Teacher

Hi,
After pursuing B.Ed you will get offered a teaching job as a permanent, temporary, part-time or full-time as per your interest. With B.Ed degree you can work in Schools, Education Department, Coaching Centers, Education consultancies, home and private tuitions, etc.
Apart from teaching in schools, you can open your own coaching institutions where you can provide tuitions to the students. This will only improve your teaching skills and knowledge but also enable you to earn more.
You can also work as academic content writers or academic counselors.
So, yes you are eligible.

There are 2 ways to become a Govt College Professor :
1.You have to clear the UGC NET or SET/SLET Exams.
2.Other option is,securing a P.hd Degree in your subject.

To become a teacher, you need to pursue B.Ed.

By taking science field and dropping biology, you may pursued for B.Sc mathematics and then MSC mathematics.
Salary doesn't matter, you get to teach maths with lot of opportunities.
Also, you have to do B.Ed for profession.

Most universities require English professors to have, at the minimum, a Masters degree in literature. With a Masters, you can teach students pursuing an associate or Bachelors degree, but you will need a Ph.D. in literature to teach graduate level students. If you hope to enter a career as a professor of English literature, knowing the general courses you need will help guide your studies.

What do you exactly want to know? Of course, B.Ed entrance exam has its relevance in each state if you are looking forwards for admission.

You can go for B.ed and chooses computer application as the specialization or go for Bachelor's or graduate degree.

In my opinion, you should pursue with UG, PG and P.hD or should qualify NET to become a teacher. In this sense, you should take admission in B.Com right after 12th in a reputed university.