yes, you can do this with PDF24 Reader (part of PDF24 Creator):
Open the PDF and choose the tool "Snapshot".
Drag a frame around the question. A menu opens: choose "Save to file" (PNG or JPG) or "Copy to clipboard".
Repeat this for all questions.
Put the saved images together into one PDF with "Images to PDF": https://tools.pdf24.org/en/images-to-pdf (the same tool is in the PDF24 Toolbox). With "Page size" set to "Use DPI" each page gets the size of the image.
The snapshot is taken from what you see on the screen, so zoom in first for a sharper result.