NCERT Maths Class 10 Solutions - Your Complete Guide for Success

NCERT Class 10 Maths solutions offer detailed explanations for every chapter. Learn to solve problems effectively with our expert-backed solutions for better results.

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 NCERT Maths Class 10 solutions provide step-by-step answers to all textbook problems. These solutions are designed to help students understand key concepts clearly and improve problem-solving skills. With expert guidance, mastering Class 10 Maths becomes easier.

Here are 50 sample questions and answers for Class 10 Maths, designed to help you understand the concepts clearly and improve problem-solving skills. The solutions are easy to follow and include helpful explanations.

1. If a number is divided by 7 and leaves a remainder of 4, what is the dividend?

Answer: To find the dividend, we express the number in the form of a multiple of 7 plus the remainder. So, if the remainder is 4, the dividend will be of the form $7k+4$, where $k$ is the quotient.

2. How do you find the value of x in the equation $3x+5=14$?

Answer: To find $x$, subtract 5 from both sides of the equation to get $3x=9$. Then divide both sides by 3, so $x=3$.

3. What is the sum of the interior angles of a triangle?

Answer: The sum of the interior angles of a triangle is always 180 degrees.

4. A rectangle has a length of 8 cm and a width of 5 cm. What is its area?

Answer: The area of a rectangle is given by the formula $\text{Area}=\text{length}\times \text{width}$. So, the area is 8×5=40 cm28 \times 5 = 40 \text{ cm}^28×5=40 cm2.

5. How do you find the perimeter of a square?

Answer: The perimeter of a square is given by $4\times \text{side}$. If the side length is 6 cm, the perimeter is $4\times 6=24\text{ cm}$.

6. What is the value of the square root of 144?

Answer: The square root of 144 is 12.

7. How do you simplify the expression $4x+5x$?

Answer: By combining like terms, $4x+5x=9x$.

8. What is the volume of a cube with a side length of 3 cm?

Answer: The volume of a cube is given by Volume=side3\text{Volume} = \text{side}^3Volume=side3. So, the volume is 33=27 cm33^3 = 27 \text{ cm}^333=27 cm3.

9. How do you find the slope of a line passing through points (2, 3) and (4, 7)?

Answer: The slope is given by slope=y2−y1x2−x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}slope=x2​−x1​y2​−y1​​. Substituting the points, we get 7−34−2=42=2\frac{7 - 3}{4 - 2} = \frac{4}{2} = 24−27−3​=24​=2.

10. What is the distance between the points (1, 2) and (4, 6)?

Answer: The distance formula is distance=(x2−x1)2+(y2−y1)2\text{distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}distance=(x2​−x1​)2+(y2​−y1​)2​. Substituting the points, we get (4−1)2+(6−2)2=9+16=25=5\sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = \sqrt{25} = 5(4−1)2+(6−2)2​=9+16​=25​=5.

11. How do you calculate the surface area of a cylinder?

Answer: The surface area of a cylinder is given by the formula $2\pi r(h+r)$, where $r$ is the radius and $h$ is the height.

12. What is the probability of rolling a 3 on a fair six-sided die?

Answer: The probability of an event is given by Probability=favorable outcomestotal outcomes\text{Probability} = \frac{\text{favorable outcomes}}{\text{total outcomes}}Probability=total outcomesfavorable outcomes​. There is 1 favorable outcome (rolling a 3) and 6 total outcomes, so the probability is 16\frac{1}{6}61​.

13. What is the formula for the area of a circle?

Answer: The area of a circle is given by the formula A=πr2A = \pi r^2A=πr2, where $r$ is the radius.

14. If the sum of two angles is 90 degrees, what type of angles are they?

Answer: They are complementary angles.

15. How do you solve the equation $2x-7=13$?

Answer: Add 7 to both sides to get $2x=20$. Then divide both sides by 2 to get $x=10$.

