Yes, solving previous years question papers of UPSC Mathematics optional subject can help in improving critical thinking skills in the following ways:

1. Enhances problem-solving abilities:
- Previous years question papers consist of a variety of complex mathematical problems.
- By solving these papers, you get exposed to different types of questions and learn various problem-solving techniques.
- This enhances your ability to analyze problems, identify key concepts, and apply appropriate strategies to find solutions.

2. Develops logical reasoning:
- Mathematics involves logical reasoning and critical thinking to arrive at solutions.
- By practicing previous years' papers, you improve your logical reasoning skills as you learn to identify patterns, make connections between different concepts, and develop step-by-step approaches to solve problems.
- This helps you in developing a structured and logical thinking process, which is essential for tackling complex problems.

3. Improves time management:
- Solving previous years' papers gives you an idea of the time constraints you will face in the actual exam.
- You can practice managing your time effectively by setting a time limit for each question and trying to solve them within that time frame.
- This helps in improving your speed and accuracy, which are crucial in competitive exams like UPSC.

4. Enhances critical analysis:
- UPSC Mathematics optional subject requires critical analysis of concepts, theorems, and their applications.
- By solving previous years' papers, you develop the skill of critically analyzing the given information, identifying important details, and applying relevant mathematical principles to solve problems.
- This enhances your ability to think critically and make informed decisions based on logical reasoning.

5. Familiarizes with exam pattern and style:
- Solving previous years' papers gives you an understanding of the exam pattern, question types, and the level of difficulty.
- This familiarity helps in reducing exam anxiety and boosts your confidence while attempting the actual exam.
- Additionally, practicing previous years' papers helps in identifying your strengths and weaknesses, allowing you to focus on areas that require more attention during your preparation.

In conclusion, solving previous years' question papers of UPSC Mathematics optional subject not only helps in gaining subject knowledge but also improves critical thinking skills, problem-solving abilities, logical reasoning, time management, and critical analysis. It is an effective method to prepare for the UPSC exam and enhance overall performance.