Class 10 Maths Chapter 1 Exercise 1.2 solutions explained. Get step-by-step solutions, tips, and strategies to master this chapter with expert-backed insights and examples.
Class 10 Maths Chapter 1 Exercise 1.2 solutions are designed to enhance your understanding of key concepts. With step-by-step explanations, you'll learn essential problem-solving techniques. These solutions are perfect for practice and revision, ensuring clarity and boosting confidence. Follow expert-backed recommendations for effective learning.
Here are 50 sample questions and answers for Class 10 Maths Chapter 1 Exercise 1.2. These questions are designed to help students practice and enhance their problem-solving skills in a user-friendly and simple way. Each answer is explained clearly, making it easy for students to follow along.
Sample Questions and Answers:
If the sum of two numbers is 10 and their difference is 2, what are the numbers?
To solve, add the two equations. The sum of the numbers is 10, and their difference is 2. By adding these two equations, we get 2x = 12, so x = 6. Now substitute x = 6 into one of the original equations, and we find the other number is 4.
A number is divided into two parts such that their sum is 20. If the larger part exceeds the smaller part by 4, what are the two parts?
Let the smaller part be x and the larger part be x + 4. Their sum is 20, so we have the equation x + (x + 4) = 20. Solving this gives x = 8, so the two parts are 8 and 12.
The sum of three consecutive numbers is 24. What are the numbers?
Let the three consecutive numbers be x, x + 1, and x + 2. The sum of the numbers is x + (x + 1) + (x + 2) = 24. Simplifying this gives 3x + 3 = 24, so x = 7. Therefore, the three numbers are 7, 8, and 9.
A man walks 4 km to the north and then turns right to walk 3 km. How far is he from his starting point?
Using the Pythagorean theorem, the distance from the starting point can be calculated as √(4² + 3²) = √(16 + 9) = √25 = 5 km.
The area of a rectangle is 60 square units. If the length is 12 units, what is the width?
The area of a rectangle is given by length × width. Therefore, width = Area / length = 60 / 12 = 5 units.
A man buys a shirt for Rs. 500 and sells it at a profit of 20%. What is the selling price?
The profit is 20% of Rs. 500, which is Rs. 100. Therefore, the selling price is Rs. 500 + Rs. 100 = Rs. 600.
If the perimeter of a square is 48 cm, what is the length of one side?
The perimeter of a square is 4 times the length of one side. Therefore, the length of one side is 48 / 4 = 12 cm.
The sum of three consecutive even numbers is 72. What are the numbers?
Let the numbers be x, x + 2, and x + 4. The sum of the numbers is x + (x + 2) + (x + 4) = 72. Simplifying this gives 3x + 6 = 72, so x = 22. Therefore, the numbers are 22, 24, and 26.
A rectangular field has a length of 15 meters and a width of 10 meters. What is the area of the field?
The area of a rectangle is length × width. Therefore, the area is 15 × 10 = 150 square meters.
A train travels at a speed of 60 km/h. How far will it travel in 2 hours?
Distance = speed × time. Therefore, the distance traveled is 60 × 2 = 120 km.
The interest is given by the formula Simple Interest = Principal × Rate × Time / 100. Therefore, the interest is 1000 × 5 × 2 / 100 = Rs. 100.
Average speed = Distance / Time. Therefore, the average speed is 100 / 2 = 50 km/h.
The perimeter of a rectangle is given by 2 × (length + width). Therefore, the perimeter is 2 × (25 + 10) = 70 meters.
The area of a rectangle is length × width. Therefore, the area is 8 × 6 = 48 square centimeters.
The total number of apples is 5 + 7 + 8 = 20 apples.
The cost of one book is 120 / 3 = Rs. 40. Therefore, the cost of 7 books is 7 × 40 = Rs. 280.
The number is 5 × 9 = 45.
By using the Pythagorean theorem, we check if 6² + 8² = 10². We find that 36 + 64 = 100, which is true. Therefore, it is a right-angled triangle.
The profit is Rs. 180 – Rs. 150 = Rs. 30.
