Expert NCERT Exemplar Class 9 Maths Solutions for Quick Learning

Get NCERT Exemplar Class 9 Maths Solutions to enhance your problem-solving skills. Detailed step-by-step explanations for better exam preparation and understanding.

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NCERT Exemplar Class 9 Maths Solutions provide a comprehensive understanding of complex mathematical concepts. These solutions guide students through each problem, offering step-by-step explanations. Designed for better comprehension, they are an essential resource for students preparing for exams. Expert-backed answers simplify difficult topics, helping learners succeed with confidence.

User-Friendly NCERT Exemplar Class 9 Maths Solutions – Questions & Answers

Sample Questions and Answers for NCERT Exemplar Class 9 Maths:

Here are 20 sample questions and answers for Class 9 Maths. Each question is followed by a detailed solution to help you understand the steps involved.

Q1: What is the formula for the area of a triangle?
A1: The area of a triangle is given by the formula:
Area = ½ × base × height.

Q2: How do you find the volume of a cylinder?
A2: The volume of a cylinder is calculated as:
Volume = π × radius² × height.

Q3: Solve for x: 3x + 5 = 20.
A3: To solve for x, subtract 5 from both sides:
3x = 15,
Then divide by 3:
x = 5.

Q4: Find the LCM of 12 and 18.
A4: The least common multiple (LCM) of 12 and 18 is 36.

Q5: What is the difference between an arithmetic sequence and a geometric sequence?
A5: An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio.

Q6: Simplify: 2x + 3x - 4x.
A6: 2x + 3x - 4x = x.

Q7: What is the value of π?
A7: The value of π is approximately 3.14159.

Q8: Find the square root of 81.
A8: The square root of 81 is 9.

Q9: Solve: 5y - 2 = 3y + 6.
A9: Subtract 3y from both sides:
2y - 2 = 6,
Then add 2 to both sides:
2y = 8,
Finally, divide by 2:
y = 4.

Q10: What is the formula to calculate the surface area of a cube?
A10: The surface area of a cube is given by the formula:
Surface Area = 6 × side².

Q11: Convert 0.75 into a fraction.
A11: 0.75 can be written as ¾.

Q12: What is the Pythagorean theorem?
A12: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
a² + b² = c².

Q13: Find the perimeter of a rectangle with length 10 cm and width 5 cm.
A13: The perimeter is calculated as:
Perimeter = 2 × (length + width) = 2 × (10 + 5) = 30 cm.

Q14: What is the formula for the area of a circle?
A14: The area of a circle is given by the formula:
Area = π × radius².

Q15: Simplify: 6x² + 4x - 3x² + 2x.
A15: Combine like terms:
6x² - 3x² = 3x²,
4x + 2x = 6x,
Thus, the simplified expression is:
3x² + 6x.

Q16: What is the probability of getting a head when flipping a coin?
A16: The probability of getting a head is ½.

Q17: Find the roots of the quadratic equation x² - 5x + 6 = 0.
A17: The roots of the equation are x = 2 and x = 3.

Q18: What is the relationship between the radius and diameter of a circle?
A18: The diameter of a circle is twice the length of its radius.
Diameter = 2 × radius.

Q19: Solve: 2x - 3 = 7.
A19: Add 3 to both sides:
2x = 10,
Then divide by 2:
x = 5.

Q20: How do you find the mean of a set of numbers?
A20: To find the mean, sum all the numbers and divide by the total number of values in the set.

Feel free to use these solutions to guide your understanding of the key topics in Class 9 Maths. The explanations are simple, clear, and aimed at making concepts easy to grasp!

Q21: What is the formula for the area of a trapezium?
A21: The area of a trapezium is calculated using the formula:
Area = ½ × (sum of parallel sides) × height.

Q22: Solve for x: 4(x - 3) = 2(x + 5).
A22: First, expand both sides:
4x - 12 = 2x + 10.
Now subtract 2x from both sides:
2x - 12 = 10.
Next, add 12 to both sides:
2x = 22.
Finally, divide by 2:
x = 11.

