Hello aspirant , hope you are doing good.

So, as you have mentioned that your domicile certificate is of J&K, so it is a matter of fact that you are eligible for all the counseling of J&K, and also the special round of CSAB counseling. But definitely, whether or not you get a seat in NIT srinagar doesn't just depends on your state of domicile, but mostly on your JEE Mains rank , and if your rank is under the cutoff rank.

State of eligibility is the state from which you have passed your class 12th board examinations from, so in your case it's Rajasthan. But that won't be an issue for you to get a seat in NIT Srinagar because your domicile certificate is still of J&K which is most important.

Hope this helps you. Good Luck !!