Right choice is (a) γ(c)=0
The explanation is: The Kutta Condition says the flow leaves the trailing edge smoothly. The trailing edge is at chord length c for a thin airfoil which gives γ(c)=0. Also, γ(x)=0 or γ(ξ)=0 is not true for all x or ξ. \(\frac {dz}{dx}\)=0 is the definition of the symmetric airfoil, not Kutta condition.