Is this right:
What should I be doing these days?
The answer can be:
You should be preparing for your exams these days.
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What should I be doing these days? - Is correct.
Since it's an exam time, you must be paving the way for it. It's obviously taken that during this time, you (or anyone) should be studying hard.
The answer could be...
Obviously, the exams are near. I should be studying all day!