Helping students learn why Gauss's law can or cannot be easily applied to determine the strength of the electric field at various points for a particular charge distribution, and then helping them learn to determine the shape of the Gaussian surfaces if sufficient symmetry exists can develop their reasoning and problem solving skills. We investigate the difficulties that students in calculus-based introductory physics courses have with the concepts of symmetry, electric field and electric flux that are pivotal to Gauss's law of electricity. Determination of the electric field using Gauss's law requires discerning the symmetry of a particular charge distribution and being able to predict the direction of the electric field everywhere if a high symmetry exists. It requires a good grasp of how to add the electric field vectors using the principle of superposition, and the concepts of area vector and electric flux. We administered free response and multiple-choice questions and conducted interviews with individual students using a think-aloud protocol to elucidate the difficulties students have with the concepts of symmetry, electric field and electric flux. Here we discuss student responses to some questions on a multiple-choice test administered to them. The test can be used both as a teaching and assessment tool.