Using the Pythagorean theorem, the distance from the starting point is √(3² + 4²) = √(9 + 16) = √25 = 5 km.
Let the number be x. Therefore, (x + 5) / 2 = 8. Solving for x, we get x + 5 = 16, so x = 11.
The perimeter of an equilateral triangle is 3 times the length of one side. Therefore, the length of one side is 36 / 3 = 12 cm.
Speed = Distance / Time. Therefore, the speed is 200 / 30 = 6.67 meters per second.
The cost of one pen is 40 / 5 = Rs. 8. Therefore, the cost of 12 pens is 12 × 8 = Rs. 96.
Speed = Distance / Time. Therefore, the speed is 120 / 4 = 30 km/h.
The total number of balls is 10 + 12 + 15 = 37 balls.
The area of a square is the square of the length of one side. Therefore, the length of one side is √64 = 8 cm.
Let the odd numbers be x and x + 2. The sum is x + (x + 2) = 48. Simplifying this gives 2x + 2 = 48, so x = 23. Therefore, the numbers are 23 and 25.
The profit is Rs. 150 – Rs. 120 = Rs. 30. The profit percentage is (30 / 120) × 100 = 25%.
The area is length × width = 14 × 7 = 98 square centimeters.
Average speed = Distance / Time. Therefore, the average speed is 150 / 3 = 50 km/h.
Let the numbers be x, x + 2, x + 4, and x + 6. The sum is x + (x + 2) + (x + 4) + (x + 6) = 52. Simplifying this gives 4x + 12 = 52, so x = 10. Therefore, the numbers are 10, 12, 14, and 16.
The perimeter is 2 × (length + width) = 2 × (18 + 6) = 48 cm.
Using the Pythagorean theorem, the distance is √(150² + 200²) = √(22500 + 40000) = √62500 = 250 meters.
Let the numbers be x and y. Therefore, x + y = 30 and x – y = 6. Adding these two equations, we get 2x = 36, so x = 18. Substituting x = 18 into one of the equations, y = 12. Therefore, the numbers are 18 and 12.
By using the Pythagorean theorem, we check if 5² + 12² = 13². We find that 25 + 144 = 169, which is true. Therefore, it is a right-angled triangle.
The area of a circle is given by πr². Therefore, r² = 154 / π, which gives r = √(154 / 3.14) ≈ 7 cm.
The loss is 10% of Rs. 500, which is Rs. 50. Therefore, the selling price is Rs. 500 – Rs. 50 = Rs. 450.
The speed of the boat in still water is the average of the upstream and downstream speeds. The speed upstream is 40 / 4 = 10 km/h, and the speed downstream is 40 / 2 = 20 km/h. Therefore, the speed in still water is (10 + 20) / 2 = 15 km/h.
The interest is 2000 × 4 × 3 / 100 = Rs. 240.
Let the numbers be x and x + 10. Therefore, x + (x + 10) = 50. Simplifying this gives 2x + 10 = 50, so x = 20. Therefore, the numbers are 20 and 30.
The perimeter of a rectangle is 2 × (length + width). Therefore, 50 = 2 × (15 + width). Solving for width, we get width = 10 meters.
Let the cost price be x. Therefore, 1200 = x + 20% of x, or 1200 = x + 0.2x = 1.2x. Solving for x, we get x = Rs. 1000.
The side length of the square is √49 = 7 cm. Therefore, the perimeter is 4 × 7 = 28 cm.
Speed = Distance / Time. Therefore, the speed is 400 / 50 = 8 meters per second.
The total number of balls is 20 + 30 + 50 = 100 balls.
The cost of 15 books is 15 × 80 = Rs. 1200.
Using the Pythagorean theorem, the distance from the starting point is √(5² + 12²) = √(25 + 144) = √169 = 13 km.
Let the numbers be x, x + 1, x + 2, x + 3, and x + 4. The sum is x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 75. Simplifying this gives 5x + 10 = 75, so x = 13. Therefore, the numbers are 13, 14, 15, 16, and 17.
