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Being a commerce stream student, you are not eligible for both the B.Sc and BCA course.
~ Only 12th standard science stream students are eligible to apply for B.Sc course.
~ 12th standard with mathematics subject students are eligible to apply for BCA course.
Since, that you are not having mathematics subject in 12th standard. So, you are not eligible for both the BCA and B.Sc course.
Being a commerce stream student that you have a lot of career options. You can apply for the Bachelor's degree courses like:
-Bachelor of Commerce
-Bachelor of Arts
-Bachelor of Business Administration
-Bachelor of Bank Management
-Chartered Accountant of India
-Cost and Work Accountant

The most common integrated law courses that students go for include:
BA LLB-Bachelor of Arts and Law programs
B.Com LLB-Bachelor of Commerce and Law Programs
B.Sc LLB-B.Sc and Law programs
Law programs (LLB) can only be pursued through a post-graduate course and a student must be a graduate to become eligible to pursue the LLB degree. However, since the integrated law course includes a Bachelor's degree course as well, the two can be combined.
Sharda University offers plenty of options for students who are interested in pursuing the integrated law course.
Benefits of Pursuing the Course:
As the course can be pursued right after class 12th, a student does not have to complete the graduate degree. This is an advantage for the students who have a clear and defined career vision.
While you study for one degree, you get two degrees in your hand.
Career options are much more for students who have pursued the integrated course as compared to the other students.
Students save a year by undertaking the integrated BA LLB course as a study option. The students can invest the time saved for pursuing some other degree.
The number of law subjects that you study in a 5-year course is more than a 3-year course. This means that you gain a better and thorough knowledge of the subject.
As a student, you can focus more on extra-curricular activities like MUN, moot courts, client counseling, and internships.
In almost the same time period and cost, you can receive two degrees, why not go for it?
After the Degree
After successful accomplishment of the degree, all you need to do is enroll with the bar council of India. And, you can start working as an advocate or lawyer.
For the students who are interested in studying law and pursuing it as a career, the integrated programme is the best way to get started.