The correct option is (a) fcr = kπ^2E / [12(1-μ^2)(d/t)^2].
Easy explanation: The elastic buckling stress fcr of thin flat plate of length L, depth d and thickness t simply supported along all four edges and loaded by shear stresses distributed uniformly along its edges is given by fcr = kπ2E / [12(1-μ^2)(d/t)^2], where buckling coefficient can be approximated by k=5.35 + 4(d/L)^2, when L ≥ d and k = 5.35(d/L)2 + 4, when L ≤ d.