In the JEE B.Arch session, if I did not give, save and next for the drawing question (attended in the booklet), will they evaluate?

Hi Usually, if you don't save but you have attempted, your answer will automatically get saved after the exam time expires. But you can just confirm by reading the instructions on the website, if there is a mock test option.

Usually when you give the exam you have to click that option otherwise your answer is not evaluated. This is subject to the instructions elsewise. So the most chances are that it will not get evaluated.