The purpose of this paper is to assess the efficiency of teaching departments in Panjab University, Chandighar. The Data envelopment analysis and Tobit analysis is used to assess the teaching and research efficiency of a set of departments. Six models are proposed based on different parameters to cover various drivers of efficiency. We used both Charnes-Cooper-Rhodes (CCR) and Banker, Charnes and Cooper (BCC) output oriented model with three inputs and three outputs. Next, we present some important differences in efficiency of these departments. We also define benchmarks for inefficient departments and quantify the gaps to be fulfilled by them in order to become efficient. Further the robustness of DEA results was tested with help of Sensitivity analysis. The paper provides evidence that among teaching performance, the majority of teaching efficient departments were from the Social Sciences group and over the years, the teaching efficiency of Sciences departments improved and that of the Languages departments decreased. It is further observed that the majority of research efficient departments were from Sciences group, indicating that these departments are good performers for research activities like publications, research projects and paper presented.