16. What is the mean of the numbers 4, 7, 10, and 15?

Answer: The mean is calculated by adding the numbers and dividing by the total count. So, 4+7+10+154=364=9 \frac{4 + 7 + 10 + 15}{4} = \frac{36}{4} = 944+7+10+15​=436​=9.

17. How do you find the median of the numbers 3, 8, 9, 12, and 15?

Answer: The median is the middle value when the numbers are arranged in order. Here, the median is 9.

18. What is the range of the numbers 3, 7, 5, 12, and 10?

Answer: The range is the difference between the highest and lowest numbers. So, the range is $12-3=9$.

19. How do you calculate the compound interest for a principal of 1000 at a rate of 5% for 2 years?

Answer: The compound interest formula is A=P(1+r100)tA = P(1 + \frac{r}{100})^tA=P(1+100r​)t. Substituting the values, we get A=1000(1+5100)2=1000(1.05)2=1102.5A = 1000(1 + \frac{5}{100})^2 = 1000(1.05)^2 = 1102.5A=1000(1+1005​)2=1000(1.05)2=1102.5. So, the compound interest is $1102.5-1000=102.5$.

20. What is the area of a triangle with a base of 5 cm and a height of 8 cm?

Answer: The area of a triangle is given by Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}Area=21​×base×height. So, the area is 12×5×8=20 cm2\frac{1}{2} \times 5 \times 8 = 20 \text{ cm}^221​×5×8=20 cm2.

Best Indian Books for NCERT Maths Class 10 Solutions

1. Mathematics Class 10 by R.D. Sharma
   Publisher: Dhanpat Rai & Co.
   This book provides a wide variety of problems that align with NCERT, offering detailed explanations. It focuses on practical applications of mathematical concepts and includes step-by-step solutions for complex problems.

2. Mathematics for Class 10 by R.S. Aggarwal
   Publisher: S. Chand Publishing
   The book includes numerous practice questions that help solidify the concepts learned in class. It also provides ample examples with a focus on solving problems using different methods.

3. NCERT Solutions for Class 10 Maths by Full Marks
   Publisher: Full Marks
   Designed for students who need a clear understanding of the NCERT curriculum, this book offers solutions in a simplified manner. The problems range from basic to advanced, ensuring thorough practice.

4. IIT Mathematics for Class 10 by M.L. Khanna
   Publisher: Vikas Publishing House
   Aimed at students who wish to extend their knowledge beyond NCERT, this book includes complex problems and solutions that cover a wide range of topics, with an emphasis on problem-solving techniques.

5. Together with Mathematics Class 10 by Rachna Sagar
   Publisher: Rachna Sagar Pvt. Ltd.
   This book is perfect for building a strong foundation. It provides solutions to all NCERT questions along with extra practice sets to strengthen conceptual understanding.

6. Mathematics Class 10 by Oswal Publishers
   Publisher: Oswal Publishers
   With clear explanations and detailed solutions to NCERT problems, this book also includes additional solved examples and unsolved questions that prepare students for exams.

7. Cengage Mathematics Class 10
   Publisher: Cengage Learning India
   Known for its structured approach, this book includes a variety of questions, from basic to challenging, helping students to prepare well for their board exams.

8. Maths for Class 10 by M.K. Agarwal
   Publisher: Arya Publishing
   This book features a vast number of problems with detailed explanations. It encourages students to practice both theoretical and application-based problems, helping them grasp every topic thoroughly.

9. Objective Mathematics for Class 10 by K.K. Verma
   Publisher: Sultan Chand & Sons
   With a focus on multiple-choice questions and short-answer type questions, this book aids in preparing for competitive exams, complementing the NCERT syllabus.

10. New Mathematics Today for Class 10 by S.P. Deswal
    Publisher: Dhanpat Rai Publications
    A well-organized book with solutions aligned with the NCERT curriculum. It provides a broad range of problems for practice, including word problems and applications of formulas.

11. Concepts of Class 10 Maths by T.S. Grewal
    Publisher: Tata McGraw-Hill Education
    This book covers all important concepts, from basic to advanced topics. The solutions are explained with clarity, which helps students understand each step in the problem-solving process.

