No, you cannot directly join a B.Sc. course from after completion of your 10th standard.

. After completion of 10+2, you can enroll in a B.Sc. program. It requires you to complete your 12th standard with subjects like PCM or PCB, including Physics, Chemistry, and Mathematics, or Biology.

Options

Complete your 12th standard:
This is the most common and the most direct way of entering the B.Sc. course. You must study more seriously in 12th standard, especially for science subjects.
Diploma Courses:
You can join a diploma program right after completing class 10th. This will, however not directly qualify you for B.Sc. You may have to give some bridge or entrance tests too.
Other Undergraduate Courses:
Other undergraduate programs include B.A. (Bachelor of Arts) or B. Com. (Bachelor of Commerce) if you have subjects for humanities or commerce. https://www.careers360.com/courses/b-sc-bachelor-of-science

To take admission to b.sc , candidates must have passed class 12th with PCM or pcb with a minimum of 50-60% marks. After 10th ,you are not eligible to take admission to b.sc, you need to pass class 12th. After 10th , you can take admission to diploma course. To know about b.sc course, check out B.sc courses .