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Hi Kanishka,
The exam for both B.Arch and B.Planning is the same. So, you will only have to give one exam to get admission in any one of the above mentioned courses. So, yes if the exam is same then, the single exam will be held on the same day only.
Refer here for more info - https://engineering.careers360.com/articles/jee-main-paper-2-analysis
Feel free to ask doubts in the Comment Section.
I hope this information helps you.
Good Luck!
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