Hey aspirant!

I am assuming that you are asking about Jee Main Paper 1 since you have not given the name of examination. Now, the NTA score which you see in your results is the actual percentile that you have secured in January JEE MAIN attempt. Do not misunderstand it to be your cumulative marks or your the average of all the subjects,rather the total NTA score is the percentile that you have achieved ie the percentage of people you are ahead of. As regarding to your query about rank, to be honest, it is difficult to predict the ranks currently as the April session has yet to take place and the actual rank will be calculated by taking into consideration your best of two JEE attempts and announced only after the April session results are declared. However, you can predict your expected rank based on January scores by this formula:-

So,(100 - your total percentile score) is the percentage of people ahead of you. Now, 869010 were the number of candidates appeared for Jan exam. So rank formula is (100 - your total score) X 869010 /100.

If, however, the number of candidates for April exam increases to another number,say 1200000 then your final rank shall be (100 - your total score) X 1200000/100

In your case( I am assuming you meant 67 percentile in your query as you haven't specified it clearly),  the rank comes out to be around 286773. Note that this is the GENERAL or ALL INDIA RANK and not the category rank as category ranks are difficult to predict at this point of time. Now, to be honest, it is very tough to get any NITs at this rank even if you belong to reserved categories. If you belong to ST or PwD category, then maybe there are small chances as there are seats reserved for these category but then too , you won't get any good NIT. However, you can go for State- level counselling to try for the colleges in your state. Also, you have not given accurate details of your category and mind you, the cutoff for different colleges vary in case of different categories, home state and gender.

As of now, it is difficult to predict the actual qualifying NTA score for JEE Advanced eligibility. However, if you have a percentile above 85-86 for any category, then you have a decent enough chance to qualify for Jee Advanced. However, you should refer to the previous year JEE Main qualifying cutoff scores by NTA as follows to understand your chances:-

Common Rank List (CRL)

89.7548849

GEN-EWS

78.2174869

Other Backward Classes (OBC-NCL)

74.3166557

Scheduled Caste (SC)

54.0128155

Scheduled Tribe (ST)

44.3345172

PwD

0.11371730

Therefore, looking at previous year's trends you have chances to qualify for Advanced only in case you belong to SC, ST or PwD category (you haven't specified your category) based on the overall score you have mentioned. Also, you have another opportunity to improve your results by performing better in the April attempt and I would advise you to concentrate on that and give it your best shot.

Here is a link of previous years' cutoffs of NITs which you can refer for understanding your chances

https://engineering.careers360.com/articles/nits-cutoff-for-top-btech-branches

Also, you can use this college predictor to predict what best colleges you would get based on January JEE MAIN scores.