NCERT solutions for class 10 maths: complete guide, chapter-wise solutions, exam preparation

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NCERT solutions for class 10 maths provide comprehensive and accurate answers to all the exercises. Designed to simplify complex concepts, they are an essential tool for effective learning and exam preparation. By following expert-backed solutions, students can build confidence, improve problem-solving skills, and score well in their board exams.

NCERT Solutions for Class 10 Maths: Questions and Answers

  • Question: Find the value of x if 5x + 4 = 24.

    • Answer: Subtract 4 from both sides: 5x = 20. Now divide both sides by 5, giving x = 4.

  • Question: Solve for y: 3y - 7 = 14.

    • Answer: Add 7 to both sides: 3y = 21. Now divide by 3 to get y = 7.

  • Question: If a triangle has sides 3 cm, 4 cm, and 5 cm, is it a right triangle?

    • Answer: Yes, because 3² + 4² = 9 + 16 = 25, which is equal to 5². This confirms it is a right triangle.

  • Question: Find the area of a circle with a radius of 7 cm.

    • Answer: Area = πr² = 3.14 × 7² = 3.14 × 49 = 153.86 cm².

  • Question: The sum of two numbers is 50. One number is 10 more than the other. Find the numbers.

    • Answer: Let one number be x. The other number is x + 10. So, x + (x + 10) = 50. Simplifying, 2x + 10 = 50, so 2x = 40, and x = 20. The numbers are 20 and 30.

  • Question: Simplify: 4(2x + 5).

    • Answer: Distribute the 4: 8x + 20.

  • Question: Solve the equation 2x/3 + 5 = 11.

    • Answer: Subtract 5 from both sides: 2x/3 = 6. Multiply both sides by 3: 2x = 18. Divide by 2: x = 9.

  • Question: What is the surface area of a cube with side length 6 cm?

    • Answer: Surface area = 6 × side² = 6 × 6² = 6 × 36 = 216 cm².

  • Question: If a rectangle’s length is 12 cm and its width is 5 cm, find its perimeter.

    • Answer: Perimeter = 2 × (length + width) = 2 × (12 + 5) = 2 × 17 = 34 cm.

  • Question: The sum of the angles of a triangle is always 180°. If two angles are 50° and 60°, what is the third angle?

    • Answer: Third angle = 180° - (50° + 60°) = 180° - 110° = 70°.

  • Question: Find the LCM of 12 and 15.

    • Answer: The LCM of 12 and 15 is 60.

  • Question: If a train travels 60 km in 1 hour, what is its speed?

    • Answer: Speed = Distance/Time = 60 km/h.

  • Question: What is the square of 14?

    • Answer: The square of 14 is 14 × 14 = 196.

  • Question: Simplify: (5x + 3) - (2x - 4).

    • Answer: 5x + 3 - 2x + 4 = 3x + 7.

  • Question: A bag contains 3 red, 5 blue, and 2 green balls. What is the probability of drawing a red ball?

    • Answer: Total balls = 3 + 5 + 2 = 10. Probability of drawing a red ball = 3/10.

  • Question: What is the volume of a cylinder with a radius of 3 cm and a height of 8 cm?

    • Answer: Volume = πr²h = 3.14 × 3² × 8 = 3.14 × 9 × 8 = 226.08 cm³.

  • Question: The length of a rectangle is 10 cm and its diagonal is 13 cm. Find its width.

    • Answer: Using the Pythagorean theorem, width = √(13² - 10²) = √(169 - 100) = √69 ≈ 8.31 cm.

  • Question: Solve for x in the equation 7x + 2 = 30.

    • Answer: Subtract 2 from both sides: 7x = 28. Now divide by 7: x = 4.

  • Question: What is the perimeter of a square with side length 5 cm?

    • Answer: Perimeter = 4 × side = 4 × 5 = 20 cm.

  • Question: Simplify: 8x² - 3x².

    • Answer: 8x² - 3x² = 5x².

  • Question: A number is divided by 7 and the result is 12. What is the number?

    • Answer: Multiply both sides by 7: The number is 12 × 7 = 84.

  • Question: Find the height of a triangle with base 10 cm and area 50 cm².

    • Answer: Area = ½ × base × height, so 50 = ½ × 10 × height. Height = 50 / 5 = 10 cm.

  • Question: A line segment has endpoints at (2, 3) and (5, 7). Find its length.

