Pune

Hello Omkar,
Yes, it is necessary to give paper 2 exam to get admission in B.Arch you can click on the link and enter your rank to know the colleges:
http://engg.entrancecorner.com/jee-main-paper-2-college-predictor/
Hope it Helps! All the Best.

Following are the good B schools where you may think about with 724 MAT composite score:
TA Pai Institute of Management, Manipal approx 700
Institute of Public Enterprise Hyderabad, 650
Balaji Institute of Modern Management Pune
ITM Khargar Navi Mumbai
Xavier's Institute of Management and Entrepreneurship Bangalore

BIT, Jaipur is a campus of Birla Institute of Technology, Noida but MIT Pune is its main campus. Also, BIT Jaipur is new. So I will suggest you to join MIT, Pune.

Yes, it is a good option because in Pune, there are good colleges for MBA.

Pune is considered as oxford of East, with best colleges offering MBA course. As you want to explore options in Pune, check this link: http://bit.ly/amform.
This is a renowned institute offering various courses operating under the Bharati Vidyapeeth University. So, get in touch with them for guidance & assistance.
All the best to you.

Greetings from Shiksha.
MIT ADT University is among good Engineering Institutes in India. And has very good scope for Computer Science Engineering in terms of education and training.

Greetings from Shiksha.
Kindly visit visit this link for top engineering colleges in Pune, Maharashtra:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-pune/44-2-0-174-0

The best college for automobile engineering in Pune is D. Y. Patil. It is one of the best reputed colleges in Pune. Placement in automobile branch is satisfactory.

Timespro MBA would be a better option.