Uttar Pradesh

Both are good college but you should try to get admission in SRM University. For better information and comparison between the colleges please check the link and compare these colleges:
https://www.shiksha.com/resources/college-comparison

B.Tech in CSE is good here. Campus life is too awesome.

Amity is one of the good colleges in Kolkata. Apart from Amity, you can also go for Xavier's which is the best for management studies.

Hello,
You may refer the links below to know the list of colleges for BBA in Noida and greater Noida:
1) https://www.shiksha.com/bba/colleges/bba-colleges-noida
2) https://www.shiksha.com/bba/colleges/bba-colleges-greater-noida

There is no harm in trying. As per my experience, your brother has done quite well but this year, the board result is high. If you really need to get a govt. college, than you have to fill the form of all colleges. In this case, you should not be choosy. So many people will apply for the same course in the same college but you need to keep patience as your name is far in the merit list.

Yes, you can apply for JIIT Noida on the basis of class 12th marks basis as your class 12th marks is good so you can apply for JIIT and you can get admission.
All the best.

Here is a link that will help you know the colleges you are eligible for, on the basis of your JEE rank/score:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes Integral university is good university for BBA Please check the college all other detail and review by the students studying here by the link given below
https://www.shiksha.com/university/integral-university-lucknow-21870