Architecture Entrance Exam

Yes, you can proceed for application in BArch.
Eligibility criteria of BArch is as:-
Pass with 50% aggregate marks in 10+2 with English, Physics, Chemistry and Mathematics and pass with 50% aggregate marks in Physics, Chemistry and Mathematics, subject to qualifying NATA 2022 Or securing 60 Percentile or above marks in JEE (Main) Paper II.
Or
Pass with 50% in Diploma (any stream) (3 years) recognized by Central or State Govt. (with Mathematics) or equivalent,
subject to qualifying NATA 2022 Or securing 60 Percentile or above marks in JEE (Main) Paper II.
Admission Criteria
Merit prepared with weightage of 50% marks for aptitude tests (NATA 2022/ JEE (Main) Paper II) and 50% marks in the qualifying examination, subject to eligibility criteria.
School of Architecture & Design Ranked 12th among all Government & Private Architecture Institutions in India
B.Arch and M.Arch (Executive) programmes are approved by Council of Architecture (COA), a statutory body of the Government of India for the regulation of the architectural education and practice of profession and for maintaining the register of architects.

No you cannot apply for B.Arch course without studying 12th with Science stream. I will suggest you to do BBA then MBA course. BBA course will give you an exposure in management field. After completing BBA you can go for MBA. MBA will provide highly challenging job for you. Different specializations are there in MBA. If you are looking for a career in marketing, then MBA in Marketing is a good option, Because now a days mostly companies recruited students for marketing jobs. The Bachelor of Business Administration degree is considered by many as the degree of the future. It is a professional degree that is rising in popularity among students who want to make a career in management right after their 12th standard exams. This degree is also apt for students who want to pursue management studies after graduation. With a BBA degree, they already have a strong base in management studies and they fare better than students who are not from a management background. Best Universities
ITER Bhubaneswar, Bhubaneswar. Geeta University, Panipat
MSRIT Bangalore - Ramaiah Institute of Technology. SRM
VIT
BITS Pilani
Amity University.

I would suggest Chandigarh University because it offers a CUCET exam by which you can get a scholarship of up to 100% and it also gives scholarship on the basis of your JEE Main score. A five-year, full-time undergraduate programme leading to the degree of "Bachelor of Architecture" is available. For candidates to acquire the art of designing, planning, and building physical structures of various types, the course combines theoretical and practical expertise. Bachelor of Architecture programmes are offered by numerous prestigious Indian universities. I would suggest Chandigarh University because it has 100% placements
For Chandigarh University students, the 2018-19 placement season was a dream come true, with over 627 top multinational corporations making 6314 INR offers to students.31.77 LPA is the most expensive package available. INFRASTRUCTURE: (Amazon, Microsoft, SAP Labs, VMWare, HP, Deloitte, Cognizant, Sapient, Hitachi, Practo Technologies, Flipkart, Gwynniebee India, and Zomato). .