Ответ:

  1. Is she a dentist or an economist?
  2. Have they got a dog or a cat?
  3. Do they want to ski or skate?
  4. Are you from Tomsk or from Rostov?
  5. Does he like football or volleyball?

Ответ: 1 — Is; 2 — Have; 3 — Do; 4 — Are; 5 — Does.