B.Arch

Please refer to the link provided below for an exhaustive list of colleges which offer courses in B.Arch from India. You should be able to navigate to a college of your choice using the filters on the web page. Additionally you can also download their brochures which consists of reviews and rankings, placement information which should help you decide on a suitable college.
https://www.shiksha.com/architecture-planning/colleges/b-arch-colleges-india

Bachelor of Architecture: Eligibility
The duration of the course is 5 years and to get admission into B.Arch. the student must be fulfilled the following conditions:
10+2 or equivalent with minimum 50% marks along with compulsory subject of mathematics.
10th + 3 years diploma in any stream from a recognized university/ board/ institution.
Cleared NATA (National Aptitude Test in Architecture) with the 80% marks conducted by Council of Architecture.

Which entrance exam are you talking about?

Minimum Eligibility to Apply
12th 75%
Additional Details
Mandatory Subjects : Chemistry, Mathematics, Physics
State wise top 20 percentile holder in class 12 exam are eligible to apply.
There are no B.Arch courses available in this college, only B.Tech courses. Above eligibility is for B.Arch courses.

Yes, an architect has to apply his creativity onto a piece of paper as well. So, one needs to have good drawing skills. But one not having good skills can also pursue it with little efforts.