M.Arch

Yes, you can get admission in various private colleges.
But, for getting a reputed college of the nation you should appear in JEE Mains exam, after that you will be eligible to get admission in various NIT and IIT.

The eligibility requirements in NIT, Trichy for M.Arch and others PG programs is as under:-
For a candidate to be eligible for M.Tech./M.Arch./M. Plan./M.Des. programme: Must have a valid GATE Score of the year 2016 / 2017 / 2018.
In qualifying degree the candidates should have passed and secured at least 6.5 CGPA (on a 10-point scale) or 60% for OC/OB, whereas 6.0 CGPA (on a 10-point scale) or 55% in case of SC/ST/PwD candidates. The above mentioned CGPA/Percentage should be awarded by a recognized University/Institute.
So you can not take admission in NIT, Trichy without a valid gate score.

Hello,
The eligibility for M.Arch in India is to have completed B.Arch.

Here are a few links to help you-
https://d13mk4zmvuctmz.cloudfront.net/assets/pdf/Reasoning1.pdf
https://d13mk4zmvuctmz.cloudfront.net/assets/pdf/Reasoning2.pdf
https://d13mk4zmvuctmz.cloudfront.net/assets/pdf/Reasoning-3.pdf
https://d13mk4zmvuctmz.cloudfront.net/assets/pdf/Aptitude1.pdf
https://d13mk4zmvuctmz.cloudfront.net/assets/pdf/Aptitude3-.pdf
For more links to the papers, please click this link too- https://www.shiksha.com/b-tech/mht-cet-exam-question-papers.

Construction management as a M.Arch specialization is offered by Dr.D.Y Patil College of Architecture.

You might get admission in some college for M.Arch. The eligibility differs from one institution to another. I would advise you to contact the colleges where you wish to apply and inquire about the eligibility criteria.

Hi Deekeshita,
B.Des results will be out probably by next week.

Hello,
Both the exam tests have similar topics and difficulty as well. It depends, if your idea is clear and focused towards CEPT only. Then, taking CEPT entrance is an option. GATE-AR would open more colleges for you.