Science

In order to seek admission in B.Sc in psychology, you have to complete 10+2 stage from a recognised board. Unfortunately, Diploma is not directly equivalent to 10+2. You will have to check with each university where ever you apply for B.Sc in psychology whether they accept Diploma in engineering as equivalent to 10+2 or not.

Vellore is one of the leading universities. You may get a better placement from this college.

All MBA specialisations have compulsory papers on Quantitative Techniques for decision making which includes basic maths and statistics. Anybody with an understanding of 10th level maths can handle this subject. Finance and data analytics requires a good understanding of maths. Therefore, you may choose any other specialisation. MBA HR will be a good option for you.

Institute of Hotel Management, run by ministry of Tourism are good places. Known as IHM, these places offer many specialisations as well. Most of the universities have their hotel management institutions like Kurukshetra University has or even Amity University, Noida has. It depends on which region are you asking about.

No Indian university offers online M.Sc in Chemistry, but you can go for distance mode of education as there are some universities offering part-time or distance M.Sc in chemistry course.

Actually, dear M.Sc in stats is a wide course related to business and economics. So I will advise you to go for this course on a regular basis. And, in terms of college, you should apply to central universities and to TATA institute also.

For the course you desire, BHU and DU are the top most universities in India.
All the best.