a resident of Patharkuva, approached her and raped her last night. He was passing through the locality at the time, Isanpur police said.
He was caught and handed over to the police.
The girl has been admitted to the civil hospital here, they said, adding that her medical report is awaited.
Shamsher will be interrogated thoroughly before being produced in a local court here for further remand, the police said.
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Meanwhile, in a separate incident in Behrampura locality of the city, a pregnant woman registered a complaint against a doctor for allegedly molesting her.
The woman has stated in her complaint at Kagdapith police station that she was undergoing treatment at one Chauhan Dalal's hospital here.
The doctor has been booked under Section 354 of the Indian Penal Code, the police said.
The doctor has also lodged a cross-complaint against the relatives of the woman.