Hello aspirant,
If you want to do MBA in government college you can give entrances like CAT ,CMAT,XAT,JMET.
Because some of the government colleges accept CAT.
And here is the list of top government MBA colleges in India:

• IIM, Bangalore
• IIM, Lucknow
• IIM, Calcutta
• IIM, Ahmedabad
• IIM, Indore

You can prepare accordingly,go through their official website and check their admission procedures.
Good luck.
Hope it helps.

Hello Aspirant,

Here I'm sharing some good government college list in a link below.

https://bschool.careers360.com/colleges/ranking/2017/top-government-mba-colleges-in-India

For more information visit the above link.

All the best!