How were these pseudo-scientific theories used to justify racist policies and imperialist expansion

Since you didn't specify one, I'll give you a little challenge: global climate change. 

yes...this is not a "historical" answer, but please bear with me as you may learn something quite a bit more useful than a history lesson... 

climate change is a very trendy topic nowand many of its proponents are absolutely convinced of its "science".. 

...however, for many this absoute faith in the "science" translates all-too-easily into an absolute faith in the righteousness of the proposed "solutions"... 

...for example, president obama recently celebrated his participation in a "landmark" international accord to combat climate change... many of his supporters lauded him for "taking a stand against global corporations and their exploitation of people and natural resources..." 

great right? 

this agreement contained two provisions that seemingly went unnoticed first, nations considered "developing" will not have to comply with the strict emmisions restrictions... second, all nations are required to designate a certain percentage of their natural forests & jungles as untouchable "preserves." 

sounds good right? please think it through... 

the agreement gives these nations the authority to displace any indigenous peoples who just happen to call those "preserves" home... over a million people are expected to be kicked off their ancestral lands in DR Congo alone. 

keep in mind that most of these people will be illiterate hunter-gatherers ... how do you think they will manage to support themselves? 

guess what? because those nations will not be required to meet environmental standards, a bunch of new factories, mines and refineries are sure to open up thereand they'll have all the cheap labor they could ever need! Yay! 

and guess who owns those businesses? that's right, mega-corporations...guess who those corporations support? that's right... the very politicians who signed the climate change deal! 

so you were asking about how "pseudo science" supports/justifies exploitation and imperialism? wellas the old rhyme goes: the wheels on the bus keep on going 'round and 'round... don't they?

The correct answer is b