CBSE 12th

Courses for Biology group students (P,C,B Subjects)
1 MBBS
2 BDS
3 B.Pharmacy.
4 B.A.M.S.
5 Pharm.D.
6 B.Sc. Nursing
7 B.H.M.S.
8 Bachelor of Physiotherapy
9 Other B.Sc. courses
10 Diploma courses
11 B.U.M.S.
12 B.A.S.L.P.
13 Management courses
14 Teaching & Education courses
15 Other Degree courses

Vajiram and Ravi IAS Study Centre.
IAS Era.
Delhi's IAS Study Circle.
Rau's IAS Study Circle.
Shristi Study Circle.
Career Shapers.
Career Point.
Sachdeva New P.T. College
Chanakya IAS Academy
All are good coaching join any one among them.

You can go for BBA or BCA and after graduation you can apply for IAS exam. Or, if you are not interested in these streams then you can go for B.Sc in History
And once you done your graduation then you can eligible for IAS exam and you can apply for it at www.upsconline.nic.in after notification which is generally issued in January or Feburary and if you want to know more about the exam you can visit www.upsc.gov.in

Yes, you will definitely get Jadavpur University with this rank.
And yes, you will definitely get admission in top branches like CSE and Electrical. Your rank falls under last year cutoff.

First try for NIT's. Go for NIT Raipur, MNIT Jaipur, NIT Patna or NIT Hamirpur. You'll most probably get a seat in one of these colleges. Else you can go for Chandigarh College of Architecture, Nirma University and there other institutes you can apply for. But I feel these options are sufficient enough for you.

You can do it from any prestigious institutions. Bachelors in such subjects will not make any difference, whether you pursue from a state university or from a central. Cracking it to the IIT will be exceptional keep in mind.

Following are the courses for science stream students:
1 Engineering courses
2 B.Sc. Courses
3 B.C.A.
4 B.Arch.
5 B.Pharmacy.
6 B.B.A.
7 Commercial Pilot training
8 Diploma Course in Fire Safety and Technology
9 Merchant Navy related courses
10 JOIN ARMED FORCES
11 Diploma courses
12 Other good courses
13 Some Design related courses
14 Bachelor of planning
15 Bachelor of Interior design
16 Teaching & Education courses
17 Pharm D
18 Management Courses
19 Degree Courses from other stream

Hello,
Kindly check the below link:
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-mumbai-all/2-2-0-10224-0
All the best!