Mastering the art of problem-solving begins with the ability to recognize the nature of the problem at hand. In JEE Advanced, the diversity of problems can be staggering, but they often fall into known categories such as algebra, calculus, physics problem-solving, or organic chemistry. Clever identification can guide you on what formulas to revisit, which principles to apply, and even dictate the strategy to tackle the question. For example, a physics question involving motion may suggest employing kinematic equations, while an algebra problem might hint at factoring or quadratic equations. It is essential to read the question carefully, understand what is being asked, and what data is provided. Also, look out for keywords such as 'maximize', 'prove', or 'calculate', as they hint towards different approaches such as optimization, proof by contradiction, or straightforward computation respectively.

The exercises in JEE Advanced are carefully designed to test depth of knowledge, application skills, and conceptual clarity across various subjects. They often require a combination of concepts and cannot be solved by rote learning alone. Engaging regularly with these exercises is key to success. Apart from just solving problems, it is also important to analyze them. Look for patterns in the types of questions asked and the concepts tested regularly. This can help you prioritize your studies towards the more weighty topics. Moreover, practice with time constraints to simulate the actual exam environment. This helps in improving speed and accuracy, both of which are critical in the JEE Advanced. Utilize resources such as previous years' papers, mock tests, and subject-specific problem books to diversify your practice regime.

After identifying the problem type and using resources to practice JEE Advanced exercises, the next step is to work on problem-solving techniques. A methodical approach to solving problems involves several key strategies. First, start by writing down what you know from the problem statement and what you need to find out. Create a plan of attack by choosing the right formulas or theories applicable to the problem. Always keep track of units and conversions as they are pivotal in physics and chemistry problems. If you're stuck, try to simplify the question or break it down into smaller, more manageable parts. This can often reveal a pathway to the solution. After arriving at an answer, take the time to double-check your work. A common mistake in JEE Advanced problem-solving is calculation errors or misreading the question, so it is crucial to review your solution thoroughly before considering it final.