Hello Safa

Yes, you can. Now it is possible to pursue Diploma and graduation degree at the same time. Previously it was not allowed by the goverment.

Many universities offer these type of courses under UGC act. But if you take my advise, then it will be nothing but a burden to you. You have to manage your time. If you can then it's well and fine.

All the best.

Dear Safa, the basic eligibility criteria for pursuing any Bachelors degree is that you should have passed 10+2 or any equivalent exam from a recognised University. Now, 10+2 and Diploma are equivalent programmes. For pursuing Diploma, the highest qualification is 10th Standard. Without having either a 10+2 or a Diploma as your  highest qualification, you cannot take up a Bachelor's degree. Either you take up Diploma and later pursue your Graduation or complete your 10+2 and then go ahead with your Bachelor's course. Safa, it is quite tempting to complete your education at the earliest because you want to start a career. While this is really a good thought, you need to be aware of what really helps you be successful and is worth all the energy and passion you put in. Whenever you come across any such advertisements that announce that you can pursue multiple courses at a given point in time, we would request you to checknthe authenticity of such information. Few years back, thousands of Indian Students who went abroad to pursue their Engineering Courses returned because the Institutiins they secured admissions from were not recognised Universities. Please go through this link: https://www.indiatoday.in/education-today/news/story/ugc-304695-2016-01-20
If the diploma and B.Sc degree are from the same stream, you cannot pursue it. And your highest qualification should be atleast 10+2 to pursue both these courses together. Because for Diploma 10th standard is good but for B.Sc you will need 10+2 qualification.
So can you let us know which stream in Diploma and which stream in B.Sc do you want to study??