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Actually, there is no way we can remove,disable, or hide options from a radio button fields base on a selection from another field because it is not available through conditions. The only possible way you try to work this out is by having multiple radio buttons fields on your form with different sets of options. Then, a particular radio button will just show/hide on the form depending on the date being selected.
Here's a sample form: https://form.jotform.com/61147453306956
In my sample form, you will see that "Full-size Cars" is not available on April 27, 2016.
Please feel free to clone the form so you can examine the fields and conditions in it.
Let us know if you have any other questions or concern. Thank you.