Class 11

Right now you are in 11th standard. And in any case it's not required to prepare for CAT at this stage. Maximum 1 year is more then enough for CAT preparation. But for your better future, it's very important to get good marks in 10th and 12th boards
Only then you will get the best college for your graduation. Try to get atleast 90% marks in 12th boards so as to get the best college. And you can start preparing for CAT in the 2nd year of graduation if you are really very serious about it.

Here are some top colleges
Abhinav Institute of Technology & Management.
Asian Institute of Health Sciences.
B. N. Bandodkar College of Science.
Birla College of Arts, Science & Commerce, Kalyan.
Dnyan Ganga Education Trust's Degree and Junior College.
Dnyanasadhana Asian Institute of Core Competence.

You can have Maths in 11th as upto 10th everyone has same subjects and in 11th it is divided into various streams.

Focus on concepts rather than writing answers by mugging up. Start practicing mock questions, previous year questions, and then your conceptual and practical knowledge will be up to the mark for JEE.

Please explain the reason of going Pune and present school. However If you are going there due to transfer of your father than seek admission in any CBSE school. Please attach the father transfer letter for better response. The name of few school are given below.
1. Pune International School
2. The Orchid School
3. Kendriya Vidyalaya No.2
4. Vikhe Patil Memorial School
5. BK Birla Centre For Education
6. Vidyashilp Public School
7. The Heritage School.

Yes, girls can apply for NDA now after 12th.

Mock test paper are available on Official website of CBSE.

You can opt for Humanities ( Political Science, History, English Economics ) or Commerce with or without Maths Accountancy, Business Studies, English Economics). If you pursue B.A. LL.B. ( 5 Years Integrated Course), almost all the subjects whether from Humanities or Commerce will help you. One thing that you must keep in mind that whatever subject you have choose, you must clear all the concepts and understand it.