Hello Candidate!!
As you said about the marks, you have got 87%ile in JEE Mains with 136000+ AIR, The marks is not that much but not bad also.
With this rank you have surely qualified for attempting the JEE Advance also. But taking JEE Mains into consideration, you can actually get good colleges.

If you will try for the NITs, IIITs then you might get good colleges also but there is less chance for the good stream also. If you will wait till the last round of Counselling, you can grab the seat.
You asked for the MANIT Bhopal, but I am Sorry to say that "Looking at the previous years cut-off trends, you will not be able to get the seat in any of the stream."

But don't lose hope, you have a lot of other options and I want to mention that, There are lot of nice private colleges also which give much better placements and through counselling, you can take admissions in that.

Because of this COVID-19 Pandemic, many colleges had declared the process of admission on the basis of both JEE Mains marks as well as 12th Board Marks also.
So , This give much better chance to all the candidates to get enrolled in the institutions.
If you have scored well in your Board Exams, then might you will get better stream with the good college also.
This is the best alternative, I feel and you can check for the colleges on your basis of marks from this link also:
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Don't at all feel bad about anything, you have tried well in the exams and All The Best for your future!!

Hope that my information helped you.

Hello aspirant. Your score is very low for getting admissions in nit and iiit. You can get state engineering college like Rajasthan engineering and many more states engineering colleges. You can predict your college by clicking on the link below
https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Hello aspirant. As you know your rank is too low for getting admissions in nit. You can get state engineering college like Rajasthan engineering and punjab engineering and many more states engineering colleges. If you belong to economically good family then you can get lpu and many more. You can predict your college by clicking on the link below https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

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