Test the intent of the code .. always :)
For example: If the point of the constructor being private is to not be seen then what you need to test is this fact and nothing else.
Use the reflection API to query for the constructors and validate that they have the private attribute set.
I would do something like this:
@Test()
public void testPrivateConstructors() {
final Constructor>[] constructors = Utils.class.getDeclaredConstructors();
for (Constructor> constructor : constructors) {
assertTrue(Modifier.isPrivate(constructor.getModifiers()));
}
}
If you want to have a proper test for the object construction, you should test the public API which allows you to get the constructed object. That's the reason the said API should exist: to build the objects properly so you should test it for that :).