First of all, this answer is pertaining to the JEE mains score. Now the percentile system tells you that you have scored better than how many candidates. So if the percentile is around 87 it means that your score is better than 87% candidates who gave the exam and worse than top 13% candidates. If we take the number of candidates appeared to be 10 lakh, then your rank will be around 1,30,000. You may or may not have cleared the cutoff on this score based on your category.
To be quite frank, the chances for you to get any top NIT is very bleak. You can get newer NITS like NIT AP, NIT Sikkim, NIT Agartala, etc. if you qualify for state quote.
Good luck!

Hi aspirant,

You have obtained 86.88 percentile in JEE Main. Based on this percentile your Common Rank list (CRL) rank would be 1,40,000 approximately and the corresponding OBC category rank would be 47,000 approximately. See this is not a good rank both in general category as well as in OBC category. With such score and rank it is not possible for you to get good college. Nevertheless, you can see your available options by using our college predictor tool by clicking on the following link: https://engineering.careers360.com/jee-main-college-predictor?ici=cp-listing_engineering&icn=JEE-Main-College-Predictor

Hope I answered your query.