NIT

Hello Rittik,
There are cut-off marks in JEE Mains for each category and if they score equal to or above those cut-off marks then they will be qualified. For admission into NITs, the ranks come into play for each NIT there are specific closing and opening ranks and these ranks differ in each round of counselling. Usually, 7 rounds of counselling are held in which the ranks are declared for other state and home state quota. So based on that, the admissions are determined.
For the official opening and closing ranks refer:
http://josaa.nic.in/Result/result/OpeningClosingRank.aspx

Hello Vignesh,
The top colleges for mechanical engineering in Tamil Nadu are:
1) Vit University
2) Srm University
3) PSG College Of Technology, Coimbatore
4) Ssn College Of Engineering
5) Anna University
6) Thiagarajar College Of Engineering, Madurai
7) Coimbatore Institute Of Technology
8) Sastra University, Thanjavur
9) B.s Abdur Rahman Crescent University, Vandalur
10) Vel Tech University

Getting a seat by donation is ruled out.You get a seat only with a good rank.

Hello Naveen,
Yes, you need to give JEE Mains and secure a good rank like 20000 and below to get good NITs. You need to prepare separately as the questions are from PCM based on class 11&12 syllabus (NCERT).

NIT is a better option for pursuing M.Sc in maths.

Hello Gourav,
Yes, it is so. For general category, it is compulsory to have at least 75% and for SC, ST and PWD candidates it is necessary to have at least 65%.
Even if you don't have 75%, it is mandatory to be in the top 20 percentile that is the top 20% of students on your board. if you don't satisfy these conditions then you cannot get any colleges under JEE counselling.

Sir, if you are talking about JEE rank then sorry you can get admission only in B.Tech course through this rank but unfortunately, this rank is not too good to get NITs or IITs. So if you are thinking for B.Sc, then go in any other college.

You won't get NIT with this rank. Try for government colleges.

Hello Manish,
As per your rank, you will surely get lower NITs but wait till the last phase of counseling, however, check here to know more:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor