Complete Solutions for Class 10 Maths Chapter 1 Exercise 1.1 with Steps

Class 10 Maths Chapter 1 Exercise 1.1 solutions explained with detailed steps. Learn how to solve all the problems in this exercise efficiently and correctly.

---

---

Here are the sample questions and answers for Class 10 Maths Chapter 1 Exercise 1.1.

Question 1:
If the sum of two numbers is 45 and their difference is 5, what are the two numbers?
Answer:
The two numbers are 25 and 20. You can find this by solving the system of equations:
x + y = 45
x - y = 5

Question 2:
What is the result when 3x + 5 = 20 is solved for x?
Answer:
x = 5. Subtract 5 from both sides and then divide by 3.

Question 3:
Simplify the expression: 3(x + 4) - 2(x - 5).
Answer:
The simplified expression is x + 22.

Question 4:
If a number is divided by 6 and then 4 is added to the result, the answer is 10. What is the number?
Answer:
The number is 36. Set up the equation as (x / 6) + 4 = 10, and solve for x.

Question 5:
What is the perimeter of a rectangle with length 10 cm and width 5 cm?
Answer:
The perimeter is 30 cm. Use the formula: perimeter = 2(l + w).

Question 6:
If a right-angled triangle has sides 6 cm and 8 cm, what is the length of the hypotenuse?
Answer:
The hypotenuse is 10 cm. Use the Pythagorean theorem: c² = a² + b².

Question 7:
Solve for y: 2y + 4 = 12.
Answer:
y = 4. Subtract 4 from both sides and then divide by 2.

Question 8:
Find the value of x in the equation 4x - 7 = 25.
Answer:
x = 8. Add 7 to both sides and then divide by 4.

Question 9:
What is the area of a triangle with base 8 cm and height 6 cm?
Answer:
The area is 24 cm². Use the formula: area = 1/2 * base * height.

Question 10:
Solve for x: 5x + 3 = 23.
Answer:
x = 4. Subtract 3 from both sides and then divide by 5.

Question 11:
Find the circumference of a circle with radius 7 cm.
Answer:
The circumference is 44 cm. Use the formula: circumference = 2 * π * radius.

Question 12:
If a number is multiplied by 9 and then 15 is subtracted, the result is 60. What is the number?
Answer:
The number is 8. Set up the equation as 9x - 15 = 60, and solve for x.

Question 13:
What is the sum of the angles in a triangle?
Answer:
The sum of the angles in a triangle is always 180°.

Question 14:
Find the simple interest on ₹5000 for 2 years at an interest rate of 5% per annum.
Answer:
The simple interest is ₹500. Use the formula: interest = (principal * rate * time) / 100.

Question 15:
Find the volume of a cube with side length 4 cm.

Answer:
The volume is 64 cm³. Use the formula: volume = side³.

Question 16:
What is the value of x in the equation 3x + 8 = 20?
Answer:
x = 4. Subtract 8 from both sides and then divide by 3.

Question 17:
Solve for y: 5y - 9 = 16.
Answer:
y = 5. Add 9 to both sides and then divide by 5.

Question 18:
What is the distance between the points (2, 3) and (5, 7)?
Answer:
The distance is 5 units. Use the distance formula: √[(x2 - x1)² + (y2 - y1)²].

Question 19:
Find the average of 10, 20, 30, and 40.
Answer:
The average is 25. Add the numbers and divide by the number of terms.

Question 20:
Solve for z: 4z - 5 = 11.
Answer:
z = 4. Add 5 to both sides and then divide by 4.

Best Indian Books for Class 10 Maths Chapter 1 Exercise 1.1 Solutions

Mathematics for Class 10 by R.D. Sharma
Publisher: Dhanpat Rai
Content: This book provides detailed solutions and a thorough explanation of various topics covered in Class 10 Maths. Chapter 1 of this book focuses on real numbers and the methods used to solve algebraic equations. The solutions are clear and well-structured, with examples and exercises that prepare students for their exams.

Mathematics for Class 10 by R.S. Aggarwal
Publisher: S. Chand Publishing
Content: R.S. Aggarwal's book is a go-to resource for Class 10 students. It includes step-by-step solutions to every problem in Chapter 1, emphasizing algebraic manipulation and understanding the relationship between variables. The exercises also feature word problems and practice questions that enhance problem-solving skills.

Together with Mathematics Class 10
Publisher: Rachna Sagar
Content: This book includes various solved examples, exercises, and practice papers. The solutions for Chapter 1 are comprehensive, and the approach is beginner-friendly. Each problem in the chapter comes with hints, explanations, and a step-by-step approach for better understanding.

