Class 9th Maths NCERT Solutions are essential for mastering key concepts and excelling in exams. These solutions provide detailed, step-by-step explanations for each chapter, helping students build a strong foundation in topics like algebra, geometry, and statistics. Expert-backed recommendations ensure effective learning, making these solutions perfect for exam preparation and practice.
Class 9th Maths NCERT Solutions: Questions and Answers
1. What is the value of x if 3x - 7 = 11?
To solve for x, first add 7 to both sides of the equation:
3x = 18. Now divide both sides by 3:
x = 6.
2. How do you find the area of a triangle?
The area of a triangle is calculated using the formula:
Area = 1/2 * base * height.
3. What is the sum of the angles of a triangle?
The sum of the angles of any triangle is always 180 degrees.
4. How do you simplify the expression 4x + 3y - 2x + 5y?
First, combine like terms:
(4x - 2x) + (3y + 5y) = 2x + 8y.
5. What is the solution to the equation 5x + 10 = 3x + 18?
Subtract 3x from both sides:
2x + 10 = 18.
Now subtract 10 from both sides:
2x = 8.
Divide both sides by 2:
x = 4.
6. How do you calculate the perimeter of a rectangle?
The perimeter of a rectangle is calculated using the formula:
Perimeter = 2 * (length + width).
7. What is the Pythagorean theorem?
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides:
a² + b² = c².
8. How do you solve for y in the equation 2y - 5 = 9?
First, add 5 to both sides:
2y = 14.
Then, divide both sides by 2:
y = 7.
9. What is the volume of a cube with side length 4 cm?
The volume of a cube is calculated using the formula:
Volume = side³.
So, Volume = 4³ = 64 cm³.
10. How do you find the square root of 49?
The square root of 49 is 7 because 7 × 7 = 49.
11. What is the difference between a rational and irrational number?
A rational number can be expressed as a fraction of two integers, whereas an irrational number cannot be expressed as a simple fraction.
12. How do you factorize the expression x² - 5x + 6?
The factors of the expression are (x - 2)(x - 3).
13. How do you calculate the mean of the numbers 2, 4, 6, and 8?
Add the numbers:
2 + 4 + 6 + 8 = 20.
Now divide by the total number of numbers:
Mean = 20 / 4 = 5.
14. What is the value of 2³?
2³ = 2 × 2 × 2 = 8.
15. How do you find the distance between two points on a coordinate plane?
The distance formula is:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²].
16. What is the probability of getting an even number on a dice roll?
There are 3 even numbers (2, 4, 6) on a six-sided dice, so the probability is 3/6 or 1/2.
17. What is the slope of a line if the coordinates of two points are (2, 3) and (4, 7)?
The slope of a line is calculated as:
Slope = (y₂ - y₁) / (x₂ - x₁) = (7 - 3) / (4 - 2) = 4 / 2 = 2.
18. How do you calculate the surface area of a sphere?
The surface area of a sphere is calculated using the formula:
Surface Area = 4πr².
19. How do you expand the expression (x + 3)(x - 2)?
Use the distributive property:
(x + 3)(x - 2) = x² - 2x + 3x - 6 = x² + x - 6.
20. What is the value of x in the equation x/2 = 6?
Multiply both sides by 2 to get:
x = 12.
21. How do you convert a fraction to a decimal?
Divide the numerator by the denominator.
22. What is the median of the numbers 1, 5, 3, 8, 7?
Arrange the numbers in ascending order:
1, 3, 5, 7, 8.
The median is the middle number, which is 5.
23. How do you calculate the area of a circle?
The area of a circle is calculated using the formula:
Area = πr².
24. What is the square of 12?
12² = 12 × 12 = 144.
25. How do you simplify the expression 3x - 4x + 2?
Combine like terms:
(3x - 4x) + 2 = -x + 2.
26. What is the LCM of 6 and 8?
The LCM of 6 and 8 is 24.
27. What is the HCF of 12 and 15?
The HCF of 12 and 15 is 3.
28. How do you solve the equation 4x + 5 = 21?
Subtract 5 from both sides:
4x = 16.
Now divide both sides by 4:
x = 4.
29. What is the formula for the volume of a cylinder?
The volume of a cylinder is calculated using the formula:
Volume = πr²h, where r is the radius and h is the height.
30. What is the perimeter of a square with side length 5 cm?
The perimeter of a square is calculated using the formula:
Perimeter = 4 * side.
So, Perimeter = 4 * 5 = 20 cm.
