The user activity for finding informative meaningful objects needed to solve the problem is considered. To formalize this activity, set theory is used. The mathematical models of formulation of request, analysis of the issued documents and selection of information objects for the solution to the user problem are presented. In addition, mathematical models of intellectual activitiesof user and cognitive processes are developed. The experimental results of the search engines such as Google, Yandex, META, Rambler, Yahoo are given. To evaluate the effectiveness of information retrieval the found documents were divided by pertinent, relevant and irrelevant. Search Performance Ratio is determined with the ratio of pertinent and relevant documents to the number of all the documents in issue. It is advised to take into account information characteristicsof the offered search engines with appropriate coefficient.