Correct option is (d) fcr = kπ^2E/[12(1-μ^2)(d/t)^2].
The best I can explain: The elastic buckling stress for thin flat plate of length L, depth d and thickness t simply supported along all four edges and loaded by bending stress distribution, which varies linearly across its width is given by fcr = kπ^2E/[12(1-μ^2)(d/t)^2], where buckling coefficient k depends on aspect ratio L/d and the number of buckles along the plate.