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JEE Main Differential Equations Practice Paper FREE PDF Download

Last updated date: 23rd May 2024
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Differential Equations Practice Paper with Solutions and Answer Key For JEE Main

The Differential Equations Practice Paper is important for JEE Main as it covers fundamental concepts like first-order, second-order, and linear differential equations which help students excel in JEE Main Maths.


JEE Main Practice Paper


Text, Images, Videos and PDF


JEE Main

Chapter Name:

Differential Equations

Academic Session:



English Medium



Available Material:

Chapter-wise Practice paper with PDF

Vedantu is helping students in their JEE Main Maths preparation with a FREE PDF download of the Differential Equations Practice Paper. This unique resource offers chapter-wise practice, ensuring you cover every critical topic. By downloading it for FREE, you can enhance your knowledge and boost your confidence in tackling questions efficiently. You will find detailed solutions and answer keys to clarify doubts and learn step-wise ways to practice questions. You can also increase the speed of solving each question by practicing Vedantu’s Differential Equations Practice Paper for JEE Main.

You can find a minimum of 2 questions from the Differential Equations chapter in the JEE Main Exam. Here is the table where you can find the weightage of the Differential Equations chapter in the past 5 years of the JEE Main Exam.


Weightage of JEE Main Questions From Differential Equations











Practice Papers for JEE Main help you to find and practice the questions that might get asked in the next JEE Main exam. Download the PDF of the Differential Equations Practice Paper today to excel in your JEE Main exams!

Subject-Wise Links for JEE Main Practice Paper

In the JEE Main exam, each of the three subjects— Maths, Physics and Chemistry—holds a weightage of 33%. Hence along with practicing the Maths Practice Paper for JEE Main, students have to practice Chemistry, as well as Physics Practice Papers. This will lead you to score more than 80% in the JEE Main exam. Here are the links for JEE Main Subject-wise Practice Paper.

Subject-wise Links For JEE Main Practice Paper

JEE Main Chemistry Practice Paper

JEE Main Physics Practice Paper

Links For JEE Main Chapter-wise Practice Paper

Maths Practice Papers needs to be worked out after each chapter since the questions from most of the Maths chapters can help you to score well in the Maths section of the JEE Main exam. This will help you to cover most of the JEE Main Maths Syllabus. You can download the Chapter-wise links for the JEE Main Practice Paper.

Important Topics From Differential Equations for JEE Main Practice Paper

It will be easy for you to work out the JEE Main Practice Paper if you have a strong understanding of the Differential Equations. You have to focus more on the important topics to answer most of the questions from the JEE Main Practice Paper of Differential Equations. Here are some of the important topics of Differential Equations.

Order and Degree:

  • Know the difference between the order (highest derivative involved) and degree (power of the highest derivative) of a differential equation.

Types of Differential Equations:

  • Differentiate between ordinary differential equations (ODEs) and partial differential equations (PDEs). JEE Main typically focuses on ODEs.

Solving First-Order ODEs:

  • Learn how to solve simple first-order differential equations using separation of variables, integrating factors, or direct integration.

Second-Order Linear ODEs:

  • Understand how to solve second-order linear differential equations with constant coefficients. This includes characteristic equations and finding particular solutions.

Homogeneous and Non-Homogeneous ODEs:

  • Be able to distinguish between homogeneous and non-homogeneous differential equations, and learn methods to solve them.

Methods for Solving Non-Homogeneous ODEs:

  • Study techniques like the method of undetermined coefficients and variation of parameters for solving non-homogeneous differential equations.

Initial Value Problems (IVPs):

  • Know how to solve differential equations with initial conditions. This involves finding a particular solution that satisfies given starting values.

Higher-Order ODEs:

  • Be aware of higher-order differential equations and how they can be reduced to a system of first-order equations for solving.

Laplace Transforms:

  • Learn the basics of Laplace transforms as a tool for solving differential equations, especially for solving linear ODEs with complex initial conditions.

Series Solutions:

  • Understand how to find series solutions for differential equations, particularly for cases where other methods are not applicable.

