Hi Surinder,
Yes, you are absolutely go to Australia for your further studies with your BBOSE.
Bihar board of open school education is a recognised board nationally, so you can easily pursue for higher education from any universities of either India or any foreign universities.
The other requirements/eligibility criteria to get into Australia university are :-
1.you must done your 10+2 from recognised board
2.you must have student visa (for this you can easily apply)
So,there are no issues and you can go further for your studies in Australia.
Good luck.
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