[Urgent help] Has any PCB student taken mathematics after passing 12th

My qualifications: I have passed 12th cbse with pcb(87%) this year

I am planning to drop a year since i scored nearly 500 in neet. So i want to prepare for jee this year but to be eligible for IITs you need to have physics, chemistry, mathematics as compulsory subjects. I wish to take maths this year itself and be eligible for jee mains and adv.

Can i do that by giving maths as an additional subject after 12th from cbse itself (private candidate), since they would give a separate marksheet for this (so then i would have 2 marksheets from cbse), would i be eligible?

Also, if i give maths from nios and opt for transfer of credit from my cbse marksheet to have just one marksheet from nios with pcmb, my year of passing would then become 2025 so would that become a problem?

Has anyone done this before pls help me out