The perimeter is the sum of all three sides. Therefore, 40 = 12 + 2x, where x is the length of each equal side. Solving for x, we get x = 14 cm.
Top Indian Books for Class 10 Maths Chapter 1 Exercise 1.2 Solutions
R.S. Aggarwal – "Mathematics for Class 10"
Publisher: S. Chand Publications
This book provides a structured approach to exercises, with detailed explanations for each solution. It includes problems that cover a wide range of difficulty levels, focusing on strengthening basic concepts. Chapter 1 focuses on real numbers and their properties, with problems requiring step-by-step breakdowns.
M.L. Aggarwal – "Mathematics for Class 10"
Publisher: Arya Publishing House
M.L. Aggarwal’s book is known for its clear explanations and extensive practice questions. Chapter 1 of this book offers questions related to real numbers, providing in-depth solutions with a focus on Euclidean division, prime factorization, and the fundamental theorem of arithmetic.
R.D. Sharma – "Mathematics for Class 10"
Publisher: Dhanpat Rai Publications
The book by R.D. Sharma is ideal for students looking to build a strong foundation. Chapter 1 includes exercises on understanding number theory concepts, offering solutions for various types of questions such as division algorithms and solving simple equations based on divisibility rules.
K.K. Gupta – "Mathematics for Class 10"
Publisher: Viva Publications
K.K. Gupta’s book provides a good balance of theory and practice, with clear-cut explanations for every topic. Chapter 1 includes questions that test knowledge of real numbers, focusing on prime factorization and the Euclidean algorithm. It is well-suited for students aiming for better exam preparation.
K.C. Sinha – "Mathematics for Class 10"
Publisher: Bharti Bhawan
Known for its engaging explanations, this book emphasizes practice and understanding. Chapter 1 contains questions on real numbers, their properties, and divisibility tests. The solutions encourage step-by-step thinking and logical problem-solving.
D.C. Pandey – "Problems in Mathematics"
Publisher: Arihant Publications
D.C. Pandey’s book offers a practical approach to mathematics. Chapter 1 includes various problem-solving techniques, including the application of the Euclidean division algorithm. It helps students practice real-life scenarios and test their understanding of mathematical principles.
R.N. Kapoor – "Mathematics for Class 10"
Publisher: Kalyani Publishers
This book focuses on clear explanations and offers numerous practice exercises. Chapter 1 solutions involve problems that require students to apply their knowledge of divisibility and prime factorization, reinforcing core concepts essential for further study.
Arihant – "Mathematics for Class 10"
Publisher: Arihant Publications
Arihant’s book covers all major topics with ample examples. Chapter 1 exercises deal with real numbers and Euclidean division, where students practice solving equations related to prime factorization and the application of the fundamental theorem of arithmetic.
S.K. Gupta – "Mathematics for Class 10"
Publisher: Dhanpat Rai Publications
This book is widely used in schools and focuses on building a deep understanding of mathematical concepts. The questions in Chapter 1 challenge students to solve problems involving real numbers, divisibility, and prime factorization in a step-by-step manner.
Laxmi Publications – "Mathematics for Class 10"
Publisher: Laxmi Publications
Laxmi Publications offers a book that provides essential questions from the core areas of Chapter 1. It explains real numbers in depth and offers problems that involve both theoretical concepts and practical application. The solutions encourage critical thinking and a deeper grasp of the subject.
M. Tyra – "Class 10 Mathematics"
Publisher: Goyal Brothers Prakashan
M. Tyra’s book is a favorite for competitive exam preparation. Chapter 1 contains questions that test students’ understanding of number theory and real numbers. With comprehensive solutions, it helps students grasp complex topics with ease.
Pradeep – "Mathematics for Class 10"
Publisher: Pradeep Publications
This book offers problems with varying levels of difficulty. Chapter 1 solutions focus on real numbers, including questions related to Euclidean division and prime factorization. The book is great for practicing basic concepts.
M.S. Chouhan – "Mathematics for Class 10"
Publisher: MS Chouhan Publications
This textbook provides in-depth explanations and numerous solved examples for real numbers. It emphasizes applications of divisibility rules and algorithms, helping students practice the core concepts in Chapter 1 effectively.