Q23: What is the formula for the volume of a cone?
A23: The volume of a cone is calculated using the formula:
Volume = 1/3 × π × radius² × height.

Q24: Simplify: 5a + 2b - 3a + 4b.
A24: Combine like terms:
5a - 3a = 2a,
2b + 4b = 6b.
Thus, the simplified expression is:
2a + 6b.

Q25: Find the square of 12.
A25: The square of 12 is:
12² = 144.

Q26: What is the formula for the surface area of a sphere?
A26: The surface area of a sphere is given by the formula:
Surface Area = 4 × π × radius².

Q27: What is the distance formula to calculate the distance between two points (x₁, y₁) and (x₂, y₂)?
A27: The distance between two points is calculated as:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²].

Q28: Find the perimeter of a triangle with sides 7 cm, 9 cm, and 12 cm.
A28: The perimeter of a triangle is the sum of its sides:
Perimeter = 7 + 9 + 12 = 28 cm.

Q29: Solve for x: 2(x + 4) = 16.
A29: First, expand both sides:
2x + 8 = 16.
Now subtract 8 from both sides:
2x = 8.
Finally, divide by 2:
x = 4.

Q30: What is the formula for the area of a rectangle?
A30: The area of a rectangle is calculated using the formula:
Area = length × width.

Top 10 Indian Books for NCERT Exemplar Class 9 Maths Solutions

1. NCERT Mathematics Exemplar Class 9
   Author: NCERT
   Publisher: NCERT
   Content: This book covers a wide range of mathematical problems with step-by-step solutions. It provides in-depth explanations of concepts, especially focusing on practical applications and theorems. Questions are categorized into different difficulty levels, from basic to advanced, making it an essential resource for Class 9 students.

2. Mathematics for Class 9
   Author: R.D. Sharma
   Publisher: Dhanpat Rai Publications
   Content: This book offers detailed solutions for Class 9 mathematics. It explains the problems in a simple language and covers a wide range of topics from Algebra to Geometry. The exercises focus on building a strong foundation and enhancing problem-solving skills.

3. Together with Mathematics Class 9
   Author: Dr. S. K. Gupta
   Publisher: Rachna Sagar
   Content: This book includes both NCERT-based and additional practice questions for Class 9. The solutions are clear and concise, offering step-by-step guidance on each problem. It is particularly useful for competitive exam preparation as it includes high-level problems.

4. Foundation Mathematics for Class 9
   Author: S.K. Gupta
   Publisher: S.Chand
   Content: A well-organized book with a focus on logical reasoning, algebra, and geometry. This book contains questions that are great for building conceptual clarity and offers solutions that simplify complex problems.

5. Mathematics Class 9 by R.S. Aggarwal
   Author: R.S. Aggarwal
   Publisher: S. Chand Publications
   Content: This book features detailed explanations and a variety of questions that help students prepare for both school exams and competitive exams. The questions range from basic to challenging, catering to a wide range of learning needs.

6. Exemplar Problems in Mathematics Class 9
   Author: A.S. Aggarwal
   Publisher: Arihant Publications
   Content: Designed as an additional practice book, this book contains a wide array of problems and solutions. It covers the NCERT syllabus and provides clear explanations to boost understanding of mathematical concepts.

7. Mathematics Class 9
   Author: S.K. Srivastava
   Publisher: R.L. Gupta
   Content: The book offers a comprehensive explanation of mathematical concepts and provides a variety of problems. It is an excellent resource for understanding the application of formulas and principles.

8. Comprehensive Mathematics Class 9
   Author: R.D. Sharma
   Publisher: Dhanpat Rai
   Content: This book is an excellent guide for students struggling with concepts. It includes a large number of practice exercises, ranging from basic drills to complex problems, and covers all topics included in the NCERT syllabus.

9. Mathematics for Class 9 (U.P. Board)
   Author: Pradeep Publications
   Publisher: Pradeep Publications
   Content: This book is designed to cater to students who are preparing for board exams and competitive exams. It includes detailed explanations and provides an ample amount of practice questions, including previous year questions.

