It possible to cover US history in one month with no prior knowledge about it?

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Yes, one can cover it even in 15 days. It depends on you.

Could you please suggest a strategy to cover all the syllabus in 15-30 days?

Read a detailed book for starters 1000+ pages should be your goal you could go ahead and download the Openstax book. Dont take more than 7 days for this, however. Once finished, move onto a guide book for revision(any will do JWT etc) and search for topics name on google with the addition of "lecture slides" so Cold War becomes "Cold War lecture slides".
Focus on oft repeated topics: Black history, Cold War and Civil War, Pakistan and USA after 9/11, and some contemporary topics especially related to US history(Trump Presidency is a hot topic).
You can skip the first step entirely and focus on the shortcut but you need a detailed character of USA which can only be gleamed with an in depth book.
Focusing just on repeated topics you can be able to solve 2/4 questions and maybe even 3 within 5 days. Of course I am assuming you are willing to put in 5-8 hours of study a day.

yes, quite possible

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Yes... its quite possible if you go through most repeated topics and covering every possible angle of the repeated topics

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