Eigenvalues and Eigenvectors:

  • Know how to use eigenvalues and eigenvectors to solve systems of linear differential equations.

Direction Fields:

  • Familiarize yourself with direction fields as a way to visualize solutions to first-order differential equations.

Equations To Score More in Practice Paper of JEE Main Differential Equations

Equations are the base to solve the JEE Main Practice Paper. You have to know which equation or formula to use while solving the Practice Paper for JEE Main. Find the important equations you need to learn while working out Practice Paper of JEE Main Differential Equations.

First-Order Linear Differential Equation:

  • $\dfrac{dy}{dx} + P(x)y = Q(x)$

Separable Differential Equation:

  • $\dfrac{dy}{dx} = f(x)g(y)$

Second-Order Linear Homogeneous Differential Equation:

  • $\dfrac{d^2y}{dx^2} + P(x)\dfrac{dy}{dx} + Q(x)y = 0$

Characteristic Equation for Second-Order Linear Homogeneous Equations:

  • $ar^2 + br + c = 0$

Particular Solution for Second-Order Linear Non-Homogeneous Equation:

  • $y_p(x) = A(x)y_1(x) + B(x)y_2(x)$

General Solution of a Differential Equation:

  • $y(x) = y_h(x) + y_p(x)$

For more formulas and equations you can refer Vedantu’s JEE Main Formula page.

What Makes Vedantu’s Practice Paper PDF of JEE Main Differential Equations Different?

The major role of Practice Paper for JEE Main is to make the students prepare for the exam by providing them with a set of questions that are in the same pattern as the JEE Main exam. Vedantu’s JEE Main Practice Papers are the exact resources that you need right after you finish your learning with each Maths chapter. Let’s take a look at the features of Differential Equations Practice Paper for JEE Main provided by Vedantu:

  • Quality Content: Vedantu's Practice Paper for Differential Equations is curated by experienced educators and subject matter experts, ensuring that the questions are relevant, accurate, and aligned with the latest JEE Main syllabus.

  • Variety of Questions: They provide a diverse range of questions, covering different difficulty levels and concepts from Differential Equations, allowing students to thoroughly practice and master each topic.

  • Detailed Solutions: Vedantu offers detailed step-by-step solutions and answer keys for Differential Equations JEE Main Practice Paper, ensuring that students understand not just the final answer but also the underlying concepts and problem-solving techniques.

  • User-Friendly Interface: Their platform is designed to be user-friendly, making it easy for students to navigate through Practice Paper and access the content they need efficiently.

  • Accessibility: Vedantu's Practice Paper are often easily accessible online and can be downloaded for FREE, allowing students to practice from the comfort of their homes.

How To Prepare For JEE Main With Differential Equations Practice Paper?

Vedantu’s Differential Equations JEE Main Practice Paper is composed of MCQs and Subjective type questions. At the end of the FREE PDF you can get the answer keys and detailed solutions for the questions. If you follow the below instructions while working out the Daily Practice Paper you can easily succeed in the JEE Main exam.

  1. Download the Daily Practice Paper of JEE Main Physics And Measurement.

  2. You can set a timer of 1 hour.

  3. Solve the easy questions first and give time for tough questions.

  4. Note your answers on a sheet of paper and check with the answer key.

  5. Each question carries 4 marks and gives a negative mark of -1 for each question.

  6. Now calculate the score and analyze yourself. 

  7. You can take the help of detailed solutions given in the PDF for the better clarity of questions and answers. 

  8. Learn how to do the incorrect answers and practice the questions again.

  9. Make a note of the time you take for each question to practice. 

When to Start Preparing With JEE Main Practice Paper of Differential Equations?

Starting your preparation with JEE Main Practice Paper of Differential Equations should ideally commence early in your academic journey to allow for comprehensive subject mastery and ample revision, ensuring exam success. To maximize your JEE Main preparation, consider the following timeline for utilizing Daily Practice Paper:

  • Foundation Building (1-2 Years Prior): Start with foundational studies and building a strong understanding of the core concepts in Differential Equations.

