Two GET methods with different query parameters

Because a resource is uniquely identified by its PATH (and not by its params). Two resources you define have the same PATH.

@Path("/questions/ask")

According to JSR-311 spec:

Such methods, known as sub-resource methods, are treated like a normal resource method (see section 3.3) except the method is only invoked for request URIs that match a URI template created by concatenating the URI template of the resource class with the URI template of the method.

Since your data model includes two distinct resources I suggest making two rest methods with different paths:

@Path("/questions/ask/type")
@Path("/questions/ask/user")

This is the RESTful way, since one URI represents one and only one resource and there should be no overloading. If one URI represents more than one resource that means you got it wrong somewhere.

You cannot overload REST requests.

In your business layer you would have to check which of the two variables are set and then you will have to do the required processing.