In the first incident, a fifth standard student of a local school in Lakadganj in the eastern part of the city, was criminally assaulted by an unknown accused early today.
The incident occurred when a young boy dragged her behind her school, gagged her and allegedly raped her.
The girl was rushed to the state-run Mayo General Hospital for treatment after bleeding profusely.
No arrests have been made have been made so far.
In an another incident, a 40-year-old man allegedly raped his own 12-year-old daughter between February 2012 and October 2012.
He also threatened the victim that her entire family would be killed, she alleged in her report filed here today.
The accused has been arrested, the police said.