How to deal with KVPY and NDA along with JEE and boards?

Dear driends and mentors, I am a class 12 student, primary targets are JEE and CBSE.
But i have KVPY and NDA in the next month.

my coaching institute(sri chaitanya) conducts weekly mains and advanced (on sat and sun) on different chapters, in which a few questions are cumiliated.

Is it okay for me to do full papers in between or just stick with the weekly test series of my institute?
i often cant finish the entire syllabus for the weeks portions..

Please help

You can surely attempt full test papers, but as you said that you are unable to finish up the entire syllabus for the weekly test then i would rather say , focus more on your ongoing syllabus and keep revising whatever you have studied earlier , because once left, these incomplete syllabus piles up and becomes backlog which at this stage of your preparation can be very harmful because you won’t be getting much time to cover them up , if you’ll try covering your backlogs then your current syllabus will be left out , so do attempt full test papers , but make sure to atleast complete whatever is being taught currently, and keep on revise the previously learned topics .

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As @Shwetanshu_2018 indicated in the above post...from now onwards try your level best to not create backlogs and for that weekly tests are gonna be very essential! Just move with the pace of the coaching make consider giving an hour or two in the morning to clear your existing backlogs. As of now you may attempt one full paper each week...and increase the frequency as you near the completion of syllabus.
Now as far KVPY and NDA preparations are concerned, you don't have to try anything new...just prepare for jee now! But you may solve the pre year KVPY papers each day.

As per JEE perspective try to solve full length papers only when you have covered at least half of the full syllabus.Go for full length papers if the topic is covered in your coaching even if you are not very confident in the topic.Full length paper solving will give you lot of perspective on how to manage your speed so don't skip it, try to do it once it 2 weeks at least.

As far as your weekly tests are concerned try to work more hours and finish their syllabus.Still if you lag behind try to smartly leave one or 2 topics that are not that important and confidently prepare other topics.But make sure you cover them before the next test.

KVPY exam is very conceptual so make sure you are confident in the core concepts before you attempt the test.Try to look at some previous papers and gauge the pattern and pepare accordingly.