Differential Equations: JEE MAIN 2024 Previous Year Questions

Question

Let  y = y(x)  be the solution of the differential equation (𝑥+𝑦+2)^2 𝑑𝑥=𝑑𝑦, y(0) = −2. Let the maximum and minimum values of the function y = y(x) in [0, π/3] be α and β, respectively. If (3𝛼+𝜋)^2+𝛽^2=𝑎+𝑏√3; a, b ∈ Z, then a + b equals

Solution

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Hello Students,

Welcome to this blog! If you are preparing for JEE Main (Joint Entrance Examination) and looking for a comprehensive resource to strengthen your Mathematics preparation, you are in the right place.

One of the questions asked in the JEE Main 2024 (conducted on 4th April 2024, during the evening shift of Phase II) is as follows:

In this blog, we dive deep into the detailed solutions of previous years’ JEE Main Mathematics questions. Our goal is to help you:

• Understand the concepts behind each problem.
• Learn efficient problem-solving techniques.
• Avoid common mistakes made by students.

Whether you’re revising concepts, practicing problems, or looking for step-by-step solutions, this blog will provide the guidance you need to excel in the Mathematics section of JEE Main. Let’s work together to make your preparation more effective and your results outstanding!

Stay tuned for regular updates and insights.

Subject: Mathematics

Topic: Matrices and Determinant

If you have any doubts regarding this question, feel free to post them in the comment box. We are eager to address your queries and provide clarification promptly!

Is PYQ sufficient for JEE Mains?

While practicing PYQs is undoubtedly crucial for JEE Main preparation, relying on them alone may not guarantee success. To excel in the exam, it is important to adopt a well-rounded approach that incorporates diverse study materials, thorough conceptual understanding, and effective problem-solving strategies.

How is PYQ helpful for JEE Mains?

Here are some key reasons why solving PYQs is essential:

Familiarity with Exam Pattern: PYQs help you understand the structure of the exam, including question types, marking schemes, and difficulty levels.

Identifying Important Topics: They highlight frequently tested topics, allowing you to focus on areas that carry more weight.

Time Management Practice: Solving PYQs under timed conditions helps you build speed and accuracy for the actual exam.

Understanding Question Trends: PYQs reveal patterns or trends in questions, making it easier to anticipate and prepare for similar problems.

Application of Concepts: They provide an opportunity to apply theoretical knowledge to practical, exam-like problems, enhancing problem-solving skills.

Boosting Confidence: Practicing real exam questions increases familiarity and confidence, reducing anxiety during the actual test.

Self-Assessment: PYQs allow you to assess your strengths and weaknesses, helping you refine your preparation strategy effectively.