Here you can download some tasks from previous Putnam Competitions that could help you prepare yourselves to the NCUMC:

Putnam 2016 results
Putnam 2015 results
Putnam 2014 results
Putnam2013B
Putnam2013A
Putnam 2012
Putnam 2011
Putnam 2010
Putnam 2009b
Putnam 2009a