Yes, the previous years question papers of UPSC Mathematics optional subject are helpful for understanding the common mistakes made by candidates. Here's why:

1. Familiarity with the exam pattern:
- By going through the previous years' question papers, candidates can get a clear idea about the exam pattern, types of questions, and the level of difficulty.
- It helps them understand the distribution of marks and the weightage given to different topics, allowing them to plan their preparation accordingly.

2. Identifying commonly made mistakes:
- Previous years' question papers provide an opportunity to analyze the mistakes made by candidates in the past.
- By carefully reviewing the solutions and explanations, candidates can identify the common errors made by others and learn from them.
- It helps in understanding the areas where candidates tend to make mistakes frequently, allowing them to focus more on those topics during their preparation.

3. Learning from different approaches:
- Mathematics is a subject that often offers multiple approaches to solve a problem.
- Going through previous years' question papers exposes candidates to different methods and strategies adopted by successful candidates in solving a particular problem.
- It helps candidates broaden their problem-solving skills and enables them to choose the most effective approach during the exam.

4. Time management:
- UPSC exams are known for their time constraints, and candidates often struggle with managing time effectively during the exam.
- By practicing previous years' question papers, candidates can develop their speed and accuracy in solving mathematical problems.
- It helps them understand the time required for each question and allows them to strategize their time management during the actual exam.

5. Self-assessment:
- Solving previous years' question papers provides candidates with an opportunity to assess their own preparation level.
- By comparing their answers with the model solutions, candidates can identify their strengths and weaknesses in different topics.
- It helps them understand where they need to put in more effort and practice to improve their performance.

Conclusion:
In conclusion, previous years' question papers of UPSC Mathematics optional subject are indeed helpful for understanding the common mistakes made by candidates. It not only provides familiarity with the exam pattern but also helps in identifying commonly made errors, learning from different approaches, managing time effectively, and self-assessment. Therefore, candidates should make use of these question papers as an integral part of their preparation strategy.