    • Answer: Length = √[(x2 - x1)² + (y2 - y1)²] = √[(5 - 2)² + (7 - 3)²] = √(3² + 4²) = √9 + 16 = √25 = 5.

  • Question: What is the mean of 5, 7, 9, 12, and 15?

    • Answer: Mean = (5 + 7 + 9 + 12 + 15) / 5 = 48 / 5 = 9.6.

  • Question: What is the area of a triangle with base 6 cm and height 8 cm?

    • Answer: Area = ½ × base × height = ½ × 6 × 8 = 24 cm².

  • Question: Solve for x: x/4 + 3 = 7.

    • Answer: Subtract 3 from both sides: x/4 = 4. Multiply by 4: x = 16.

  • Question: Find the square root of 144.

    • Answer: The square root of 144 is 12.

  • Question: Find the perimeter of a right-angled triangle with sides 6 cm, 8 cm, and 10 cm.

    • Answer: Perimeter = 6 + 8 + 10 = 24 cm.

  • Question: What is the volume of a cube with side 4 cm?

    • Answer: Volume = side³ = 4³ = 64 cm³.

  • Question: Solve for x: 3x - 5 = 16.

    • Answer: Add 5 to both sides: 3x = 21. Now divide by 3: x = 7.

  • Question: If a book costs ₹200 and is discounted by 10%, what is the discount amount?

    • Answer: Discount = 10% of ₹200 = 0.10 × 200 = ₹20.

  • Question: Find the simple interest on ₹1000 for 3 years at 5% per annum.

    • Answer: Simple Interest = P × R × T / 100 = 1000 × 5 × 3 / 100 = ₹150.

  • Question: What is the perimeter of a rhombus with side 7 cm?

    • Answer: Perimeter = 4 × side = 4 × 7 = 28 cm.

  • Question: What is the sum of the interior angles of a hexagon?

    • Answer: Sum of interior angles = (n - 2) × 180°, where n = 6. So, sum = (6 - 2) × 180° = 4 × 180° = 720°.

  • Question: If a circle has a radius of 5 cm, what is its circumference?

    • Answer: Circumference = 2πr = 2 × 3.14 × 5 = 31.4 cm.

  • Question: Find the mode of the numbers 2, 4, 6, 4, 8, 9, 4.

    • Answer: The mode is 4, as it occurs most frequently.

  • Question: What is the hypotenuse of a right triangle with sides 9 cm and 12 cm?

    • Answer: Hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15 cm.

  • Question: Solve for x: 5x - 3 = 12.

    • Answer: Add 3 to both sides: 5x = 15. Divide by 5: x = 3.

  • Question: Find the area of a trapezium with parallel sides of lengths 8 cm and 12 cm, and height 6 cm.

    • Answer: Area = ½ × (sum of parallel sides) × height = ½ × (8 + 12) × 6 = ½ × 20 × 6 = 60 cm².

  • Question: Find the average of 10, 20, 30, and 40.

    • Answer: Average = (10 + 20 + 30 + 40) / 4 = 100 / 4 = 25.

  • Question: What is the value of (3x + 2) when x = 5?

    • Answer: Substitute x = 5: 3(5) + 2 = 15 + 2 = 17.

  • Question: Find the value of y if 5y = 25.

    • Answer: y = 25 / 5 = 5.

  • Question: What is the perimeter of a triangle with sides 7 cm, 9 cm, and 12 cm?

    • Answer: Perimeter = 7 + 9 + 12 = 28 cm.

  • Question: A rectangle has length 15 cm and width 10 cm. Find its area.

    • Answer: Area = length × width = 15 × 10 = 150 cm².

  • Question: If 3x + 5 = 20, find x.

    • Answer: Subtract 5 from both sides: 3x = 15. Now divide by 3: x = 5.

  • Question: Find the sum of the first 10 natural numbers.

    • Answer: Sum = 10(10 + 1) / 2 = 10 × 11 / 2 = 55.

  • Question: What is the volume of a rectangular prism with length 8 cm, width 4 cm, and height 3 cm?

    • Answer: Volume = length × width × height = 8 × 4 × 3 = 96 cm³.

  • Question: Find the greatest common divisor (GCD) of 24 and 36.

    • Answer: The GCD of 24 and 36 is 12.

  • Question: Simplify: 3(4x + 7).

    • Answer: 12x + 21.

  • Question: What is the square of 9?

    • Answer: The square of 9 is 9 × 9 = 81.

