Hello Payalpriya,

Yes, you can apply in CDS(Combined Defence Services) Exam , after BCA from 

private Institution, but you can't apply in Indian Naval Academy,you can apply 

in other courses IMA,AFA,OTA Women.

You can also visit the career360 link regarding it-

https://competition.careers360.com/articles/cds-eligibility-criteria

Thank You.

Hope it was helpful.

Hello Payal Priya singh 

Yes ,you are eligible to apply for CDS (Combined Defence Services examination). If you are pursuing your final year BCA Course then also you can apply for CDSExamination. This is most famous examination conducted by UPSC, two times in a year and you have to apply for this examination online only.

Hope your doubts are clear if not ask me in comment section. 

Thank you