31. What is the value of 7²?
7² = 7 × 7 = 49.
32. How do you calculate the hypotenuse of a right-angled triangle with sides 6 cm and 8 cm?
Use the Pythagorean theorem:
Hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
33. How do you solve the equation 3x - 4 = 5x + 6?
First, subtract 3x from both sides:
-4 = 2x + 6.
Now subtract 6 from both sides:
-10 = 2x.
Divide both sides by 2:
x = -5.
34. What is the product of 6 and 7?
The product of 6 and 7 is 42.
35. How do you find the area of a rectangle with length 8 cm and width 5 cm?
Area = length × width = 8 × 5 = 40 cm².
36. How do you find the sum of the angles of a quadrilateral?
The sum of the angles of any quadrilateral is 360 degrees.
37. What is the square root of 81?
The square root of 81 is 9 because 9 × 9 = 81.
38. What is the formula for the circumference of a circle?
The circumference of a circle is calculated using the formula:
Circumference = 2πr.
39. What is the product of 5 and 9?
The product of 5 and 9 is 45.
40. What is the value of 3³?
3³ = 3 × 3 × 3 = 27.
41. How do you simplify the expression 2x + 3y - x - y?
Combine like terms:
(2x - x) + (3y - y) = x + 2y.
42. How do you calculate the area of a trapezium?
The area of a trapezium is calculated using the formula:
Area = 1/2 * (a + b) * h, where a and b are the lengths of the parallel sides and h is the height.
43. How do you factorize the expression x² - 9?
This is a difference of squares:
(x² - 9) = (x - 3)(x + 3).
44. How do you solve for z in the equation 3z + 4 = 16?
Subtract 4 from both sides:
3z = 12.
Now divide both sides by 3:
z = 4.
45. What is the value of 2 + 3 × 4?
Follow the order of operations:
2 + (3 × 4) = 2 + 12 = 14.
46. What is the volume of a cone with radius 3 cm and height 5 cm?
The volume of a cone is calculated using the formula:
Volume = 1/3 * πr²h.
Substitute the values:
Volume = 1/3 * π * 3² * 5 = 1/3 * π * 9 * 5 = 15π cm³.
47. How do you solve the equation 5x - 3 = 2x + 12?
Subtract 2x from both sides:
3x - 3 = 12.
Now add 3 to both sides:
3x = 15.
Divide both sides by 3:
x = 5.
48. What is the perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm?
The perimeter of the triangle is the sum of its sides:
Perimeter = 3 + 4 + 5 = 12 cm.
49. How do you simplify the expression 5x + 2y - 3x - y?
Combine like terms:
(5x - 3x) + (2y - y) = 2x + y.
50. What is the value of 4²?
4² = 4 × 4 = 16.
Top 10 to 20 Indian Books for Class 9th Maths NCERT Solutions
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Mathematics for Class 9 by R.S. Aggarwal (S. Chand Publishing)
- This book covers all topics of Class 9 Mathematics, providing a large number of practice problems and detailed explanations. It helps in building a strong foundation in mathematics.
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NCERT Mathematics Solutions Class 9 by R. D. Sharma (Dhanpat Rai Publications)
- A great guide for students, this book provides clear explanations and solutions to the problems in NCERT textbooks. It also contains additional questions for practice.
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Class 9 Mathematics for ICSE by M.L. Agarwal (Agarwal Publishers)
- This book includes comprehensive solutions with well-structured explanations and is excellent for preparing for both the board exams and competitive tests.
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Mathematics Class 9 (Chapter-wise Solutions) by M.K. Jain (S. Chand Publishing)
- A detailed guide with step-by-step solutions to the NCERT exercises, this book simplifies concepts and ensures a deeper understanding of each chapter.
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Mathematics Class 9 - Self Study Guide by K.K. Verma (Vikas Publishing House)
- Designed to help students solve complex problems with ease, this book offers solutions to all exercises in the NCERT textbook along with tips and tricks for exam preparation.
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Target Class 9 Maths by G.P. Sharma (Target Publications)
- This is a well-structured book with explanations, practice sets, and MCQs. It ensures that students can work through the problems with clarity and confidence.
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Mathematics for Class 9 by O.P. Malhotra (Arihant Publications)
- Known for its straightforward explanations, this book provides multiple sets of problems for practice and helps develop problem-solving skills.
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Mathematics NCERT Solutions by Dr. S. K. Gupta (S. Chand Publishing)
- A great companion for students who need in-depth solutions and additional exercises for practice. It enhances conceptual clarity with a structured approach.
