IIT Madras - Indian Institute of Technology

Hello Varun,
Aerospace engineering in IIT M, has good reputation besides placement record. Cutoffs for this year's JEE Mains has not been announced yet. You need to be in club of 70 percentiles minimum to get choice of your liking.
Best wishes.

It's not possible to get admission in UG program without any entrance exam. You must clear IIT-JEE Mains or Advanced along with 75% in 12th to make into IITs.

No, it's a single branch and you don't get subject branches at UG level but in PG level you may have.

Firstly, you should apply for JEE mains but it's date is over. So, go for other exams which you like.

Your 11th and 12th related chapters are important for JEE mains.

Generally, CAT cut off for SJSOM IIT-M is around 90-95 percentile so you do have good chances to get a call from it. Also you have a good academic profile.

You have chances to get call at a score around 90 percentile.

IIT - Madras is better than Kanpur.
1) Chennai is a prime location for many good companies in India as compared to Kanpur.
2) IIT - Madras is older than Kanpur and it's the best IIT among all IIT's as per the ranking by MHRD.
3) The average package of IIT - M is Rs.12 LPA and IIT - Kanpur is Rs.10 LPA.

You need to get 100 to 200 rank in open category to crack JEE Advance. It is possible with 70% score.

You have good chance for a call from IIT Madras. Prepare well for the next stage. All the best.