NIT

For getting admission in IIT, you first need to crack JEE Mains. Then you will be eligible for giving the JEE Advance. By crossing the cut-off, you can get yourself into IIT. For getting into NIT, you need to score well in JEE Mains. If you are from SC or ST, you need at least 120 marks for NIT. If you are from OBC or general, you need to obtain 160+ marks for an NIT. You need to gain 75% marks in 12th for appearing for the JEE advance.
Thanks.

JEE Mains 2018 College Predictor
Use your JEE Mains 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of JEE Mains 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor.

First of all, congratulations for your good result!
You can easily get good NIT or IIIT with top branches like EC, CS, IT, etc. You can predict the best college here-
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor
Do your JEE counselling.
Hope this helps you. Thanks.

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).