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Hi,
Which college you are asking for? B.Tech mechanical course fee changes with every college. In government colleges it is low as 25k per annum and private colleges cost 1 Lacs per annum. So, specify your college.

https://www.shiksha.com/b-tech/jee-main-exam-cutoff
Here is the excepted cut-off, kindly follow the link to get an idea about the cut-off of the different colleges.

https://www.shiksha.com/b-tech/jee-main-exam-cutoff
Here is the link you can refer to check all the excepted cut-off for IIT's and other colleges.

Hi
AFCAT eligibility
Education : Graduation (min 3 years) in any discipline with min 60% marks and have passed Maths and Physics as subject at 10+2 level B.E/ B.Tech from a recognised University with min 60% marks. Age Limit : 20 to 24 years.

Hi,
Yes after completion you will become eligible for government jobs. But, it is not available in distance mode. You can opt for a college where attendance is not mandatory. https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0

Hi,
You will have to go through the prospectus of the course provided by the college to know more about the admission procedure, fees, eligibility etc.I advise you to go to the college website. They will provide you with every detail you require. You can also contact the authorities. below is the link of shiksha which is a link about the college admission procedure, fees, eligibility etc.
https://www.shiksha.com/college/aalaska-group-of-education-rohini-delhi-35503/questions

To pursue an MBA one has to write an Entrance Exam like CAT GMAT XAT MAT CMAT ATMA NMAT are mandatory since you mentioned that you have not cleared the Exam it is possible to get admission in MBA without Entrance examination. You can get Direct MBA admission in Top B schools particularly Private Universities through management Quota. Here are some Top MBA Colleges:
1. ISBR Business school Bangalore
2. Alliance school of Business Bangalore
3. IMS MBA Ghaziabad
4. Alliance university MBA
5. Christ University MBA
6. Symbiosis MBA School
7. IFIM-Business School
8. ISBR Business school
9. ISBM Pune
10. ITM Navi Mumbai
11. ISME Bangalore

Yes, you can apply for ICAR AIEEA.