Here are suitable words to fill in the blanks:

1. **accommodation**
2. **ask**
3. **which**
4. **some**
5. **If**
6. **find**
7. **for**
8. **about**
9. **few**
10. **several**

So the completed passage would read:

If your application for a place at university is successful, you will need **accommodation** to live. You should immediately contact the university and **ask** for information about their "halls of residence," **which** are rooms for students. Most universities don't have **some** accommodation for all their students. **If** you are unlucky and the university doesn't offer you a room, it is your responsibility to **find** somewhere. Start looking **for** a room in a shared house or flat. Many students have **about** finding somewhere to live very near the university, but if you are prepared to travel a **few** kilometers, you should be **several** to find a room reasonably quickly.