(A) Assume the upward direction is y and the horizontal direction is x. Then = 0 everywhere and does not change as you go in the x direction ( does, however, change as you go in the y direction). Thus,
So, the equation is obeyed.
(B) shows a constant magnetic field, which is clearly divergenceless.
(C) shows the magnetic field due to a current loop, which is clearly possible.
(D) shows the electric field due to a point charge (i.e. an electric monopole); since magnetic monopole's do not exist (which is equivalent to the state ), this field configuration is not possible. Thus, answer (D) is correct.
(E) is the magnetic field around a wire, which is clearly possible.