For calculating the motional emf across the length of the wire, let us project wire such that \\vec{B}, \\vec{v}, \\vec{l} becomes mutually orthogonal. Thus d\\varepsilon =Bv_0dy=B_0\\left[1+\\left(\\dfrac{y}{L}\\right)^{\\beta}\\right]V_0dy \\varepsilon =\\displaystyle\\int^L_0B_0\\left(1+\\left(\\dfrac{y}{L}\\right)^{\\beta}\\right)V_0dy =B_0V_0L\\left[1+\\dfrac{1}{\\beta +1}\\right] emf in loop is proportional to L for given value of \\beta .for \\beta =0; \\varepsilon =2B_0V_0L \\beta =2; \\varepsilon =B_0V_0L\\left[1+\\dfrac{1}{3}\\right]=\\dfrac{4}{3}B_0V_0L The length of the projection of the wire y=x of length \\sqrt{2}L on the y-axis is L thus the answer remain unchanged.Therefore, answer is 1, 2, 4 .