For most of the important processes in DNA metabolism, a protein has to reach a specific binding site on the DNA. The specific binding site may consist of just a few base-pairs while the DNA is usually several millions of base-pairs long. How does the protein search for the target site? What is the most efficient mechanism for a successful search? Motivated by these fundamental questions on intracellular biological processes, we have developed a model for searching a specific site on a model DNA by a single protein. We have made a comparative quantitative study on the efficiencies of sliding, inter-segmental hoppings and detachment/re-attachments of the particle during its search for the specific site on the DNA. We also introduce some new quantitative measures of efficiency of a search process by defining a relevant quantity, which can be measured in in-vitro experiments. © 2009 World Scientific Publishing Company.