  • Question: A book is priced at ₹250. If the price increases by 20%, what will the new price be?

    • Answer: Increase = 20% of ₹250 = 0.20 × 250 = ₹50. New price = ₹250 + ₹50 = ₹300.

  • Question: What is the area of a circle with a radius of 14 cm?

    • Answer: Area = πr² = 3.14 × 14² = 3.14 × 196 = 615.44 cm².

Best Indian Books for NCERT Solutions for Class 10 Maths

  1. ematics for Class 10 by R.S. Aggarwal
    Publisher: S. Chand Publishing
    Content: This book is a comprehensive guide for solving NCERT Class 10 Math problems. It provides step-by-step solutions to each chapter and includes a variety of exercise problems for practice. The book helps students to improve their problem-solving skills, focusing on concepts and strategies needed for the board exams.

  2. Selina Publishers Concise Mathematics for Class 10
    Publisher: Selina Publishers
    Content: This book is perfect for students who need in-depth solutions to NCERT problems. It covers the entire syllabus and includes detailed solutions, examples, and practice questions. The questions range from easy to difficult, enabling students to grasp both basic and advanced concepts.

  3. Mathematics for Class 10 by R.D. Sharma
    Publisher: Dhanpat Rai Publications
    Content: This book is known for its clear explanations and easy-to-understand solutions. It offers a variety of examples and practice questions aligned with NCERT guidelines, making it a great resource for students to master all the topics in Class 10 Maths.

  4. Exemplar Problems Class 10 Mathematics
    Publisher: NCERT
    Content: The Exemplar book provides a set of problems that challenge the student’s understanding and analytical skills. It includes both easy and tough problems to cater to a wide range of abilities, helping students improve their logical reasoning and problem-solving techniques.

  5. Mathematics for Class 10 by P.S. Verma
    Publisher: Dhanpat Rai Publications
    Content: This book explains complex topics with simple and practical examples. It contains solved examples, unsolved exercises, and solutions that are well-explained to make learning effective for Class 10 students.

  6. Maths Magic for Class 10 by Vikas Gupta
    Publisher: VK Publications
    Content: Vikas Gupta’s book focuses on interactive learning. It includes various tips and tricks to solve mathematical problems faster and with accuracy. Ideal for students aiming to develop quick problem-solving skills.

  7. Together with Mathematics for Class 10
    Publisher: Rachna Sagar
    Content: This book provides NCERT-based solutions along with a variety of questions that are perfect for practice. The book is divided into sections based on each chapter and helps build clarity on different math topics.

  8. NCERT Solutions Class 10 Mathematics
    Publisher: S. Chand
    Content: This book offers detailed and accurate NCERT solutions to every exercise in the textbook. It is ideal for students who need extra practice and a better understanding of each chapter’s concepts.

  9. Kumon Mathematics for Class 10
    Publisher: Kumon India
    Content: Kumon’s approach focuses on mastery through practice. This book is designed to help students practice various levels of difficulty in Maths and improve their skills gradually.

  10. NCERT Solutions for Class 10 Mathematics by A.D. Sharma
    Publisher: Arihant Publications
    Content: This solution book provides an extensive set of problems and their step-by-step solutions for all NCERT exercises, making it highly beneficial for students who want to strengthen their math skills and score better.

  11. Simple Mathematics for Class 10 by S. K. Gupta
    Publisher: Pragati Prakashan
    Content: This book offers solutions that simplify the learning process for students. It contains a variety of problems and also includes additional practice problems for better understanding.

  12. Problems in Mathematics by V. S. Jaiswal
    Publisher: Vikas Publishing House
    Content: A great collection of problems with solutions that are aligned with NCERT’s curriculum. It challenges students’ problem-solving ability and provides hints for tough questions.

  13. All in One Mathematics for Class 10 by Arihant Experts
    Publisher: Arihant Publications
    Content: This is a complete guide that combines theory, solutions, and practice questions in a single book. It helps students in every aspect of preparation and improves their performance in exams.

  14. Mathematics for Class 10 by S. Chand
    Publisher: S. Chand Publishing
    Content: This book offers an in-depth understanding of mathematical concepts with a variety of problems that enhance critical thinking and problem-solving skills.

  15. Cengage Mathematics Class 10
    Publisher: Cengage Learning India
    Content: The Cengage book focuses on conceptual understanding and application. It offers detailed explanations, solved problems, and unsolved questions from all major topics of Class 10 Maths.

