Hi

Assuming you from general category.

Yes you can definitely get into top engineering colleges like NITs IIIT gfti even  if you have only 66% in your class 12th as this year there is no 75% criteria in class 12 in order to be eligible for NITs etc

With     96 percentile

• Your rank  will be roughly around 40920 - 46000

Now,

Making  prediction is difficult as  cutoff  depends upon various factors like :-

-----------) number of students/ candidates  that appeared in the  jee main exam,

-----------) number of available seats,

-----------) jee main examination difficulty level.

-----------) the branch you want,

-----------) the category you belong etc.

-----------) your rank in jee main

But yes,

When we go through previous year trend then

>>>>>>>>> For your  rank

You have chances in following  which are listed below along with their closing rank in 6th round of josaa counselling 2021 under other state/ all india quota   :-

--------------------)National Institute of Technology, Mizoram :- ECE :-43465

---------------------)National Institute of Technology, Andhra Pradesh:- civil engineering:- 49142

---------------------)National Institute of Technology Agartala:- civil engineering:-52016

---------------------)National Institute of Technology Sikkim:- civil engineering:-54730

---------------------)National Institute of Technology Agartala:- btech biotechnology:- 56064

And a few more

You can check the closing ranks  at official website of josaa by going through the link given below

JOSAA 2021:- https://josaa.nic.in/Counseling/seatallotmentresult/currentorcr.aspx

Or

For previous year cut offs of top colleges like NITs, IIITs , you can also refer our page at :-

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

IIITs:- https://engineering.careers360.com/articles/jee-main-cutoff-for-top-iiits

Above prediction has been made  considering  past year cut off data but  closing rank for colleges varies every year depending upon many factors like jee main question paper difficulty, number of students writing the exam etc so

To have a personalised report on your chances of getting a college you can go through our college predictor, it will give you complete list of colleges which you can get on the basis of the category you belong to,  your home state, your gender etc, the link for  jee main college predictor is provided below

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

To help you  further,

To give an idea of jee main 2022 qualifying cut off ,

Minimum percentile in jee main 2021 to qualify it to be eligible for jee advanced is given below :-

--------) general :-87.8992241 percentile

--------) EWS:- 66.2214845 percentile

--------) OBC-NCL :- 68.0234447 percentile

--------) SC :- 46.8825338 percentile

--------) ST:- 34.6728999 percentile

--------) PWD :- 0.0096375 percentile

You can check the same at our page the link is provided below

https://engineering.careers360.com/articles/jee-main-cutoff

Thankyou