Mathematics is a subject that many students find challenging, and class 10 Maths can be particularly daunting. However, it is essential to have a solid understanding of Maths at this level, as it is the foundation for higher education in various fields such as engineering, sciences, and economics. This is where NCERT solutions for class 10 Maths Chapter 1 come in. In this article, we will provide a detailed overview of NCERT solutions for class 10 Maths Chapter 1, which deals with Real Numbers based on NEW NCERT 2023

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Select Exercise (only 2 exercises in new NCERT)

## Class 10 Maths Exercise 1.1 Solutions

### 1 Express each number as a product of its prime factors:

(i) 140

(ii) 156

(iii) 3825

(iv) 5005

(v) 7429

Solution:

### 2. Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = Product of the two numbers:

(i) 26 and 91

(ii) 510 and 92

(iii) 336 and 54

Solution:

### 3. Find the LCM and HCF of the following integers by applying the prime factorization method:

(i) 12, 15 and 21

(ii) 17, 23 and 29

(iii) 8, 9 and 25

Solution:

### 4. Given that HCF (306, 657) = 9, find LCM (306, 657).

Solution:

### 5. Check whether 6^{n} can end with the digit 0 for any natural number n.

Solution:

### 6. Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.

Solution:

7. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction. After how many minutes will they meet again at the starting point?

Solution: Lcm of 12 and 18 is 36. so the minimum time when they will meet again at starting point is 36 minutes

## Class 10 Maths Exercise 1.2 Solutions

### 1. Prove that √5 is irrational.

Solution:

### 2. Show that 3 + √5 is irrational.

Solution:

### 3. Prove that the following are irrational.

Solution: