There is no change in the volume of a wire due to the change in its length on stretching. The Poisson's ratio of the material of the wire is:

Volume of cylindrical wire, V = πx2L4, where x is diameter of wireDifferentiating both sidesdVdx = π4[2xL+x2.dLdx]Also volume remains constant    dVdx = 02xL +x2dLdx= 0 ⇒ 2xL = -x2dLdx⇒ dxxdLL = -12⇒Poisson's ratio = -12So the correct choice is (b).