Here are the verbs in the correct tense:

1. My brother passed the exam into university last year.
(Past simple for a completed action in the past.)


2. She has been studying about people’s health for years.
(Present perfect continuous for an action continuing over a period of time.)


3. The visit to the Temple of Literature was so meaningful to me.
(Past simple for a completed event in the past.)


4. All the homework was done by Peter this morning.
(Past simple passive for a completed action.)


5. John enjoys arranging flowers in the morning.
(Gerund after "enjoys.")


6. Junk food and seafood sometimes give an allergy.
(Present simple for a general truth or habit.)


7. All the students in our school have visited the first University in Viet Nam.
(Present perfect for an action that happened at an unspecified time in the past.)


8. You had better not spend much time on TV.
(Bare infinitive after "had better.")


9. David and his father visited the Temple of Literature last week.
(Past simple for a completed action in the past.)


10. A new university will be established in our province in the near future.
(Future passive for an event expected to happen.)