S. Chand – "Mathematics for Class 10"
Publisher: S. Chand Publications
A detailed textbook that offers in-depth explanations and various problem-solving methods. The chapter on real numbers includes exercises on Euclidean algorithms, with a focus on clarity and step-by-step solutions for students to practice.
N.C.E.R.T. – "Mathematics Class 10"
Publisher: National Council of Educational Research and Training
N.C.E.R.T. books are considered the primary resource for Class 10 students. Chapter 1 focuses on real numbers, offering theoretical insights and practical exercises that cover topics like prime factorization and division algorithms.
R.P. Mehta – "Class 10 Mathematics"
Publisher: Mehta Publications
This book offers practical solutions for problems involving real numbers. It covers prime factorization, Euclidean division, and fundamental theorems, helping students solidify their grasp on Chapter 1 concepts.
S. K. Mittal – "Mathematics for Class 10"
Publisher: Laxmi Publications
This textbook is known for its clear-cut explanations and practical approach. Chapter 1 includes easy-to-follow examples on divisibility and number theory, ideal for reinforcing foundational concepts.
G.S. Ratan – "Class 10 Mathematics"
Publisher: Ratan Publications
G.S. Ratan’s book focuses on conceptual clarity and easy problem-solving. Chapter 1 includes exercises on divisibility rules and number theory, helping students master these essential topics through structured solutions.
K. K. Sharma – "Mathematics for Class 10"
Publisher: New Saraswati House
K.K. Sharma’s book is designed to build a deep understanding of real numbers. Chapter 1 offers practice problems on Euclidean algorithms and prime factorization, reinforcing key topics necessary for Class 10 exams.
S. P. Koiry – "Mathematics for Class 10"
Publisher: Koiry Publications
This book emphasizes strong problem-solving skills with a variety of exercises. Chapter 1 includes solutions for real numbers, focusing on divisibility, prime factorization, and applying the Euclidean algorithm.
Chapter 1 in Class 10 Maths focuses on real numbers, a fundamental concept that lays the foundation for higher mathematics. Exercise 1.2 provides students with a series of problems designed to test their understanding of topics such as Euclidean division, the fundamental theorem of arithmetic, and prime factorization. These exercises require students to apply mathematical reasoning, step-by-step methods, and various divisibility rules.
Real numbers play an essential role in day-to-day life and further mathematics, so mastering this chapter is crucial. For students working through Exercise 1.2, the primary focus is on understanding the properties of real numbers and how they interact with one another. This includes solving equations, simplifying expressions, and proving that certain numbers cannot be factored in simpler ways.
One of the key components of Exercise 1.2 is the Euclidean division algorithm, which helps to break down numbers into smaller, manageable parts. By understanding this algorithm, students can solve complex division problems with greater ease. It’s important to work through the steps slowly and methodically, ensuring that each part of the division process is thoroughly understood.
Prime factorization is another important concept covered in this exercise. By breaking down numbers into their prime factors, students gain a deeper understanding of how numbers relate to one another. This also aids in simplifying fractions, finding the greatest common divisor (GCD), and determining whether two numbers are relatively prime.
Students can also expect to encounter word problems in this chapter, which require them to apply their knowledge of real numbers to solve practical problems. These problems might involve finding the least common multiple (LCM) of two numbers, determining whether one number divides another evenly, or proving whether two numbers have common factors.
Expert-backed recommendations for approaching this exercise include practicing regularly, reviewing the concepts behind each problem before solving, and breaking down each solution into manageable steps. Consistency in practice helps reinforce these mathematical concepts, ensuring that students understand not only how to solve the problems but why these methods work.
Teachers often recommend that students first focus on understanding the theory behind each question before diving into the exercises. This helps build a solid foundation and makes problem-solving smoother. Afterward, tackling a variety of problems at different levels of difficulty can ensure that students are prepared for any type of question that might appear on exams. The key to mastering this chapter lies in continuous practice, clear reasoning, and logical application of the fundamental principles of real numbers.
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