The relevance of the research is due to the need of taking into account the learners' cognitive characteristics in the educational process. Knowing the personal qualities of people is also important when choosing an occupation or employment. This is why the paper is aimed at describing the opportunities of the newest Web and mobile applications for studies and self-diagnostics of users based on the cloud technology of diagnosing the human individual and cognitive abilities. The leading approach to studying this problem is the projective and recursive strategy that allows viewing the problem of expert statistics accumulation and user diagnostic results analysis in an integrated way. The paper presents the developments in problem-solving computer environments for diagnosing human individual and integrated abilities. Grounds are given for diagnostics of the main human cognitive abilities: the scope of memory and attention; information processing, reading, typing speeds and others. The website for developing the new diagnostics and conducting studies can be accessed by everyone with any browser via http://selftest.ufoproger.ru. The website has been developed by the university students under the guidance of professor N.I. Pak. The materials of the paper are of practical value for teachers designing the educational process up to the learners' individual characteristics.