hello aspirant,

87 percentile would fetch you a rank around 132990-149500.As of now its tough to say because the analysis and also cutoffs change every year due to many factors like total students appearing for exam,difficulty level of paper etc.as you did not mention your category considering you from general category,based on your rank you have tough to no chances to fetch seat in nits,iiits.you need better percentile of 98+  to fetch seat in top nits,iiits.you can try in private engineering colleges using your jee percentile.workhard for the upcoming jeemain sessions..you can get closing rank for josaa official website: https://josaa.nic.in/Result/Result/currentorcr.aspx

.for more information to get a personalised report on what all chances you have for your rank refer to: https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

hope this helps,

thankyou.