B.Des

If it is clashing, then you will have to appear only for one and let go of another one.

For admission in this course, you need to have given NID entrance exam.
To know more visit:
https://www.shiksha.com/design/communication-design/course/b-des-in-animation-film-design-national-institute-of-design-ahmedabad-paldi-255171

See, the rank depends upon the number of seats occupied by the upper ranks students like in 2015 the closing rank for this course was 25K but in 2017 it lowered down to 39K this is about the rank and cut-off.

Bachelor of Design (B. Des or B. Design) is an undergraduate degree course in the field of Design, where the key aspects are innovation and creativity. Students who have an edge over imagination and a good taste in designing may opt for this course. Duration :
The duration of the course is 3 years and 6 semesters in some colleges while some college offer 4 years and 8 semesters of Bachelor of Design (B. Des or B. Design). .

It will cost you around 70k per year for the tuition fees, plus all other amenities like hostel and mess and laundry etc. So, for that you have to pay more but these amenities are optional if you want you otherwise they are not compulsory.

You can see the fee structure on this link- https://presidencyuniversity.in/content/uploads/2019/03/DESIGN.pdf
Contact details are here https://presidencyuniversity.in/contact-us/.

Yes, Chandigarh University provide B.Des in interior design and this course is for the 3 years and admission to this course is done on the basis of NATA score.

The best for interiors would be B. Des, as B.Sc will give you knowledge of Science. Except basic maths, no part of Science is needed for Interiors. So, it's better to go with B. Des. This will help you get trained with your hand drawings, sketching and lines, which is in fact very useful in interiors. All the best.

You can download previous question papers of NIFT to have an idea https://www.shiksha.com/design/nift-entrance-exam-question-papers.