Hello sir!
There are thousands of engineering colleges which are functioning in our country. However, there are only a few hundred which are highly esteemed and ensure a bright future.
Talking about Government colleges, then the available options are IITs, NITs, and IIITs on the national level. The top 5 IITs are:

1. IIT Bombay
2. IIT Delhi
3. IIT Kharagpur
4. IIT Kanpur
5. IIT Madras

All the other IITs are ranked below these but are highly esteemed.
The top 5 NITs are:

1.NIT Tiruchirappalli
2.NIT Rourkela
3.NIT Surathkal
4.NIT Warangal
5.VNIT Nagpur

To get into IITs is to clear JEE Advanced after clearing JEE Mains. There is no other way to get an admission into the IITs.
To get into NITs, one needs to have a high score in JEE Mains.

Talking about Private colleges in India for engineering then the top 5 colleges are as follows:

1.Birla Institute of Technology and Sciences, Pilani [BITS Piliani]
2.IIIT Hyderabad
3.Dhirubhai Ambani IICT, Gandhinagar
4.Vellore Institute of Technology, Vellore
5.Birla Institute of Technology, Mesra, Ranchi

Most of the private institutes conduct their own entrance exams like BITS, Pilani has BITSAT; VIT conducts VITEEE and so on. In order to get admission into these colleges, one needs to clear the entrance exams with exuberant colors.

For further information:
https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-India?page=1
https://engineering.careers360.com/colleges/ranking

Now coming on to BBA, the following are the top five colleges of our country:
1.IIM, Indore [ Entrance Exam: IPM Aptitude Test]
2.Shaheed Sukhdev College of Business Studies, Delhi [Entrance Exam: DU JAT]
3.Keshav Mahavidyalaya, Delhi [Entrance Exam: DU JAT]
4.Deen Dayal Upadhyay College, Delhi [Entrance Exam: DU JAT]
5.Gargi College, Delhi [Entrance Exam: DU JAT]

For more information refer to this link :
https://bschool.careers360.com/articles/top-bba-colleges-in-india