Useful methodologies for solving complex problems in UPSC examinations include the problem-solving approach and critical thinking. Candidates can employ the SWOT analysis technique to identify strengths, weaknesses, opportunities, and threats related to various issues. Moreover, breaking down problems into smaller parts facilitates better understanding and tackling of intricate questions. Using the analytical method for case studies and organizing information systematically enhances clarity in answers. Practicing with mock tests also helps in developing time management and decision-making skills required for effectively handling challenging questions.