1. He was afraid of (take) for another person. being taken Yes. 2. Under police questioning he admitted (invent) the story. having invented Yes. (But 'inventing' is also possible) 3. I remember (read) about it in one of the historical novels. reading Yes. (But 'having read' is also possible) 4. He got out his jacket, which had the appearance of (put) away for a long time. being put No. You need a passive here. 5. It hadn’t been worth (leave) Paris. leaving Yes. 6. Victoria displayed a distinct pleasure at (allow) to tell her story. having allowed No. You need a passive here. 7. She gave me the impression of (be) through much and of (be) sure of herself. being There are two verbs needed here. The first needs to be in the perfect form. 8. After carefully (examine) the room several times I returned my attention to the mountain. having examined. Yes (but 'examining' is also possible) 9. She mentioned (see) me on television the previous night. You don't seem to have completed this sentence. 10. For fear of (delay) by Paul she had not gone up to bed. being delayed Yes. An odd sentence, but grammatically OK.