Engineering Entrance Exam

Yes, you can apply for it.

sorry friend , if you are from general category then you will not BE able to get any good branch at nit , iwill suggest you to go for some good private colleges

All India Rank is declared by CBSE but I think you are eligible for getting admission in NITs.
Best of luck.

Dear Aspirant,
Thanks for forwarding your query.
You need to fill an online application form by visiting at www.amity.edu/mumbai and appear for the written test and interview. for the upcoming test scheduled in June 2017
Warm Regards
Amity University Mumbai

Pratik ! based on your score ,it is a tough call to get in government institutes but you can choose various private industries that are doing equal good.these institutes will provide you assured placements along with good scholarship.some of these institutes are:
1.Lovely Professional University
2.BITS
3.SIBM
Lovely Professional University provides an excellent infrastructure, even the university is having tie-ups with more than 50+ countries providing stage where they can sharpen their skills at most.this year IT giants set a record by selecting the highest number of students from this university

Dear Aspirant,
Thanks for forwarding your query.
The test schedule will be available in the next admission session. However it will be conducted somewhere between the month of April to May 2017.
Warm Regards
Amity University Mumbai

If you don't belong to general category then you have chance.

You should apply for NITs. You may get admission in new IITs, IIITs, Central universities, DTU, etc.