10. NCERT Solutions Mathematics Class 9
    Author: NCERT
    Publisher: NCERT
    Content: It provides step-by-step solutions to the problems given in the NCERT textbook. It is an essential resource for clearing doubts and practicing a wide range of problems.

11. New Math’s Solutions Class 9
    Author: Dr. M. L. Aggarwal
    Publisher: Arya Publishing House
    Content: This book offers a wide range of questions with step-by-step solutions, making it easier for students to understand mathematical concepts. The book includes a diverse set of problems from various topics, such as algebra, geometry, and trigonometry, to develop a thorough understanding of Class 9 Maths.

12. Practice Book Mathematics Class 9
    Author: P.K. Sharma
    Publisher: K.K. Publication
    Content: A great supplementary book, it provides a mix of challenging problems and solutions. It is designed to enhance problem-solving skills and increase accuracy. The book covers all essential topics of Class 9, including number systems, algebra, coordinate geometry, and more. This book focuses on repetitive practice to improve speed and accuracy in solving problems.

13. Advanced Mathematics for Class 9
    Author: M.L. Agarwal
    Publisher: Arya Publications
    Content: This book includes an extensive collection of problems to sharpen problem-solving skills. Each topic is explained in simple language with step-by-step solutions, making it an excellent resource for preparing for both school and competitive exams.

14. Mathematics Class 9 (R.S. Aggarwal)
    Author: R.S. Aggarwal
    Publisher: S. Chand
    Content: It provides in-depth solutions and numerous practice exercises for every topic in Class 9. The problems progress from easy to complex, ensuring gradual improvement in students' mathematical abilities.

15. Mathematics for Class 9 by Laxmi Publications
    Author: Laxmi Publications
    Publisher: Laxmi Publications
    Content: This book emphasizes the application of formulas and concepts in various mathematical problems. It includes easy-to-understand explanations, followed by plenty of solved examples and exercises to help students build a solid foundation.

16. CBSE Chapterwise Solutions for Class 9 Mathematics
    Author: R. S. Aggarwal
    Publisher: S. Chand Publications
    Content: This book organizes problems chapter-wise and includes all types of questions asked in past exams. The step-by-step solutions make it a great resource for board exam preparation.

17. Class 9 Mathematics - Simplified
    Author: R.S. Aggarwal
    Publisher: S. Chand
    Content: Focuses on breaking down complex problems into simple, easy-to-understand steps. It includes plenty of practice problems, and the book also offers solutions that are in line with the NCERT syllabus.

18. Mathematics for Class 9
    Author: J. P. Sharma
    Publisher: Krishna Prakashan
    Content: This book is known for its clear and concise explanations, along with detailed solutions. The book is a helpful resource for students who want to master topics like algebra, geometry, and trigonometry.

19. Exemplar Mathematics Class 9
    Author: NCERT
    Publisher: NCERT
    Content: It provides a variety of problems along with answers and explanations that align perfectly with the NCERT syllabus. The questions encourage logical reasoning and critical thinking.

20. All-in-One Mathematics Class 9
    Author: Arihant Experts
    Publisher: Arihant Publications
    Content: This book offers comprehensive solutions to all the problems in the NCERT textbook. The book also features tips, tricks, and strategies to solve mathematical problems more efficiently.

21. S. Chand’s Mathematics for Class 9
    Author: S. Chand
    Publisher: S. Chand Publications
    Content: A detailed book with a large number of problems and solutions designed to improve mathematical proficiency. The stepwise approach ensures thorough understanding.

22. NCERT Solutions Class 9 Mathematics
    Author: NCERT
    Publisher: NCERT
    Content: A go-to reference book for students to clarify doubts and enhance their learning. It contains systematic solutions for all problems in the Class 9 NCERT book.

