i am perusing distance education from nagarjuna university A.p bbm final year can i apply for cat 2017 my 10th with 86% and 12th with 82%

Yes you can apply in CAT and other management exams. As per the basic eligibility criteria you need minimum 50% as a general candidate to apply for CAT.

Also in IIM's specifically there are past academics considered therefore you have decent records.

You should aim at the preparation, and a good percentile like really good so that your academics are not a barrier in between if in any case they tend to be.
Otherwise its not exactly that you will not get good colleges. If you get the good percentile and crack the interview and impress the panel you can make it to the admissions in good bschools.

Studying from an open school is not a barrier.

Colleges accepting CAT score including IIM's are list below:

MBA colleges through CAT
All the best!