Hello Devansh,

Yes, you can take CUET-PG with an active backlog since eligibility is generally having passed a qualifying degree before the admission. But, universities like DU require you to clear all the backlog and submit all final results by a particular deadline (most likely late July).  If your result of the 6th semester is delayed and beyond that timeout, then it may jeopardize your admission, as some systems like IIT JAM admissions close around that same time.

Yes, since most universities, including DU, accept "appearing candidates," you can take the CUET-PG exam in your sixth semester even though you have an active backlog.
However, until you clear the backlog and turn in your final grade, your admission will be provisional.
Results for the sixth semester are usually released by DU by the end of July, which may coincide with the dates for CUET-PG admission.

Your admission may be cancelled if the backlog is not cleared prior to the final document verification.
Since IIT JAM's admissions process ends in late July, you need to make sure that results and backlogs are cleared in time.