I have done 12th. Do I need to write any entrance exam for studying B.Sc in maths from government colleges?

Yes, there are certain government exams conducted by the universities in India if you want do B.Sc. From there you have to write entrance exam and qualify them in order to get a good seat. B.Sc. Entrance exams are conducted by many universities like BHU, Allahabad, DU, etc.

In most of the government-run colleges in India, the educational requirement for entering into the course of B.Sc. Mathematics is that candidates must have completed their 10+2 examination with good percentage of marks and with mathematics as a subject in 10+2 stream.