VIT Vellore

No, it is not necessary to do Maths, but it will be difficult for you without Maths in B.Tech.

The candidate must have completed class 10th with 60 percentage marks. And, completed class 12th with 60 percentage marks. No exam is required.

There is no entrance examination.
Candidates who have studied in Regular, Full time and Formal Education are alone eligible to apply.
Candidates whose date of birth falls on or after 1st July 1998 are eligible to apply.
Application form will be available from the first week of April 2018.
The Admission will be on the basis of the performance in the qualifying examination (10+2).
The candidates are short-listed based on their merit will be called for the counselling.

Placement for biotech are average here, but VIT provide an opportunity to complete your graduation abroad, which increase the chance of a very good placement.

Please don't go for both, because both are private and expensive too. Do the following things. In the month of May look for NITs notifications for DASA (Direct Admissions of Students Abroad). They charge around 6000 $ only. NITs are very prestigious one and run by direct central government. You don't need to apply for JEE Mains exam etc. Direct Admissions are done.

You can easily get these books online. Books for exams like JEE, BITSAT VITEEE are available there.

Yes, why not. VIT takes admissions from all over India.

I do not know about the other two, but for SRM it is good, though not equivalent to CSE.

VJTI and VITEEE are the best among all the colleges you have mentioned for mechanical engineering but according to their fee structure, VJTI is good because it's fee is less than VITEEE.

Last year, 25 companies came to SRM University, Sonepat
but they have not shared any information regarding the highest package offered by them.