India

There are four test administrations or admins for the SAT in India. These occur in the months of March, May, October, and December. The test is administered at over 80 test centres in more than 40 cities across India.
Date of Exam Saturday October 5, 2019 (tentative), Saturday December 7, 2019 (tentative)
To receive the SAT Fee reduction voucher and take the SAT for free, follow the below steps:
STEP 1 Go to www.buddy4study.com/collegeboard
STEP 2 Apply for SAT Fee reduction voucher
STEP 3 Pay discounted SAT Fee and register for the exam

Mechanical has the strongest competition, hope you get.

That depends on the particular University and various other factors. You should contact the University, they will guide you to get admission.

It is not possible for you to get admission in any of the colleges with this rank. There are some institutes which accept admission based on class 12th score. You can try in those institutes.

Registration will start from mid of June, so you can apply for admission. Good luck.

The best colleges under MAKAUT offering B.Tech in IT are IEM, Heritage, St. Thomas, Meghnad Saha College, etc. You can get admission in either of these without giving Entrance Examination, through management quota. Contact the college to know more about the details, fee structure, and procedure.
Best of luck.

The best college to pursue MBA in Bangalore or Delhi are as follow:
IIM Bangalore
FMS
IMT ghaziabad
MDI
IMI New Delhi
IIFT Delhi
Fore
Christ University
Amity University.

As per your score in NATA and class 12th board, you are eligible to take admission in VIT Vellore. But, you need to appear in VITEEE to get a seat in Bachelor of architecture courses in this college. Best of luck.