Can you please check these sentences and tell me which one are possible?

Thank you.

1) He didn't let on the secret to anyone.
He didn't let out the secret to anyone.
2) He didn't let on that he knew Mary's secret.
He didn't let out that he knew Mary's secret.
3) Write 5 phrasal verbs related to work, 5 related to work (I don't know how to write this: I want students to write phrasal verbs like get off work, to be laid off, to take time off work etc.)
She asked me how many people had turned up at the party.
4) She offered to take on the responsibility for the firm.
5) When her husband died, she took over as the head of design.

1. Neither is good.

2. 1st one is OK; 2nd one is not.

3. Write five phrasal verbs that are related to work and jobs.

2nd sentence is OK.

4. OK

5. OK

To determine which sentences are possible, let's analyze each one:

1) He didn't let on the secret to anyone.
He didn't let out the secret to anyone.

Both of these sentences are possible. "Let on" means to disclose or reveal something, while "let out" means to release or reveal something that was previously kept secret. These sentences express that the person did not disclose the secret to anyone.

2) He didn't let on that he knew Mary's secret.
He didn't let out that he knew Mary's secret.

Both of these sentences are also possible. They convey the idea that the person kept the knowledge of Mary's secret to themselves without revealing it to others.

3) Write 5 phrasal verbs related to work, 5 related to work (I don't know how to write this: I want students to write phrasal verbs like get off work, to be laid off, to take time off work, etc.)

To complete this task, you can ask your students to write five phrasal verbs related to work. Here are a few examples:
- Show up for work
- Clock in/out at work
- Put in extra hours at work
- Work out a solution
- Break down at work

The specific examples can vary, but the idea is to have the phrasal verbs relate to work activities or situations.

4) She offered to take on the responsibility for the firm.

This sentence is possible. "Take on" means to accept or assume a responsibility or task. It suggests that she volunteered or offered herself to be responsible for the firm.

5) When her husband died, she took over as the head of design.

This sentence is also possible. "Take over" means to assume control or leadership of something. In this case, it implies that she assumed the role of the head of design after her husband passed away.

I hope this helps! Let me know if you have any more questions.