Should I use "is" or "are" with "any of X"?

Solution 1:

Any: Determiner and Pronoun sg. & pl.

Although its origins lie as an indeterminate derivative of one, which is of course singular by definition, any can be used both in the singular and the plural.

Per the OED, in the singular, any means:

A __ no matter which; a __ whichever, of whatever kind, of whatever quantity.

And in the plural, any means:

Some __ no matter which, of what kind, or how many.

So that admits dual possibilities, and this remains true whether it’s used as a determiner or a pronoun.

Singular

• Is any man ready?
• I haven’t seen any man who is ready.
• Is any man ready to captain this vessel?
• Has any man stepped forward to lead us?
• Has any of the men stepped forward to lead us?
• Has any stepped forward to lead us?

Plural

• Are any men ready?
• I haven’t seen any men who are ready.
• Are any of the men ready to leave?
• Have any men volunteered to crew the first boat?
• Have any of the men volunteered to crew the first boat?
• Have any volunteered to crew the first boat?

When used pronominally, there is no head noun to guide you the way there is in the any X or any of the X cases. So it depends on the writer’s intent whether to use singular concord or plural.

In your particular situation, you would use singular if only one selection is expected to be true (perhaps because they are mutually exclusive), but you would use plural if more than one could be true. I don’t know without further context, but I suspect that this is what you were thinking, and so why you felt that the plural would be called for in your situation.