  • Concept Mastery (6-12 Months Prior): About a year before the exam, begin incorporating Practice Paper of JEE Main Differential Equations into your routine. 

  • Intensive Revision (3-6 Months Prior): As the exam date approaches, intensify your Practice Paper usage. Take full-length Practice Paper to simulate exam conditions, improve time management, and identify weak areas.

Additional Materials To cover With  JEE Main Differential Equations Practice Paper

After learning with the Differential Equations chapter, you need to make sure that you are mastering the contents you learn, so that you can perform well in JEE Main. Practice Papers for JEE Main prepared by Vedantu is the best resource for this. Right after your revision with the Differential Equations you can practice the JEE Main Practice Paper. But this is not enough if you want to score more than 85% in JEE Main exam. Here are some additional materials that you can choose while preparing for JEE Main.

Try Our Online Practice Paper Test For Maths

Once you are done with practicing the JEE Main Practice Paper for Differential Equations, you can test your online skills for JEE Main Maths. Vedantu is also providing you an online practice paper test where you can get a real experience of attempting JEE Main Exam.

Mastering Differential Equations With JEE Main Practice Paper

The JEE Main Differential Equations Practice Paper is a great way to practice for the exam. It covers a lot of important topics, and the solutions and answer key help you check your work. By practicing with this JEE Main Practice Paper, you can learn the material better and get better at solving problems. You can also learn how to manage your time better and figure out where you need to focus your studies. So, if you're preparing for the JEE Main, be sure to download and practice Vedantu’s Differential Equations Daily Practice Paper for FREE!

JEE Mains Sample Paper: Differential Equations

JEE Mains is a highly competitive exam, and students need to be well-prepared to secure a good score. By practicing with JEE Main 2025 Sample Papers, students can get a feel of the actual exam and identify their strengths and weaknesses. The Differential Equations chapter is a crucial section of the JEE Mains syllabus, and it is essential for students to have a thorough understanding of the concepts covered in this chapter. Our sample papers include questions from all the important topics in this chapter, helping students to assess their preparation level and identify areas where they need more practice.

With the help of JEE Main Model Papers and JEE Model Question Papers, students can also get an idea of the types of questions that are frequently asked in the exam. This can help them to develop effective strategies for answering different types of questions, which can be beneficial in improving their overall score. By practicing with these sample papers, students can boost their confidence and improve their chances of success in the JEE Mains examination.

FAQs on JEE Main Differential Equations Practice Paper FREE PDF Download

1. What is the importance of practicing differential equations for JEE Main?

Practicing differential equations is crucial for JEE Main because it's a fundamental topic in mathematics and often appears in the exam. It helps you develop problem-solving skills and boosts your confidence.

2. What topics in differential equations should I focus on for JEE Main practice paper?

You should focus on topics like first-order differential equations, linear differential equations, homogeneous and non-homogeneous equations, and applications of differential equations relevant to JEE Main.

3. Are solutions provided along with the practice paper?

Vedantu provides detailed solutions for the Differential Equations Practice Paper for JEE Main. These solutions are essential for understanding the problem-solving process.

4. Can I download the practice paper and answer key for offline use?

Yes, you can usually download the practice paper and answer key from Vedantu's website or app to use them offline.

5. How can I evaluate my performance using the answer key?

Compare your answers with the solutions provided in the answer key. Vedantu's answer key will help you identify areas where you need improvement.

6. Can I get help or clarification on specific problems from Vedantu's support team?

Vedantu often offers doubt-solving sessions and doubt forums, where you can seek help and clarification on specific problems.

7. Is the practice paper designed according to the latest JEE Main syllabus and pattern?

Yes, Vedantu's practice paper is usually aligned with the latest JEE Main syllabus and pattern to provide relevant practice.

8. How can I use the practice paper effectively to improve my JEE Main preparation?

Use the practice paper as a diagnostic tool to identify your weak areas. Focus on improving those while also revising the concepts you've mastered.