Indian Institute of Technology, IIT Bombay

Yes, you will get admission directly in second year.
Check whether there is an entrance exam for admission in this college.

Hello Mr Ravindra,
I am afraid, you are ineligible for this dual degree program. It is open to the students having done graduation in either mathematics or statistics only. I am attaching a link that will give you all the required information about this course.
http://www.ieor.iitb.ac.in/acad/msc_phd

https://www.shiksha.com/university/amp/indian-institute-of-technology-bombay-Mumbai-54212
You can check it here all the details. Good luck!

Hi Ankit Dubey, Eligibility is as below:
Minimum Eligibility to Apply
Qualification: Graduation: 55%
Entrance exam IIT JAM followed
For more details, click below
https://www.shiksha.com/science/course/m-sc-in-applied-geophysics-indian-institute-of-technology-bombay-powai-Mumbai-296886.

It doesn't matter much. But you should have a minimum of 75% aggregate in class 12th board examination.

You require rank around 20 in UCEED for IDC.

Hello,
If you want to study in IIT Bombay then you can give GATE exam, as you are an engineering student GATE exam is for engineering graduates who want to pursue PG from different IITs.

I don't know the exact figure but it is not more than 15k INR.

Both the IIT's are good, but in my opinion IIT-Bombay is better than IIT-Roorkee, because IIT-Bombay provides good quality of faculty members with good course curriculum.

Crack JEE Mains and JEE Advanced exam with good marks, so that you can secure a good rank. Then, you will surely get admission in IIT-Bombay.