(c) q/2ε0​ .According to Gauss's Law, the flux through a closed cylindrical Gaussian surface is q/ε0. But the question is about an open cylindrical vessel. Now, take another identical vessel and make a closed Gaussian surface enclosing the charge.Total flux linked with the closed Gaussian surface,ØT =q/ε0​ Flux linked with the surface of a open ended cylindrical vessel, Ø=(ØT)/2=q/(2ε0​)