I had a similar problem like you for question (a) for my first exam. If you have the textbook Organic Chemistry, 8th ed., by Francis Carey et. al, he explains cis vs. trans. stability in cycloalkenes on page 198.
In part A, the compound is a cyclodecene, and 10 is less than 12, so cis is more stable than trans in this case. Don't know if there's a deeper logic behind it like TheHitokiri suggested, but hope it helped a little.
Edit: Sorry, was not aware of issues for copying text directly from book. Don't know if this is a better way, but here's a McGraw-Hill link available to all instead of direct text:
http://dev6.mhhe.com/textflowdev/genhtml/0073402613/5.7.htmLast paragraph has the same exact information.