AEEE

Yes, you can get admission in Amrita University. Your rank is good enough to get you a seat in this college. You can apply with your category also to get reservations benefits. And keep all the documents ready for verification at the time of admission.
Best of luck.

Actually, you have to specify the branch in which you want to take admission then only you can get a clear cut answer. Do mention your category. You can go for any branch except for CS.

Yes, you can get admission in either EEE or civil branch in Coimbatore, Bangalore or Chennai. Your rank is enough to get you a seat. You should participate in the counselling process.
Best of luck.

Well, your rank is under 10K, there is a great chance of getting admission under said score. For more information, you can follow this link:
https://www.shiksha.com/college/cit-Coimbatore-Coimbatore-institute-of-technology-19322

Hi Elangovan,
You cannot get admission in CSE, but other branches are available for you like electrical, mechanical, civil etc. Even you can try for information technology. Best of luck.

Hi Muni,
Yes, you will get a seat in Andhra Pradesh. You should participate in the counselling and apply for the branches like civil, mechanical, electrical etc. As per your interests. Best of luck.

Yes, definitely you will get I think you can try for NIT also for counselling.

It depends. Are you from Tamil Nadu? If yes, then it's enough to have a rank below 6000 or 7000 for a department of your choice. If you want a department of your choice (the popular ones i.e. , ECE CSE mech), around 3000 will be your last resort. But there's also an option to change your department after 1st year, basic requirement being not having any backlogs. Also, there'll be competition. So, GPA above 8 in 1st year helps.

Maybe, yes you get seat in AEEE college must try it also other.