hello aspirant,

67 percentile would fetch you a rank around 337590-379500.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 chances to fetch seat in nits,iiits you need better percentile of 98+  to fetch seat in nits,iiits .even 94-95 percentile would help you land in nits like nit agartala,sikkim in least cutoff branches.you can get closing rank for josaa official website: https://josaa.nic.in/Result/Result/currentorcr.aspx  .

you can try in few top private engineering colleges like :

for top private engineering colleges you can try  for the below colleges through jeemains:

thapar university

BIT mesra

sastra university

srm university

amritha vishwa vidyapeetham

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

refer to: https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-India-accepting-jee-main-score

hope this helps,

thankyou.