NCERT Exemplar Class 12 Mathematics Solutions & Practice Questions (Download PDF)

The NCERT Exemplar for Class 12 Mathematics is one of the most valuable resources for students aiming to secure top marks in their mathematics exam. Designed to help students understand complex mathematical concepts in-depth, this book is a perfect companion for Class 12 students. It contains a wide range of solved problems, practice exercises, and challenging questions that go beyond the textbook.

In this guide, we will provide you with everything you need to know about the NCERT Exemplar for Class 12 Mathematics, including detailed solutions, important practice questions, and how to download the Exemplar PDF. Whether you are looking to strengthen your understanding or find answers to difficult problems, this article will help you navigate the content effectively.

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Here we have provided NCERT Exemplar Solution for Class 12 Mathematics in english Language, Just select the chapters below to get Exemplar Solution of the same:

Relations and Functions

Inverse Trigonometric Functions

Matrices

Determinants

Continuity and Differentiability

Application of Derivatives

Integrals

Application of Integrals

Differential Equations

Vector Algebra

Three Dimensional Geometry

Linear Programming

Probability

1. Why NCERT Exemplar is Essential for Class 12 Mathematics

Understanding the Importance of NCERT Exemplar

The NCERT Exemplar is designed to complement the NCERT textbook and offer students an opportunity to explore more advanced problem-solving techniques. While the NCERT textbook provides foundational knowledge, the Exemplar book pushes students to apply their learning through a wide range of problems that test conceptual clarity and problem-solving abilities.

For Class 12 students, the NCERT Exemplar is especially useful in preparing for exams like CBSE, JEE, and other competitive tests. The problems in the Exemplar are of varying difficulty, making it suitable for students at all levels of understanding.

Key Features of NCERT Exemplar for Class 12 Mathematics

• Varied Difficulty Levels: The book contains problems ranging from easy to complex, allowing students to gradually increase their proficiency.
• Clear Solutions: Each question is followed by a detailed, step-by-step solution that helps students understand the process involved in solving mathematical problems.
• Problem-Solving Focus: It encourages critical thinking and problem-solving, essential skills for mastering Mathematics.
• Helps in Exam Preparation: The Exemplar questions often resemble the patterns found in competitive exams like JEE Main, making it an excellent resource for students preparing for such exams.

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2. How to Use NCERT Exemplar Class 12 Mathematics Effectively

Step-by-Step Approach to Mastering Mathematics with NCERT Exemplar

To get the most out of the NCERT Exemplar for Class 12 Mathematics, follow these strategic steps:

1. Start with the NCERT Textbook: Begin with the NCERT Mathematics textbook to grasp the basic concepts. The Exemplar is a supplement to this, designed to test and expand your understanding.

2. Read Each Question Carefully: The Exemplar book contains a variety of question types—some are direct applications of textbook concepts, while others require deeper analysis. It’s important to read each question carefully and understand what’s being asked.

3. Work Through the Solutions: Once you’ve attempted a problem, refer to the detailed solution provided. This helps you understand the methodology and the thought process behind solving each question.

4. Practice Regularly: The more you practice, the better your grasp on the subject will be. Make sure to solve a mix of easy, medium, and challenging problems from each chapter.

5. Focus on Conceptual Understanding: Instead of just memorizing formulas or solutions, focus on the underlying concepts. This will make it easier to solve complex problems.

6. Use NCERT Exemplar for Revision: As exams approach, use the Exemplar to test your knowledge and assess your preparedness. The more problems you solve, the more confident you’ll feel.

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3. NCERT Exemplar Class 12 Mathematics Chapter-Wise Solutions

Each chapter of the NCERT Exemplar Class 12 Mathematics book covers a different topic and includes both theory and practice problems. Here, we’ll provide a brief overview of key chapters and their focus areas:

Chapter 1: Relations and Functions

• This chapter introduces relations, functions, and their properties. Key problems in this chapter involve understanding different types of functions such as one-to-one, onto, and composite functions.

Chapter 2: Inverse Trigonometric Functions

• The focus here is on solving trigonometric equations and understanding the inverses of trigonometric functions. Solved examples help reinforce these concepts.

Chapter 3: Matrices

• This chapter includes matrix operations, determinants, and their applications. It’s a critical chapter for students preparing for exams like JEE, where matrices and determinants frequently appear.

Chapter 4: Determinants

• This section covers the properties and applications of determinants. The Exemplar provides a variety of problems involving minors, co-factors, and the evaluation of determinants.

Chapter 5: Continuity and Differentiability

• Problems in this chapter focus on understanding the continuity of functions, the concept of derivatives, and their applications.

Chapter 6: Application of Derivatives

• Here, students will encounter real-world problems related to rates of change, tangents, normals, and optimization.

Chapter 7: Integrals

• A foundational chapter where students practice various techniques for evaluating integrals, including definite and indefinite integrals.

Chapter 8: Application of Integrals

• This chapter deals with problems involving the area under curves and finding the area between curves.

Chapter 9: Differential Equations

• The Exemplar for this chapter helps students solve first-order and second-order differential equations.

Chapter 10: Vectors and 3D Geometry

• Problems in this chapter help students understand vector algebra and its applications in geometry.

Chapter 11: Linear Programming

• This chapter deals with optimization problems, where students apply linear programming to real-life situations.

Chapter 12: Probability

• The chapter covers various concepts of probability and provides numerous problems that require applying the fundamental theorem of probability.

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4. NCERT Exemplar Class 12 Mathematics Important Questions

Top Important Questions from NCERT Exemplar Class 12 Mathematics

Here are some examples of important questions from different chapters that every student should practice:

1. Chapter 1: Relations and Functions

   • Prove that a function can be both one-to-one and onto.

2. Chapter 3: Matrices

   • Show that the product of two matrices is not commutative in general.

3. Chapter 5: Continuity and Differentiability

   • Prove that a function is continuous if the limits at all points in the domain exist.

4. Chapter 7: Integrals

   • Evaluate the integral of trigonometric functions like sin(x), cos(x), etc.

5. Chapter 12: Probability

   • Find the probability of drawing a certain type of card from a standard deck.

By practicing these important questions, students will gain confidence and improve their chances of scoring high marks.

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5. How to Download NCERT Exemplar Class 12 Mathematics PDF

Step-by-Step Guide to Download NCERT Exemplar Class 12 PDF

1. Visit the Official NCERT Website: Go to the official NCERT website (ncert.nic.in).
2. Navigate to the "Publications" Section: Under the "Books" section, select "Exemplar Problems."
3. Choose Class 12 Mathematics: Select Class 12 and Mathematics as your subject.
4. Download the PDF: The NCERT Exemplar PDF for Class 12 Mathematics is available for free download. Simply click on the download link to save the file on your device.

Alternative Download Link: You can also find downloadable PDFs from trusted educational portals like IndiaBIX, or other online resources that provide free educational material.

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6. Conclusion

The NCERT Exemplar Class 12 Mathematics book is an indispensable resource for students looking to excel in their exams. By understanding how to effectively use the book, practicing regularly, and referring to solutions, students can improve their problem-solving skills and boost their confidence. The chapter-wise solutions, important questions, and practice exercises make it an ideal tool for exam preparation.

Remember, consistent practice, understanding concepts deeply, and solving Exemplar questions will not only help you excel in your Class 12 Mathematics exam but also lay a strong foundation for future studies in mathematics.