Dear aspirant,

As you have already passed 12th with PCM in science stream from UP board. You can again appear in class 12th exam from Rajasthan's board.

But not all school give you admission directly to class 12 it is preferable that you choose open school for class 12 Rajasthan board.

Note : If you have already passed 12 with good marks why should you want to appear for 12th again. It would be a serious valuable year loss.

As for the fact, if you didn't claim any domicile reservation while looking for admission in any universities/colleges, other than there would be no extra benefit from which state you have passed.

For preparation tips of JEE Mains, you can visit the link given below,

https://engineering.careers360.com/articles/how-prepare-for-jee-main

Hope it helps you..

Best of luck..