What I understood from your question is you got a 59.6% in your 12 boards but rounding off it comes 60. Am I right?

See as per eligibility rules, one needs to have 60 now the question is how do you count 60%. In 2016, during my documentation check in AIIMS Delhi, the officer responsible added all my individual marks and made an average. If you go by this procedure then you are not eligible as it will come <60 and they counted the decibel points too. That time counselling was offline

The other way which is accept the percent given by the boards. In that manner you are eligible. 

As the Counselling process have changed in years, I am unsure which one they might follow. The best way is give your exams, if you are called for counselling , go and see in person what happens.

Donnot bar yourself from giving the exams.