IIT

Hello Mahesh,
Yes, GATE exam is for BE graduates to get into IITs for pursuing ME or M.Tech. GATE scores are also being accepted by many other universities for M.Tech or ME programs.

Admission in NIT is based on JEE Mains score. You may use following link to predict in which college you can get admission based on JEE Advanced score: https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

You may use following link to predict in which IIT you can get admission based on JEE Advanced score: https://www.resonance.ac.in/reso/news/jee-advanced-branch-allotment.aspx

You are eligible to seek lateral entry admission in B.Tech Aeronautical Engineering after Diploma in Mechanical Engineering. You may refer to following link for seeking lateral entry admission in B.TEch at Manipal University: https://manipal.edu/mit/programs/program-list/btech/btech-lateral-entry.htmla

Hello Muhammad,
You need to get at least 75% in board exams (12th). So, if you have only scored 72.2% then even if you clear JEE Mains and Advanced, you cannot get admission.

With those marks in JEE Advanced, I think getting into it is a bit difficult, and with a rank of 6500, you can get a good branch at top 6 or 7 NIT.

For a general category students, minimum marks required are 130+.
These marks will lead to admission in newly opened IITs that were opened in recent past years.

The best coaching institute in Rajasthan with a huge success rate are:
Resonance
Allen Career Institute
Motion Kota, IIT, JEE
Rao-IIT
Best of luck for your future.