Taking up a dual Degree course after completing Class 12 in science

A Dual Degree program is a combination of two academic programs. This two degree will be offered as a single academic program. it combines a UG and PG program. The UG & PG combination offered as one/single integrated academic program. For example – B.Sc. + M.Sc. Integrated course, B.Tech. + MBA Integrated course and B.Com. + MBA Integrated course.
A 12th passed candidates can acquire UG and PG Degrees at one go! They need not apply for UG and PG admission separately, once they choose a dual degree course. Completing a UG and PG program (separately) takes 6 years. Whereas a Dual Degree program can be usually completed in 5 years. This helps the student save one year. In addition to that, the candidate need not apply two times. Onetime application is sufficient.
There are many universities offering these courses. BITS Pilani, Andhra University and some other institutes offering these dual degrees. Absolutely there is no problem and the UGC approved institutes can be selected for your admission.

There is some lack of clarity in the question. Do you want to do two B.Sc. degrees simultaneously or you want to apply for a dual degree program of the universities like B.Sc. followed by M.Sc. If you want the former thing then as per UGC guidelines, it is not allowed and two regular courses cannot be attempted simultaneously. However you can do one regular B.Sc. and another through correspondence mode in your part time. If your contention is the latter option then you have to apply for dual degree course right in the beginning and then do it one by one sequentially. It would take the total time as per the time of doing B.Sc. plus M.Sc. You will have to specify the subjects beforehand.

The Dual Degree program combines with the academic programs. It combines two programs and add to it and offers as a single academic program. Usually, dual degree programs offered in bachelors, doctorate and PG level. Some of the dual degree programs are mentioned as follows.

1. Master of Applied Management
Those who have completed 12th science program they can go for a five-year integrated course. Here BBA and MBA course are coupled as one bundle and offered as a dual degree. After completing the course you will be getting two degrees and job prospects will be good.

2. Master of Computer Management
This program is a five-year integrated program where the BCA and MCA degrees are merged as one course. Students who complete this course successfully will get software jobs in industry and related computer fields.

3. Enginnering and Masters
This is a dual degree program in engineering field where the course combines B.Tech Degree and M.Tech Degree and offers as one course. The total duration of the programs in five to six years.

4. Engineering and Management
This is also a dual degree program where the Engineering degree is coupled with a Management degree. B. Tech and MBA course is coupled into one course. The total duration of the course is five years.

5. B.SC, M.SC Programs
This is a dual degree program in the science field. The program combines B.SC and M.SC programs into a single course. The total duration of the course is about four to five years. Those who have completed plus two science with appropriate subjects can apply for the course.

6. B.COM, LLB Programs
It is a Dual Degree program which combines a commerce course with law course. The total duration of the program is five years.

7. B.PHARM, M.PHARM Programs
This is a dual degree program which is related to the pharmaceutical field. It bundles B.PHARM and M.PHARM into one course. The total duration of the program is six years.

Opting for the dual programme sometimes saves the time in completion both of the courses and in the event of taking the courses one by one could amount to total summation of the duration of each course. The other advantage could be the elimination of the entrance of the entrance test needed to pass in the separate mode of the course. There are certain courses which fall in such categories and such dual programme is mentioned below -
1) Integrated programme of BCA and MCA - There are some universities imparting such a dual course. If you take up BCA the duration of which is three years and later MCA is to be taken up, the extent of duration is the same and hence it follows that there is no saving of time while taking up these courses separately but the dual programme would of five year duration saving your one year valuable time.
2) B.com + LLB programme - The total duration of such a programme is of five year but doing the same separately would have consumed six year time span.
3) B.Tech + MBA - Such a dual programme is advantageous for the aspirants interested to have both the degrees in a single shot. The advantage while taking up such a programme is that they would save full one year since the duration of this dual programme is only five year in lieu of six years if done separately. There is no separate procedure for the entrance test for the MBA programme.
4) Integrated programme of Masters in Physics, Chemistry and Mathematics offered by IIT - Though for seeking admission in the Master's course in any of the subject, you need to appear the JEE main and JEE advanced and depending upon your scores in such tests and your inclination, you may be inducted in any one of the programmes though the the course consists of five year giving you no weightage in relation to saving of years in the academic cycle but the tag attached with the course could offer you benifits in terms of your employment in teaching line, research etc.
5) Integrated course of B.Sc and M.Sc - Though the number of years invested in such a dual programme is not likely to offer you any relief in terms of time which is of five year duration but this is providing you a secured admission in M.Sc without the entrance test conducted in some universities or the the minimum eligibility of marks of the qualifying examination to secure admission for M.Sc programme.

You cannot do two degree courses simultaneously, It is not allowed. Yes, you can do one diploma and one degree course at the same time from the same university or a different universities.

After completing your class 12 in science you have many options to go ahead like doing B.Sc. or trying for some entrance exam for engineering degrees etc. Now you want to do multiple degree courses at one go but that is not allowed by the UGC guidelines. At the most what you can do is go for a regular course say B.Sc. in Mathematics and then go for some correspondence course in the next interest line as per your liking. You can even think of something like management line course though you have a science background. For example doing a BBA. By doing this you can complete one regular and one correspondence course at one go. There is one small catch here that would you be able to cope up with these two courses undertaken simultaneously? In many cases some students go for this mode but their scoring in both the courses is sometimes adversely affected. So, you have to take a call on this aspect and remember one in hand is better than two in the bush.