Sure, here are the correct words to fill in the blanks:

1. It’s not fair. You’re always picking **on** me.
2. You look very guilty. What have you been getting **up to**?
3. My parents are not **interested** in modern music. They are **behind** the times.
4. At that time they were poor, and they went **through** a difficult time.
5. He gained ascendancy **over** all his main rivals.
6. We have to go **on with** our work right now, or we won’t finish it on time.
7. The two trains came **within** ten metres of collision.
8. The skyscraper stands out **against** the blue sky.
9. I got **into** the Arts Faculty at the University of London to study history.
10. As the detective stories become popular once again, the publishing house decides to bring **out** a new edition of Christie’s work.