Top wo Nerae: Cybernetic High-School III

An official strip-quiz game featuring characters from the Gainax OVA. It was actually developed by Gainax itself. It was only released in Japan, in 1990.

The third game in the Dennou Gakuen/Cybernetic High School series features characters from Gunbuster.  You play as a generic unnamed character who is training to become another pilot; for various reasons, you can encounter each of the three girls at various places around the Exelion; they challenge you with quizzes, and (naturally) remove articles of clothing should you get enough answers correct. You need to get at least 70% correct in order to "win" a round of quizzing, anything less is an immediate game over. Each girl asks questions about different subject matter that is of interest to them; ex., Noriko focuses on sports and anime trivia while Jung asks questions relating to science, Russia, and porn.   


Takaya Noriko: The main character of Top wo Nerae, she is initially a clumsy pilot, but has great potential. She initially idolizes Kazumi. 
Jung Freud:  Named after two famous psychologists, she is a Soviet pilot and a genius. She's also a bit mean-spirited at times, but still becomes a good friend of Noriko and Kazumi. 
Amano Kazumi: An incredibly talented pilot, she's in love with coach Outa.