  16. Success Package Mathematics for Class 10
    Publisher: Success Publications
    Content: This book contains questions and solutions for a thorough practice session. It provides students with well-explained solutions and additional practice sets to cover a wide variety of questions.

  17. Mathematics Made Simple by K.C. Sinha
    Publisher: R. Chand & Co.
    Content: This book is known for its easy-to-understand approach. It simplifies the entire Class 10 syllabus and includes hundreds of practice questions for in-depth revision.

  18. Foundation Mathematics for Class 10 by M.L. Agarwal
    Publisher: Nival Publications
    Content: Aimed at enhancing the basic skills of students, this book features detailed examples and practice exercises to strengthen their foundation in mathematics.

  19. Mathematics for Class 10 by R.C. Gupta
    Publisher: R.C. Gupta Publications
    Content: Offers well-structured content, including problems, solutions, and model papers, allowing students to prepare effectively for their exams.

  20. Real Mathematics for Class 10 by P.K. Gupta
    Publisher: S. K. Jain
    Content: This book focuses on building practical skills and reasoning abilities, offering NCERT-style problems and solutions that help students apply concepts in real-world scenarios.

Mathematics is one of the most essential subjects in Class 10, and mastering it requires dedication, practice, and the right resources. NCERT solutions for Class 10 Maths play a pivotal role in helping students understand concepts, strengthen their foundation, and perform well in exams. Whether you're struggling with quadratic equations or trying to ace geometry, these solutions can help clarify doubts and improve problem-solving skills.

Why Choose NCERT Solutions?

NCERT solutions are designed to align perfectly with the curriculum prescribed by the Central Board of Secondary Education (CBSE). These solutions are created by experts in the field of education and offer a structured approach to problem-solving. By providing step-by-step explanations, they ensure that students grasp the concepts thoroughly. NCERT solutions also provide detailed methods and alternative approaches to solving problems, making it easier for students to understand complex topics.

A Structured Approach to Learning

One of the biggest advantages of using NCERT solutions is the organized structure they follow. Each chapter is broken down into smaller, manageable sections, which makes learning more efficient. For example, topics like Real Numbers, Polynomials, and Linear Equations are introduced gradually, allowing students to develop a deeper understanding of each concept before moving on to the next.

Additionally, NCERT solutions provide a variety of problems, ranging from basic to advanced levels. This diversity in question types helps students practice different methods and techniques, making them more prepared for their exams.

Enhancing Problem-Solving Skills

Maths is a subject that requires consistent practice, and NCERT solutions are packed with ample practice problems. These problems help students refine their problem-solving abilities and prepare them for the various question formats they may encounter in exams. The step-by-step solutions also serve as a guide, showing students the correct approach to tackling different types of questions.

Moreover, by practicing regularly, students can also identify areas where they might need additional help. This allows them to focus on their weaknesses and improve before their exams.

Improving Conceptual Clarity

NCERT solutions do more than just provide answers—they explain the reasoning behind each solution. This helps students build conceptual clarity, which is crucial for higher-level math topics. For instance, in topics like Trigonometry and Probability, a solid understanding of the basic concepts is essential for solving more advanced problems. The explanations in NCERT solutions make it easier for students to break down complex problems into simpler steps.

Ideal for CBSE Board Exam Preparation

If you're preparing for the CBSE Class 10 board exams, NCERT solutions should be a part of your study routine. The solutions are designed to cover all the important topics in the syllabus and provide a comprehensive revision tool. Many students rely on NCERT solutions as their primary reference material, as they not only help in understanding the theory but also offer plenty of practice questions for exam preparation.

Expert Recommendations for Effective Use

To make the most of NCERT solutions, experts recommend that students follow a consistent study plan. Start by reading the chapter thoroughly and understanding the theory behind each concept. Once you have a good grasp of the theory, move on to the exercise problems. Begin with the easier questions and gradually work your way up to the more difficult ones.

It's also helpful to solve previous years' question papers and sample papers to familiarize yourself with the exam pattern. This can help you manage your time effectively during exams and boost your confidence.

Key Takeaways

NCERT solutions for Class 10 Maths offer a comprehensive and efficient way to master the subject. They are an invaluable resource for students looking to improve their problem-solving skills, gain conceptual clarity, and excel in their exams. With regular practice and a structured approach, students can unlock their full potential and perform confidently in their board exams.

 

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