NIT

You should visit: josaa.nic.in and check previous year's cut-offs of NITs.

Yes, you can definitely get NIT Jalandhar with the rank of 66685 in B.Tech Biotechnology. The 12th percentage is also calculated while taking the admission. Best of luck for your future and if there's any query, feel free to ask.

Hello Adrija,
According to your current rank you can get admission in following NITs-
NIT Meghalaya
NIT Srinagar
NIT Agartala
NIT Arunachal Pradesh
NIT Puducherry
NIT Mizoram
NIT Manipur
NIT Sikkim
Adrija, don't just think about the top ten, see you have so many options open to you. Don't remain confined to a group of colleges.
You have a decent rank which can help you land in a great college. Please think wisely. All the best for your future.

What is your category?
Your chances of top NIts is very less.
You need to try for other institutions.

No, there is no other way/test for admission in these institutions.

According to me, you may get a seat in NIT.
But for a clearer idea, you should visit josaa.nic.in
and check previous years' cut-offs of NITs of home state and other states quota and also for various categories (general, OBC, SC, ST, etc).

You will get your preferred branch in some NIT and core branches in Good NIT. Even you have a chance of getting get BIT Mesra (not CSE).
I hope it helps.

You can check the prevoius year's cut-offs of your dream institute on the website of that college. For NITs and IITs, you should visit: JOSAA.NIC.IN.

IT all depends upon the rank of the JEE MAIN paper. You can check the previous year's cut-offs of various institutions on JOSAA's website.