Maharashtra

Yes, they take CMAT scores accepted through DTE rounds. 96 percentile is the general cutoff.
You can check the below mentioned link:
https://www.shiksha.com/getListingDetail/30895/institute/college-Department-Of-Management-Sciences-Savitribai-Phule-Pune-University-Pumba-Pune-India

1. JBIMS.
2. IIT – Bombay.
3. SP Jain.
4. NMIMS.
5. SYDENHAM.
6. KJ Somaiya.
7. SIESCOMS.

Kindly visit the link mentioned below:
https://www.shiksha.com/mba/colleges/mba-colleges-in-maharashtra

Jamana Lal institute of Management Studies and NITIE are the best institutes for MBA in Mumbai.

Yes, you can get benefit of your caste.

Hi dear,
You can chose following colleges:
1. S.P.jain
2. Jamnalal Bajaj
3. Narsee Monarjee
4. NITIE
5. Wellingkar
6. ITM navi mumbai

For mechanical engineering :
https://www.shiksha.com/top-mechanical-engineering-colleges-in-pune-rankingpage-48-0-0-174-0
For automation engineering :
Planet Automation Systems
Chintamani Nagar, Kondhwa Khurd, Pune
09850396034
Prolific System ans Technologies pvt ltd
www.prolifictraining.com
Office No. 36, First Floor, Preet Chambers, Mumbai Pune Road, Wakde Wadi, Pune
020 25533691
PLC Automation Training
www.plctrg.com

Padmashree D Y Patil College of Architecture, Vidya Pratishthan's College of Engineering (VPCOE) and Bharati Vidyapeeth College of Architecture are the top colleges for B.Arch in Pune.

First of all, congratulations on securing such a high score in NATA. Yes definitely you will get admission in colleges outside Maharashtra. Some good colleges for your reference would be -
CEPT, Ahmedabad
SPA, Delhi
Department of Architecture, IIT Roorkee
Sir J J College of Architecture, Mumbai
Department of Architecture, NIT Tiruchirapalli
Department of Architecture, NIT Calicut
BGS School of Architecture and Planning, Bangalore
R V School of Architecture, RVCE, Bangalore

They offer integrated BBA LLB course. Think well before joining the institute.