Birth certificate vs passport

Hello sir I was born on 10 nov 1987 and i have a birth certificate of that date...but in my 10th 12th and all other documents it is 18 05 1989 .but in same year my sister was born in august 1989 ..i need passport .passport authority said that it is mandatory to submit birth certificate for peoples who born after 26 jan 1989.i want to change my dob in cbse board 10th certificate..is it possible to change my date of birth in 10th certificate through court because at present cbse is changing within 2 years of 10th exam ....but i am graduated .what should i do because documents showing me and my younger sister both born in 1989 just three month gap ..what to do please help me in this matter i want to go right with 10 nov 1987.