Identifying strengths and weaknesses while solving previous years' question papers of UPSC Mathematics optional subject is a crucial step towards effective preparation. It helps in understanding which areas need improvement and which topics you are already proficient in. Here's a detailed approach to identifying your strengths and weaknesses:

1. Understand the Syllabus:
- Familiarize yourself with the entire syllabus of the UPSC Mathematics optional subject.
- Divide the syllabus into different topics and subtopics.

2. Solve Previous Years' Question Papers:
- Obtain previous years' question papers of UPSC Mathematics optional subject.
- Start solving the papers in a time-bound manner, just as you would during the actual exam.
- Attempt as many papers as possible to get a comprehensive understanding of your strengths and weaknesses.

3. Analyze Your Performance:
- After solving each paper, analyze your performance objectively.
- Categorize the questions based on the topics they belong to.
- Note down the questions you answered correctly and the ones you struggled with.
- Keep a record of the time taken for each question and the overall time management.

4. Identify Strengths:
- Look for topics or types of questions where you consistently perform well.
- Analyze the accuracy and speed of your answers in these areas.
- Note down the topics where you have a high success rate and perform well within the given time frame.

5. Identify Weaknesses:
- Identify topics or types of questions where you face difficulties or make errors consistently.
- Pay attention to areas where you take a longer time to solve problems.
- Note down the topics where you have a low success rate or struggle with time management.

6. Create a Study Plan:
- Based on the analysis, prioritize the topics that need improvement.
- Allocate more time for studying and practicing the areas where you are weak.
- Devise a study plan that includes regular practice, revision, and mock tests.

7. Seek Guidance:
- If you find certain topics particularly challenging, seek guidance from subject matter experts or experienced mentors.
- Join online forums or discussion groups where you can clarify doubts and exchange knowledge with fellow aspirants.

8. Regular Practice:
- Continuously practice questions from both your strengths and weaknesses.
- Gradually increase the level of difficulty to enhance your problem-solving skills.
- Monitor your progress regularly and make necessary adjustments to your study plan.

By following this structured approach, you will be able to accurately identify your strengths and weaknesses while solving previous years' question papers of UPSC Mathematics optional subject. This will enable you to focus your efforts on the areas that require improvement and enhance your overall performance in the subject.