23. Mathematics Class 9 (Cengage Learning)
    Author: Cengage Learning
    Publisher: Cengage Learning
    Content: This book provides students with a deeper understanding of mathematical theories, offering well-structured explanations and a variety of exercises to solve, helping students improve their mathematical concepts.

24. Objective Mathematics Class 9
    Author: R. S. Aggarwal
    Publisher: S. Chand
    Content: This book focuses on practicing objective-type questions and multiple-choice questions, which are highly beneficial for entrance exams. It also offers clear, step-by-step solutions.

25. Mathematics Made Easy Class 9
    Author: R.D. Sharma
    Publisher: Dhanpat Rai
    Content: A simple yet effective guide for Class 9 students, it provides step-by-step solutions for each problem and focuses on practical applications of mathematical concepts.

26. Mathematics Class 9
    Author: S.K. Gupta
    Publisher: S. Chand Publications
    Content: This book offers numerous practice problems, focusing on developing a solid understanding of algebra, geometry, and other major topics in Class 9 mathematics.

27. NCERT Exemplar Problems Class 9
    Author: NCERT
    Publisher: NCERT
    Content: This book includes more challenging problems to deepen understanding. The solutions are detailed, aiding students in mastering difficult concepts.

28. Class 9 Mathematics (R.S. Aggarwal)
    Author: R.S. Aggarwal
    Publisher: S. Chand
    Content: R.S. Aggarwal's book features a wide array of problems from different chapters and detailed solutions to help students excel in exams.

29. Mastering Mathematics Class 9
    Author: S. Chand
    Publisher: S. Chand Publications
    Content: Focuses on simplifying complex mathematical problems, with multiple solved examples and practice exercises to boost problem-solving skills.

30. Complete Mathematics for Class 9
    Author: M.K. Singhal
    Publisher: Goyal Publishers
    Content: A comprehensive guide for Class 9, covering every aspect of the syllabus. The book provides solutions for each problem, focusing on building logical reasoning and mathematical skills

Mathematics in Class 9 can often be intimidating, but with the right approach, it can be a subject that builds both confidence and skill. The NCERT Exemplar Class 9 Maths Solutions guide students through complex topics with step-by-step explanations, ensuring a strong foundation in mathematics. These solutions not only help students tackle problems effectively but also enhance their problem-solving abilities, making them ready for both school exams and competitive tests.

The Exemplar book for Class 9 Maths is designed with a primary focus on the application of fundamental concepts. It includes a wide variety of problems, ranging from simple to challenging, to cater to the learning needs of all students. Each chapter begins with a theoretical understanding of the topic followed by a set of problems that require careful application of these concepts. What sets this book apart is its emphasis on learning the problem-solving techniques in a logical and structured manner.

Incorporating these solutions into your study routine provides a significant advantage. The step-by-step approach in the Exemplar solutions helps break down complicated problems into manageable parts, ensuring students are not overwhelmed by advanced topics. This method builds confidence, enabling students to gradually increase their level of difficulty as they progress.

The content in the NCERT Exemplar Class 9 Maths book also includes application-based problems, helping students see the practical use of mathematics in real-world scenarios. This approach not only strengthens conceptual understanding but also fosters critical thinking. Moreover, the Exemplar book includes questions that closely follow the pattern of exams, making it an excellent tool for exam preparation. The book features a variety of question types, such as fill-in-the-blanks, true or false, match the following, and more, which ensures that students are well-prepared for diverse problem formats.

For students who aim to excel in their exams, these solutions provide an in-depth understanding of all the chapters. From algebra and geometry to statistics and probability, each concept is thoroughly explained, making learning easier. Additionally, the questions range in complexity, allowing students to gradually build their proficiency. This structure ensures that students are not just prepared for exams but also for any competitive math challenges they may face.

By practicing the problems from this book, students can develop a strong grasp on the various topics in the Class 9 syllabus. The Exemplar solutions are not only a great way to revise but also to dive deeper into subjects, ensuring a well-rounded understanding. They serve as an excellent companion alongside the regular NCERT textbook, making learning both enjoyable and effective.

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