Here are the correct answers for each sentence:
C may
(May I use your phone, please?)A was built
(This school was built in the 1960s.)C was
(Maths was my favourite subject when I was at school.)A would become
(If I had a good voice, I would become a singer.)C job
(Stewart wants to get a job as an accountant.)A boat
(Don't worry; everyone came in late today, so we're all in the same boat.)B whose
(Mark, whose cousin works on the ISS, wants to become an astronaut too someday.)A to fix
(Tom finally managed to fix his computer when he had understood the case of the problem.)C will you take
(What time will you take Susan to her piano lesson this afternoon?)B will have been waiting
(By the time Linda gets here, we will have been waiting for her for more than an hour.)A get
(Don't forget to call Mr. Smithers when you get to the office.)A keep
(With four little children running around, it's not always easy for Sarah to keep the house tidy.)B shelter
(If you're looking for a dog, why don't you get one from the animal shelter?)B had done
(After Barney had done his chores, he had some rest.)C has only sold
(Jane has only sold five of her paintings so far, but she hopes she'll sell more.)