B.A Psychology

Yes, you can do Bachelors in Psychology with Commerce.
DU guidelines:
1. You can apply in DU if you opted for psychology in class 11th and 12th, you have to include it in BFS (best four subjects), else, you will face a deduction of some percentage.
2. You can apply even if you haven't studied psychology in high school but then you will face deduction in BFS.
Other institutes:
Universities like Christ Bangalore, Jamia Milia Islamia conduct entrance test and you can appear with commerce stream even without having studied psychology in high school. General Psychology is where you learn about the facets of the mind, various theories which have shaped the course of psychology, personality, memory, learning and so on. It teaches the problem and the solution only. Applied Psychology is a specialised stream of the field where one learns to put the theories and principles of psychology to practical and tangible use in the everyday world. It specialises you in any of the fields: Child Counselling, Industrial, Sports Psychology, etc. It teaches not only the problem-solution but also how to apply the solutions in real life.

Bachelor of Arts vs. Bachelor of Science
So what is it that distinguishes a BA In Psychology from a BS in Psychology? A B.A. In Psychology Involves More Liberal Arts Courses
Generally speaking, a Bachelor of Arts degree focuses on more liberal arts general education courses. Students who choose this degree may also be required to complete a foreign language component. The BA Option usually involves taking fewer courses in psychology and more classes in subjects outside of the major field area. A BS in Psychology Requires More Science, Math, and Psychology Courses
A Bachelor of Science degree will focus on more Science and mathematics courses. Students pursuing a BS in Psychology may have to take more lab and statistics general education classes. The BS option involves a stronger concentration on the major area of study and students take more psychology courses than those who are pursuing a BA. The subject-matter area of the degree may also focus more on research methods and applied psychology courses.

B.A. Psychology and B.A. (hons) Psychology are two courses on the same subject. There is difference in the syllabus and in job opportunities. B.A. Psychology involves study of mind processes, motives, reactions, feelings, conflict resolution, crisis management, group think, motivation and nature of the mind. There are so much more job opportunities with this course such as Career Employment Specialist, Developmental Psychologist, Career Counselor, Day-care Center Supervisor, Child Support Specialist etc. B.A. (hons) Psychology on the other hand, teaches about general psychology, statistics, physiological psychology, social psychology, research methods & psychology testing, abnormal psychology, development psychology, organizational psychology, child and adolescent psychology, industrial psychology etc.