JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
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The new Google Sites doesn't seem to be available on my account just yet, so I am unable to test it. However, I checked the Google Sites help page and it looks like to add a form to the google sites, simply click the INSERT button from the menu on the right and then select Embed URL. You can also check this guide for more info: Add text, images, & other content
To get the URL of your form, simply follow this guide: Where to Find My Form URL?
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