Sure! Here are the correct answers along with explanations for each question:

1. **Question**: Henry was really a silly boy when we were at high school. I still remember _____ very stupid questions.
- **Correct Answer**: **A. him asking**
- **Explanation**: The phrase "I still remember him asking very stupid questions" is grammatically correct. The verb "remember" can be followed by a gerund (verb + -ing), which describes an action that one remembers occurring. In this context, "him asking" fits appropriately.

2. **Question**: I don't think you have been watering the plants near the gate. She felt ____.
- **Correct Answer**: **A. left out**
- **Explanation**: The phrase "She felt left out" is idiomatic and means that she felt excluded or neglected in some way. The other options do not fit conventionally as there are no such common phrases like "turned out," "omitted out," or "gone out" that would fit logically in this context.

So the complete correct answers are:
1. **A. him asking**
2. **A. left out**