NCERT Solutions for Class 10 Maths
Publisher: National Council of Educational Research and Training
Content: This official guide provides precise solutions to all the exercises in Class 10 Maths. For Chapter 1, the book covers real numbers, laws of exponents, and the Euclidean algorithm, ensuring a strong foundation for algebraic topics.

Exemplar Problems Class 10 Mathematics
Publisher: NCERT
Content: This book is focused on providing challenging problems that push students to think critically. It is ideal for students who want to deepen their understanding of mathematical concepts, particularly in real numbers, as seen in Chapter 1.

S.Chand’s Mathematics Class 10
Publisher: S. Chand
Content: Known for its easy-to-understand explanations, this book breaks down concepts in Chapter 1 into manageable steps. The exercises are designed to test the application of theories, with a blend of basic and advanced problems.

Oswal Publishers’ Mathematics Class 10
Publisher: Oswal Publishers
Content: This comprehensive guide covers all essential topics in Class 10 Maths. Chapter 1 focuses on various algebraic operations and solutions for real numbers. The exercises in this book range from basic problems to more complex ones, perfect for revision.

CBSE Chapterwise Solutions Class 10 Maths
Publisher: Arihant Publications
Content: This book provides solutions to all the chapters with detailed explanations. Chapter 1 has a focus on real numbers and algebraic expressions, helping students practice both theoretical and application-based questions.

Modern’s ABC of Mathematics for Class 10
Publisher: Modern Publishers
Content: A popular book, this one offers well-explained solutions for all topics, including Chapter 1. The book emphasizes exercises related to real numbers, Euclidean algorithms, and properties of integers, helping students grasp the content quickly.

Laxmi Publications’ Mathematics for Class 10
Publisher: Laxmi Publications
Content: The book provides detailed solutions for exercises in Chapter 1. The focus here is on helping students solve real-number problems using the Euclidean algorithm, with special attention given to simplification techniques.

Class 10 Maths Chapter 1 Exercise 1.1 Solutions: A Comprehensive Guide to Mastering Real Numbers

Class 10 Maths Chapter 1 Exercise 1.1 Solutions deals with the fundamentals of real numbers, one of the essential topics in the syllabus. This chapter is foundational for students, as it introduces concepts like the Euclidean algorithm, laws of exponents, and the understanding of irrational and rational numbers. To master this chapter and tackle Exercise 1.1 effectively, students need a solid understanding of the underlying principles and ample practice.

The first step in solving the problems of Exercise 1.1 is understanding the properties of real numbers. Real numbers are divided into rational and irrational numbers. Rational numbers are those that can be expressed as fractions (p/q), while irrational numbers cannot be expressed as fractions and have non-terminating, non-repeating decimals. Key concepts in this exercise include learning how to simplify square roots and understanding the concept of Euclidean division.

For example, one of the key skills emphasized is the application of the Euclidean algorithm to find the greatest common divisor (GCD) of two numbers. This method involves repeatedly dividing the larger number by the smaller one until the remainder is zero. The last non-zero remainder is the GCD of the two numbers, an essential concept for solving various types of problems in this chapter.

Another essential topic covered in Chapter 1 is the laws of exponents. These rules help simplify expressions involving powers and make it easier to handle complex algebraic equations. Exercise 1.1 provides several problems where students can apply these laws to simplify expressions and solve for unknown variables. Mastery of these laws is vital for progressing in higher mathematics.

While the questions in Exercise 1.1 are mostly focused on real numbers and algebraic expressions, the importance of conceptual clarity cannot be overstated. Many of the problems require students to apply basic algebraic operations such as addition, subtraction, multiplication, and division. With regular practice, students will gain proficiency in these fundamental operations, setting the stage for success in more advanced chapters.

For students looking to strengthen their grasp on the subject, it is recommended to use a combination of textbooks and reference materials. Books like R.D. Sharma, R.S. Aggarwal, and NCERT provide clear and step-by-step solutions for Chapter 1, making them excellent resources for students to practice. Solutions from these books often break down complex problems into simple steps, making it easier for students to follow and understand.

While preparing for exams, it is crucial for students to practice consistently and seek help whenever needed. Teachers and tutors can provide valuable insights, but self-study and regular practice are key to mastering the solutions in Exercise 1.1. Additionally, students should try to solve previous years' question papers to get a sense of the exam pattern and the type of questions that may appear in the actual test.

 

---