RS Aggarwal Solutions for Class 10 Maths Chapter 1 Exercise 1.2 Real Numbers
In this article we have provided RS Aggarwal Solutions for Class 10 Maths Chapter 1 Exercise 1.2 prepared by our experts to help students to prepare better for their examinations.
Ananya Gupta26 Jun, 2024
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RS Aggarwal Solutions for Class 10 Maths Chapter 1 Exercise 1.2: RS Aggarwal's solutions for Class 10 Maths, Chapter 1, Exercise 1.2, focus on real numbers and their properties. This exercise helps students understand the fundamental theorem of arithmetic, which states that every composite number can be expressed as a product of prime numbers uniquely, except for the order of the primes.
The problems in this exercise involve finding the prime factorization of given numbers, determining the highest common factor (HCF) and least common multiple (LCM) using prime factorization, and solving word problems based on these concepts. By working through these solutions, students can strengthen their grasp of prime numbers and their applications, laying a strong foundation for more advanced topics in mathematics.RS Aggarwal Solutions for Class 10 Maths Chapter 1 Exercise 1.2 Overview
The RS Aggarwal Solutions for Class 10 Maths Chapter 1, Exercise 1.2, have been carefully prepared by the subject experts at Physics Wallah. These solutions help students understand real numbers, focusing on prime factorization, the highest common factor (HCF), and the least common multiple (LCM). The clear explanations and step-by-step methods make it easy for students to learn and use the fundamental theorem of arithmetic. With these expert solutions, students can build a strong foundation in real numbers, improve their problem-solving skills, and feel more confident in their math abilities.RS Aggarwal Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.2 PDF
The PDF link provided below contains the RS Aggarwal Solutions for Class 10 Maths Chapter 1, Exercise 1.2. By focusing on prime factorization, the highest common factor (HCF), and the least common multiple (LCM), these solutions make it easier for students to grasp and apply the fundamental theorem of arithmetic. This comprehensive PDF will help students in building a strong foundation in real numbers, enhancing their problem-solving skills and boosting their confidence in mathematics.RS Aggarwal Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.2 PDF
RS Aggarwal Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.2
Here we have provided RS Aggarwal Solutions for Class 10 Maths Chapter 1 Exercise 1.2 for the ease of students so that they can prepare better for their exams.
Question 16.
Solution:
We can represent any integer number in the form of: pq + r, where ‘p is divisor, ‘q is quotient’, r is remainder*. So, we can write given numbers from given in formation As : 43 = pq1 + r ...(i) 91 = pq2 + r ...(ii) And 183 = pq3 + r ...(iii) Here, we want to find greatest value of ‘p’ were r is same. So, we subtract eq. (i) from eq. (ii), we get Pq2 – Pq1 = 48 Also, subtract eq. (ii) from eq. (iii), we get pq3 – pq2 = 92 Also, subtract eq. (i) from eq. (iii), we get Pq3 – Pq1 = 140 Now, to find greatest value of ‘p’ we find HCF of 48, 92 and 140 as, 48 = 2 x 2 x 2 x 2 x 3 92 = 2 x 2 x 2 x 2 x 2 x 3 and 140 = 2 x 2 x 5 x 7 So, HCF (48, 92 and 140) = 2 x 2 = 4 Greatest number that will divide 43, 91 and 183 as to leave the same remainder in each case = 4.Question 17.
Solution:
Remainder in all the cases is 6, i.e., 20 – 14 = 6 25 – 19 = 6 35 – 29 = 6 40 – 34 = 6 The difference between divisor and the corresponding remainder is 6. Required number = (LCM of 20, 25, 35, 46) – 6 = 1400 – 6 = 1394
LCM of 2 x 2 x 2 x 3 x 5 = 120 min. (2 hr)
They will toll together after every 2 hours Total time given = 30 hours
Number of times, there will toll together in 30 hours = = 15 times
Total numbers of times = 15 + 1 (of starting time) = 16 times
Benefits of RS Aggarwal Solutions for Class 10 Maths Chapter-1 Exercise 1.2
- Clear Understanding : Provides detailed explanations, making it easier to grasp concepts like prime factorization, HCF, and LCM.
- Step-by-Step Solutions : Helps students follow a logical approach to solving problems, enhancing their problem-solving skills.
- Conceptual Clarity : Strengthens the foundational understanding of real numbers and the fundamental theorem of arithmetic.
- Confidence Boost : Builds confidence by helping students master essential math concepts, ensuring they are well-prepared for higher-level math topics.
RS Aggarwal Solutions for Class 10 Maths Chapter 1 Exercise 1.2 FAQs
What topics are covered in Exercise 1.2 of Chapter 1 in RS Aggarwal's Class 10 Maths?
Exercise 1.2 focuses on the fundamental theorem of arithmetic, prime factorization, the highest common factor (HCF), and the least common multiple (LCM) of numbers.
How does prime factorization help in finding the HCF and LCM?
Prime factorization breaks down numbers into their prime factors. The HCF is found by multiplying the smallest power of common prime factors, while the LCM is obtained by multiplying the highest power of all prime factors.
Why is the fundamental theorem of arithmetic important?
The fundamental theorem of arithmetic states that every composite number can be expressed as a product of prime numbers uniquely, except for the order of the primes. This theorem is essential for understanding the structure of numbers and for finding HCF and LCM.
Are there any common mistakes to avoid when solving problems in Exercise 1.2?
Common mistakes include incorrect prime factorization, confusing HCF with LCM, and not simplifying the final answers properly. Double-checking calculations can help avoid these errors.
Can these solutions help with competitive exams as well?
Yes, a strong grasp of real numbers, prime factorization, HCF, and LCM is beneficial for various competitive exams. Practicing these solutions can enhance problem-solving skills and mathematical understanding required for such exams.
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