Yes, attempting previous years' sociology optional papers across different difficulty levels can improve your versatility in answering questions. Here's why:

1. Enhances familiarity with exam pattern and question types:
- Solving previous years' papers helps you become familiar with the pattern and structure of the exam.
- You can identify the types of questions asked, such as short-answer, essay-type, or case-study based questions.
- This familiarity allows you to prepare accordingly and develop effective strategies for answering different types of questions.

2. Improves time management skills:
- By attempting previous years' papers, you can practice managing your time effectively during the exam.
- You will become more proficient in allocating time to each question based on its difficulty level and marks weightage.
- This helps in avoiding time wastage on tough questions and ensures that you can attempt all questions within the given time frame.

3. Enhances understanding of key concepts and theories:
- Previous years' papers often cover a wide range of topics and concepts from the sociology syllabus.
- By attempting these papers, you can reinforce your understanding of important theories, thinkers, and sociological concepts.
- This strengthens your knowledge base and enables you to provide comprehensive and accurate answers during the exam.

4. Improves analytical and critical thinking skills:
- Sociology optional papers often require candidates to analyze and evaluate social issues, theories, and empirical studies.
- By solving previous years' papers, you can practice applying analytical and critical thinking skills to different scenarios and questions.
- This enhances your ability to critically analyze sociological problems, develop logical arguments, and present coherent answers.

5. Identifies knowledge gaps:
- Attempting previous years' papers helps you assess your preparation level and identify any gaps in your knowledge.
- You can identify areas where you need to focus more attention and revise thoroughly.
- This targeted approach ensures that you cover all the important topics and improve your overall understanding of sociology.

Conclusion:
Solving previous years' sociology optional papers across different difficulty levels is an effective strategy to improve your versatility in answering questions. It enhances familiarity with the exam pattern, improves time management skills, strengthens understanding of key concepts, enhances analytical and critical thinking skills, and helps identify knowledge gaps. By incorporating this practice into your preparation strategy, you can boost your confidence and perform better in the UPSC exam.