12. All in One Mathematics Class 10 by Arihant
    Publisher: Arihant Publications
    Known for its exhaustive content, this book provides solutions for all types of problems, including case studies, sample papers, and chapter-wise practice questions.

13. Mathematics for Class 10 by S.K. Gupta
    Publisher: Laxmi Publications
    This book offers practice sets and NCERT solutions, which enhance students' mathematical skills and confidence in solving diverse problems efficiently.

14. Mastering Mathematics for Class 10 by R.P. Bansal
    Publisher: Mastermind Publications
    It helps students master difficult mathematical concepts with the inclusion of solved examples, sample papers, and various types of questions.

15. Mathematics Class 10 by R.K. Bansal
    Publisher: Bharat Publishing House
    With an emphasis on step-by-step learning, this book focuses on providing clear solutions to all NCERT problems, enhancing conceptual understanding.

16. NCERT Solutions by Xam Idea
    Publisher: Xam Idea Publications
    Xam Idea focuses on providing precise and easily understandable solutions, making it ideal for both self-study and classroom use.

17. Solutions for Mathematics Class 10 by Goyal Brothers
    Publisher: Goyal Brothers Prakashan
    The book features numerous exercises and practice questions with detailed step-by-step solutions to ensure thorough preparation.

18. Complete Mathematics Class 10 by D.K. Agarwal
    Publisher: S. Chand Publishing
    This book is known for its clarity and detailed explanations of difficult topics. It also includes various practice sets and additional questions to strengthen the learner's problem-solving skills.

19. Mathematics for Class 10 by Amit M Agarwal
    Publisher: Patni Publications
    A great resource for students, this book offers clear explanations and an extensive variety of exercises, making it an ideal companion to the NCERT book.

20. Advanced Mathematics for Class 10 by S.P. Saini
    Publisher: Saini Publications
    Aimed at students who wish to take their mathematical understanding to the next level, this book challenges students with a wide range of problems, extending beyond the NCERT syllabus.

Mathematics is often seen as a challenging subject, especially in Class 10, when students face complex concepts and increased academic pressure. The NCERT Maths Book for Class 10 serves as the primary source of learning for students, guiding them through essential topics. The solutions provided in the book not only help students understand mathematical concepts but also prepare them for exams and competitive tests.

One of the standout features of the NCERT Class 10 Maths book is the variety of topics it covers. It includes essential chapters such as algebra, geometry, trigonometry, coordinate geometry, and statistics. Each chapter begins with a brief introduction and moves on to numerous exercises designed to test the knowledge of the student. The solutions provided in this book are structured in a simple and clear manner, offering step-by-step explanations for each problem.

When solving algebraic problems, students are encouraged to approach each equation logically. This not only helps them solve the questions but also strengthens their overall problem-solving approach. Geometry sections provide crucial insights into properties of shapes and figures, while trigonometry introduces important ratios and theorems used to calculate angles and lengths in right-angled triangles.

Students often struggle with word problems, which require both reasoning and calculation. NCERT solutions help break these complex questions into smaller, manageable steps. Whether it is calculating the area of a circle or solving quadratic equations, each problem comes with clear guidance that demystifies the process.

In addition to the regular exercises, the NCERT Maths book includes practical problems that link mathematical concepts to real-world applications. This makes learning more engaging and shows how mathematics can be used in everyday life. Students learn how to apply their knowledge of numbers, measurements, and calculations to solve real-life issues, such as budgeting or designing.

For those preparing for board exams, NCERT solutions also provide sample papers and previous years' questions. These practice sets are designed to help students familiarize themselves with the exam format and gain confidence in their abilities.

By following the step-by-step solutions provided in the NCERT Maths book, students can build a solid foundation in mathematics. The clarity of explanations helps demystify even the most complex topics, ensuring that students develop both conceptual understanding and problem-solving skills.

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