Everyone was excited (of/about) the trip to the mountains. We are going to play basketball, would you...

Everyone was excited about the trip to the mountains.

We are going to play basketball, would you like to join us?

The new road is going to connect the two cities.

I introduced myself to my new classmates.

They’ll have to consider the new facts.

Have you bought tickets to Australia yet?

Where are your seats? - They are in the circle, in Row Two.

Andrew devoted most of his time to painting.

They tried hard to find the answer and they found it in the end.

Hold on a minute, I’ll just get a pen!

I will never agree with you on this matter.

Be attentive to your younger brothers and sisters.

Can you see to my pets while I’m away?

Brian admires his talented cousin.

He entered the university in 2005 and graduated from it in 2010.

This fruit salad is made of apples, plums and apricots.

The toy tower was built with a lot of tiny instruments.

They are responsible for the cooking.

My little brother is ill. He must be looked after.

The campers put out the fire before leaving.

Jim has been putting off his work for years.

Sure, let's analyze each sentence to determine the correct prepositions or particles to use. Here are the detailed explanations:

1. Everyone was excited (of/about) the trip to the mountains.

   • Correct: about
   • Explanation: The preposition "about" is used to indicate the cause of excitement. "Excited about" is a common collocation.

2. We are going to play basketball, would you like to join (-/to) us?

   • Correct: -
   • Explanation: The verb "join" is directly followed by the object "us" without any preposition.

3. The new road is going to connect (to/-) the two cities.

   • Correct: -
   • Explanation: The verb "connect" can be used without a preposition when followed directly by the objects. "Connect the two cities" is the correct form.

4. I introduced myself (to/for) my new classmates.

   • Correct: to
   • Explanation: "Introduce" is followed by "to" when referring to presenting oneself to someone.

5. They’ll have to consider (with/-) the new facts.

   • Correct: -
   • Explanation: The verb "consider" does not require a preposition before the object. "Consider the new facts" is correct.

6. Have you bought tickets (in/ to ) Australia yet?

   • Correct: to
   • Explanation: "Tickets to" a destination is the correct prepositional phrase.

7. Where are your seats?- They are (on/in) the circle, (in/-) Row Two.

   • Correct: in, in
   • Explanation: "In the circle" and "in Row Two" are the correct prepositions for seating arrangements.

8. Andrew devoted most of his time (for/to) painting.

   • Correct: to
   • Explanation: The preposition "to" is used to indicate the activity or cause to which time is devoted.

9. They tried hard to find the answer and they found it (at/in) the end.

   • Correct: in
   • Explanation: The phrase "in the end" means "finally" or "eventually," indicating the conclusion of an effort or process.

10. Hold (on/up) a minute, I’ll just get a pen!

    • Correct: on
    • Explanation: The phrasal verb "hold on" means to wait for a short period.

11. I will never agree (with/to) you on this matter.

    • Correct: with
    • Explanation: "Agree with" is used when referring to people or their opinions and statements.

12. Be attentive (to/with) your younger brothers and sisters.

    • Correct: to
    • Explanation: "Attentive to" means giving attention or care to someone.

13. Can you see (to/off) my pets while I’m away?

    • Correct: to
    • Explanation: "See to" means to take care of or look after something.

14. Brian admires (of/-) his talented cousin.

    • Correct: -
    • Explanation: The verb "admire" does not require a preposition before the object. "Admires his talented cousin" is correct.

15. He entered (in/-) the university in 2005 and graduated (from/-) it in 2010.

    • Correct: -, from
    • Explanation: "Entered the university" is correct without a preposition. "Graduated from" is the correct phrase.

16. This fruit salad is made (from/of) apples, plums, and apricots.

    • Correct: of
    • Explanation: "Made of" is used when the materials are still recognizable in the final product.

17. The toy tower was built (with/by) a lot of tiny instruments.

    • Correct: with
    • Explanation: "Built with" is used to indicate the tools or materials used in construction.

18. They are responsible (for/to) the cooking.

    • Correct: for
    • Explanation: "Responsible for" indicates the duty or task someone is in charge of.

19. My little brother is ill. He must be looked (for/after).

    • Correct: after
    • Explanation: "Look after" means to take care of someone.

20. The campers put (out/down) the fire before leaving.

    • Correct: out
    • Explanation: "Put out" is a phrasal verb meaning to extinguish a fire.

21. Jim has been putting (off/down) his work for years.

    • Correct: off
    • Explanation: "Put off" means to postpone or delay something.

These explanations should help clarify why each preposition or particle is used in the given context.