Definition/classification of holonomic and non-holonomic constraints

I am a mathematics student. I have Lagrangian and Hamiltonian mechanics as an elective I have taken in this sem. Today I had a test in which I was asked a question:

1. A ball is constrained to move inside a spherical cage. The constraint imposed by the cage is (a) Non-holonomic (b) Holonomic (c) Rheonomic (d) None of these.

I gave the answer as none of these as I thought that constraints imposed by an inequality $rleq a$ (where $r$ denotes distance from origin and a denotes radius of sphere) is unilateral in nature.
But I am told that the answer would be non-holonomic.
Now I was a bit confused as nothing was mentioned about the velocity or time or anything on which the motion would depend inside the sphere. What should be the answer? Is non-holonomic correct?