Dual

You should work somewhere in IT or some software developing in online, code contributing you need some of these experience or if you have experience then do what you want to study.

It is better to do specialised area of study and when you do Masters you will further do advanced. When you continue in the same line you become more employable and also can easily do your Ph.D with a stipend.

Board marks are nothing to do with VIT admission but you have to eligible for it atleast 60% in physics, chemistry, maths in intermediate.You have to give VITEEE exam to take admission in VIT.
Additional Information: Predict engineering colleges you can get on the basis of your JEE Rank: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=8321427.

Board marks are nothing to do with VIT admission but you have to eligible for it atleast 60% in physics, chemistry, maths in intermediate. You have to give VITEEE exam to take admission in VIT. Hope this helps. Additional Information: Predict engineering colleges you can get on the basis of your JEE Rank: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=cconnect&utm_medium=CR_JEECP&utm_campaign=8321427.

Yes, NIT does offer an integrated course of B.Sc+M.Sc.

Dear,
Integrated M.Sc B.Ed in chemistry is available in Central University Rajasthan.
Eligibility:
1. You have to complete B.Sc in Chemistry as one of the main subjects with 50%/45% (for SC/ST/OBC.
2. You have to qualify CUCET exam.
Best wishes.

In my opinion, better don't waste your time leaving the existing course and again preparing for JEE. If you have that much interest and dedication, prepare in parallel without leaving your present course.

Dear student,
In order to do a Ph.D, it would be necessary to finish up with your Masters and then apply for a seat to study Ph.D. in a university that offers the stream of your choice. To know which are your best options when it comes to studying Ph.D. abroad, visit Shelldreams Overseas website. They are expert study visa consultants who can guide you in this matter as they specialize in the stream of Ph.D. abroad.

Mostly integrated like B.Tech+MBA, B.Tech+M.Tech etc is of 5 years tenure but in case of BCA+MCA, it's always 6 years.