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Comprehensive Mathematics for Class 9 by J.P. Soni (S. Chand Publishing)
- This book offers clear solutions and a thorough breakdown of the topics to help students master the subject, with ample practice exercises.
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Class 9 Mathematics Problems and Solutions by D.C. Pandey (Arihant Publications)
- Ideal for problem-solving practice, this book is filled with explanations and various problem-solving techniques for every concept in Class 9 maths.
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Mathematics for Class 9 (Explained with Solved Examples) by P. L. Soni (K. L. Chopra Publications)
- This book is perfect for students seeking additional examples and clear step-by-step guidance to solve problems from every chapter.
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Maths Made Easy for Class 9 by R.N. Gupta (Kalyani Publishers)
- Featuring simple explanations and a variety of practice questions, this book helps students work through challenging problems with ease.
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Step-by-Step Guide to Class 9 Mathematics by Dinesh Khattar (Vikas Publishing)
- A useful book to understand the fundamental concepts of mathematics with detailed solutions and easy-to-follow explanations.
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Maths Workbook Class 9 by N.C.E.R.T. (NCERT Publications)
- This workbook focuses on enhancing skills through practice. It provides comprehensive exercises that align with the NCERT syllabus.
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Mathematics for Class 9 by Amit M Agarwal (Arihant Publications)
- This book is particularly well-known for its practical approach and easy-to-understand language, making complex topics approachable for students.
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New Mathematics for Class 9 by M.L. Bhargava (Bhargava Publications)
- A comprehensive guide with clear explanations, this book is designed to build a strong foundation for students in mathematics through rigorous exercises.
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Class 9 Mathematics Simplified by H.C. Verma (HarperCollins Publishers)
- This book emphasizes the importance of understanding the theory behind each concept and has a variety of exercises to ensure mastery of the topic.
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Concepts of Class 9 Maths by V. K. Sharma (New Saraswati House)
- Offers an insightful approach to concepts and is packed with challenging problems, making it ideal for practice and skill development.
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Quick Guide to Class 9 Maths by S. P. Mittal (Mittal Publishers)
- This book is perfect for quick revision, with neatly explained concepts and example problems to aid in exam preparation.
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Mastering Class 9 Mathematics by P.K. Yadav (S. Chand Publishing)
- An ideal book for building conceptual clarity, it is loaded with step-by-step solutions and practice problems, making it a great resource for students.
Class 9th is a crucial stage in a student's academic journey, and mastering mathematics in this grade is essential for building a solid foundation for higher studies. The Class 9 Mathematics NCERT Solutions serve as a comprehensive guide to tackling the chapters in the curriculum. From algebra to geometry, these solutions are designed to make complex concepts easy to grasp.
The first benefit of using the NCERT Solutions is that they offer a structured approach to understanding each topic. Whether it’s algebraic expressions, polynomials, coordinate geometry, or probability, the book divides each chapter into manageable sections. Each section begins with simple concepts and gradually builds on them, helping students gain confidence and mastery over the subject.
NCERT textbooks focus on conceptual clarity rather than rote learning, making it easier for students to understand the core principles behind every mathematical formula. This becomes especially important as students progress to higher grades where critical thinking and problem-solving skills become paramount. With clear solutions and step-by-step explanations, students can easily follow and replicate the problem-solving method, ensuring they don’t miss any important steps.
One of the key features of NCERT Solutions is the variety of problems it offers. From basic to advanced levels, the questions are carefully curated to cater to different learning needs. Some of the problems test a student's fundamental understanding of concepts, while others challenge them to apply these concepts in real-life scenarios. This range of problems encourages students to think creatively and strengthens their analytical abilities.
The NCERT Solutions also emphasize the importance of regular practice. With a mix of theoretical and practical problems, students are encouraged to solve as many exercises as possible. This repetition not only reinforces learning but also helps students become familiar with the pattern of questions that are likely to appear in exams. By solving different types of problems, students develop a flexible approach to handling any question that comes their way.
For students who struggle with mathematics, the NCERT Solutions provide an invaluable resource for clarification. The solutions are written in an easy-to-understand manner, with no complicated jargon, making it accessible to all learners. Additionally, the well-organized format ensures that every student can find the right approach to a problem, even if they are revisiting a concept they find challenging.
In summary, Class 9 Maths NCERT Solutions offer a perfect blend of theory and practice, fostering a deep understanding of mathematical principles. With regular use, students not only prepare effectively for their exams but also equip themselves with the problem-solving skills needed for future success.