Commerce

Yes, you can do B.Sc. In Mathematics, The Mathematics B.Sc. Programme is broad-based, meaning that you'll develop your skills across a wide range of areas. You will study many aspects of pure and applied mathematics, together with general concepts of mathematical modelling. As per my understanding, Following are the Private Engineering Colleges in North India:-
Birla Institute of Technology and Sciences (BITS), Pilani. Birla Institute of Technology (BIT), Mesra. VIT Bhopal University. SRM University Sonepat. Amity University Noida. Geeta University
Nirma University of Science and Technology.

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You cannot decide to get into college of your choice in Mcom in Delhi University. Admission is based on 2 criteria:
Direct Admission - Here, you will get admission based on your percentage in graduation. For Dse, Srcc it goes up to 95 + for general category, for example.
Indirect Admission - University conducts an entrance. The paper carries negative marking. So, it depends on your marks & relative ranking.
On the basis of your either score in graduation or entrance, you will be given admission in top colleges like Delhi School of Economics, SRCC, Rajdhani etc.

You can check colleges offering hotel management course and apply for them. Some colleges offering the same are IHM Pusa, IHM Delhi, IHM Mumbai.

According to me B.Com in English medium is more versatile and can get you a job easily you can do Masters too easily. As you have completed your 12th from gujrati medium it will be a little difficult for you to adjust to English medium but it will be worth your efforts.

Yes, you can do it. But before that check eligibility criteria where you apply because like dse, JNU has the eligibility criteria for Maths. But other institutions don't have it.

It's totally entrance based exam. You should check their official website for it and cut off too.

The first semester fees for the 3 year bcom programme is INR 5350.

There are several colleges in India's that provides you Diploma in banking and financial course
Birla Institute of Management Technology Greater Noida. UNIPUNE - Savitribai Phule Pune University (SPPU) Ganeshkhind, Pune. Great Lakes Institute of Management, Gurgaon
University of Madras - Institute of Distance Education Chepauk, Chennai.