Hello,

Your rank is more than enough for securing your seat in even tier-I NITs for the Biotechnology. You should rest assured for that. You can even get NIT Warangal or NIT Calicut which are the two best NITs offering a degree in the branch of BioTechnology. While the situation is not very bright for aerospace engineering. Considering colleges which participate in JoSaa and take JEE Mains marks, Only IIEST Shibpur is an option. It closed in 13560 in round 7 of JoSaa and thus you may or may not get it. IIEST is a good institute for aerospace engineering and you should hope for the best.

My best advice to you is to fill Aerospace engineering fairly above other NITs for BioTechnology so that you have an option for upgrade. As you will be getting biotechnology in Tier-I or Tier-II NITs in initial rounds only. I wish you have given JEE Advanced too as it will open your options in a lot of other Aerospace Engineering colleges including some of the Best IITs.

Hi ! Yes, you can get any nit or any government colleges with aerospace engineering or biotechnology. For government engineering College to study aerospace I will prefer you to go IIEST shibpur and for biotech you can have any nit and government college except nit Trichy and nit Warangal. So hope you understand and best of luck to you. Given below a link will be an useful one for you. 

https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/jee-main-college-predictor&ved=2ahUKEwjbo-W4mOHiAhVaU30KHbnhDd4QFjABegQIAhAB&usg=AOvVaw1pTMu5LewXe0n3JPiA8V2U