Science

Hi Abhjeet,
Surprisingly, you want to do BSC (Hons) now at this age.
Happy to know this.
Yes, you are eligible to study further. There is no age bar.
Just out of Curosity : Do you want to further study due to passion or to enhance your career further ?
If it is for career I have a different suggestion. Let me know.

You have secured very good rank and you should be able to get admission in the main campus at max by the 2nd round of counseling.

DU has a very efficient and reliable placement cell. You don't need to worry about the placements as you will easily get good one.

37 is a very good rank and you should definitely get call for admission in the first round of counseling itself.

For getting admission you will have to take an entrance exam and there is no direct way of admission

IIT kharagpur has excellent placements records. If you go to the website, official placement records are available there.

best 4 subjects

Yes, you will get admission as you have got a good rank, if not on sc seat then you will get in the general category

The placements from IIT are very good and need no elaboration. The energy department is also in demand these days and you can get 12 lakh/annum starting packages.