is necessary to take coaching in 11th and 12th in state board
Hello student no its not necessary if you're enough focused in the class room and Do all your work properly you need not to join any coaching institute however if you feel that you need an extra support/guidance you can join a coaching institute as per you need. Prefer NCERT or books referred by your class teachers to build your basic concept.
Feel free to comment if you have any doubt
Good luck