Analyzing the solutions of previous year papers can indeed be beneficial in improving critical thinking and problem-solving skills, especially when it comes to Public Administration questions. Here's a detailed explanation of how it can help:

1. Understanding question patterns:
- By analyzing the solutions of previous year papers, you can identify the recurring patterns and types of questions that are commonly asked in the Public Administration exams.
- This understanding of question patterns enables you to anticipate and prepare for similar types of questions in the future.
- It also helps you familiarize yourself with the specific areas of knowledge that are frequently tested, allowing you to focus your studies accordingly.

2. Learning effective problem-solving techniques:
- By reviewing the solutions of previous year papers, you can observe the problem-solving techniques and strategies employed by successful candidates.
- This exposure to different approaches can broaden your own problem-solving toolkit and enhance your ability to tackle similar questions effectively.
- You can learn from the mistakes made by others as well as the innovative solutions they have devised, which can further refine your critical thinking skills.

3. Enhancing subject knowledge:
- Analyzing the solutions of previous year papers gives you the opportunity to deepen your understanding of the subject matter.
- By carefully examining the explanations and reasoning provided in the solutions, you can gain valuable insights into the concepts, theories, and frameworks relevant to Public Administration.
- This process of continuous learning helps build a strong foundation of subject knowledge, which is crucial for effective critical thinking and problem-solving.

4. Identifying knowledge gaps:
- While analyzing the solutions, you may come across questions or concepts that you find difficult to comprehend or answer correctly.
- This serves as a valuable diagnostic tool to identify your knowledge gaps and areas that require further attention.
- By recognizing these weaknesses, you can focus on strengthening your understanding of specific topics, thereby improving your overall problem-solving skills.

5. Boosting confidence:
- Regularly practicing with previous year papers and analyzing their solutions can boost your confidence levels.
- As you become more familiar with the exam format and the types of questions asked, you gain confidence in your ability to approach and solve them effectively.
- This confidence is essential for maintaining clarity of thought, making logical connections, and arriving at well-reasoned answers during the actual exam.

In conclusion, analyzing the solutions of previous year papers is a valuable strategy for improving critical thinking and problem-solving skills in Public Administration. It helps you understand question patterns, learn effective problem-solving techniques, enhance subject knowledge, identify knowledge gaps, and boost confidence. Regular practice and analysis of previous year papers can significantly contribute to your success in the UPSC exams.