Yes, you can get admission to government BCA universities with both marksheets, as long as they meet the university's eligibility criteria. Your state board marksheet will validate your overall 12th completion, while the NIOS marksheet for Mathematics as an additional subject fulfills specific subject requirements for BCA, where Mathematics is often mandatory. Ensure both are officially recognized and submit them during the admission process. Confirm with the university if they accept this combination before applying.

For more details you can visit the link given below

https://it.careers360.com/colleges/list-of-bca-colleges-in-kukas

Yes, you are eligible for CUET if you completed 12th with Commerce from a State Board and took Mathematics as an additional subject from NIOS. CUET considers candidates who have passed 12th from recognized boards, including state boards and NIOS. For admission to DAVV Indore, ensure you meet their specific course requirements, as some programs may require Mathematics in 12th. Verify the CUET eligibility criteria and DAVV's admission guidelines to confirm your subject combination is acceptable.

For more details you can visit the link given below

https://university.careers360.com/cuet-college-predictor

National institute of open school ( NIOS) is accepted in all the universities. NITs and IITs both accept the NIOS marksheet. You can appear for entrance examination with NIOS marksheet.

If you get score in entrance exam ,you can get admission to any IITs and NITs on basis of your score. No institute legally can deny on basis of NIOS marksheet.

Yes, you can write the NIOS exam a year after passing 12th standard. There is no restriction on appearing for NIOS based on the gap since your previous 12th board exams.  NIOS qualification is perfectly acceptable for JEE Mains. You just need to meet the eligibility criteria, which includes passing 10+2 with Physics, Chemistry, and Mathematics. JEE Mains considers the year of your first attempt at 12th board exams (NIOS or any other board) to determine eligibility. You can only appear for JEE Mains for three consecutive years after that first attempt year.

Similar to JEE Mains, BITSAT also accepts NIOS qualifications. BITSAT eligibility is based on the year you passed or appeared for your 12th board exams (current year and previous year). So, you can appear for BITSAT the year you take the NIOS exam and the following year as well.

https://www.careers360.com/exams/bitsat

I hope it helps!