NIT

Hi Gautam,
Since you have scored 90 marks in JEE Mains, you are eligible to get any NIT, IIIT or GFTIs and also to write JEE Advanced.
But, your score is too low to get admission in an NIT. So, you try your luck in counselling.
The counselling website is www.josaa.nic.in and the applications start only after JEE Advanced exam.
You can get other colleges that accept JEE scores as well as board exam marks easily.

Hi Gadde Karan,
The admission is based on your all India rank and category rank. The following link gives you the closing and opening ranks for the year 2016:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx

Hello Dhyaneshwar,
For admission into any of the IITs, you need to score more than 150 marks in JEE Avanced.

IITs and NITs do not have provision for lateral entry admission in 2nd year of B.Tech for Diploma holders in engineering from polytechnic.

Following are the top NITs for mechanical engineering in order of precedence: Tiruchirappalli, Surathkal and Warangal. You may refer to All India ranking of mechanical engineering colleges at: https://www.shiksha.com/b-tech/ranking/top-mechanical-engineering-colleges-in-india/48-2-0-0-0

You are advised to appear in JEE Mains exam to seek admission in NITs for graduation courses. You can seek admission in post graduation degrees by appearing in GATE examination.

You are eligible to seek admission in MCA at NITs.

Hi Murali Krishna,
Yes, you can surely get an NIT with this rank of 10000 if this is your all India rank.
If this is your category rank then you may or may not get.
Please click the following link to see the closing ranks for the year 2016:
http://josaa.nic.in/Result2016/result/OpeningClosingRank.aspx
Since the official closing and opening ranks are not released I have given the last year ranks.
You can apply for JoSAA counselling through www.josaa.nic.in.
The counselling and the applications for counselling will be started only after the JEE Advanced exams only.