Hey Sachin,

Aadhar card is one of the most Secure and best way of identification. And government has made changes to it easy enough. It can be updated within couple of hours. Just Go to a nearby Aadhar card centre tell them your issue. Mostly a form. Is also filled. Detailing the issue. And then he/she would update your Father name on Aadhar. It gets updated within Few Hours. Then you won't have any problem while applying for Any Exam.

Best of luck