how do i prepare for barc and isro online exam

There is no specific syllabus for BARC, Gate syllabus would be enough for the same except general aptitude. And it can also help you to face the interview in later stage. And the questions will be asked from technical specific subjects including mathematics and GA/GK questions will not be there.

And if we talk about ISRO then it is also little bit same as BARC. There is no pre-defined syllabus, it is only based on curriculum taught in graduation and similar as Gate pattern. But it is advisable to focus on research and understanding the topics rather than memorizing them all. It will be helpful for your interview as well.

I hope my answer solved your query.

Good Luck!!!