Class 10 Exam > Class 10 Notes > NCERT Exercise 1.2 Solution - Real Numbers, Class 10, Mathematics
NCERT Exercise 1.2 Solution - Real Numbers, Class 10, Mathematics PDF Download
NCERT Exercise 1.2 Solution
(Page 11)
Q1: Express each number as product of its prime factors:
Ans:
Q 2: Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
Ans:
Q 3: Find the LCM and HCF of the following integers by applying the prime factorization method.
Ans:
Q 4: Given that HCF (306, 657) = 9, find LCM (306, 657).
Ans:
Q 5: Check whether 6n can end with the digit 0 for any natural number n.
Ans:
If any number ends with the digit 0, it should be divisible by 10 or in other words, it will also be divisible by 2 and 5 as 10 = 2 × 5
Prime factorization of 6n = (2 ×3)n
It can be observed that 5 is not in the prime factorization of 6n.
Hence, for any value of n, 6n will not be divisible by 5.
Therefore, 6n cannot end with the digit 0 for any natural number n.
Q 6: Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Ans:
Numbers are of two types - prime and composite. Prime numbers can be divided by 1 and only itself, whereas composite numbers have factors other than 1 and itself.
It can be observed that
7 × 11 × 13 + 13 = 13 × (7 × 11 + 1) = 13 × (77 + 1)
= 13 × 78
= 13 ×13 × 6
The given expression has 6 and 13 as its factors. Therefore, it is a composite number.
7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 = 5 ×(7 × 6 × 4 × 3 × 2 × 1 + 1)
= 5 × (1008 + 1)
= 5 ×1009
1009 cannot be factorised further. Therefore, the given expression has 5 and 1009 as its factors. Hence, it is a composite number.
Q 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?
Ans:
Ravi takes lesser time than Sonia for completing 1 round of the circular path. Since they are going in the same direction, they will meet again at the same time when Ravi will have completed 1 round of that circular path with respect to Sonia.
And the total time taken for completing this 1 round of circular path will be the LCM of time taken by Sonia and Ravi for completing 1 round of circular path respectively i.e., LCM of 18 minutes and 12 minutes.
18 = 2 × 3 × 3
And, 12 = 2 × 2 × 3
LCM of 12 and 18 = 2 × 2 × 3 × 3 = 36
So, Ravi and Sonia will meet together at the starting point after 36 minutes.
FAQs on NCERT Exercise 1.2 Solution - Real Numbers, Class 10, Mathematics
| 1. What is the importance of studying Real Numbers in Class 10 Mathematics? |  |
Ans. Studying Real Numbers in Class 10 Mathematics is important as it is the foundation of many mathematical concepts. Real Numbers are used in various mathematical operations, like solving equations, finding roots of polynomials, and many more. Understanding Real Numbers helps in understanding advanced mathematical concepts in higher classes.
| 2. What are the different types of Real Numbers? | |
Ans. Real Numbers can be classified into various types, namely Rational Numbers, Irrational Numbers, Integers, and Whole Numbers. Rational Numbers are those which can be expressed in the form of p/q, where p and q are integers and q is not equal to zero. Irrational Numbers cannot be expressed in the form of p/q and have non-terminating and non-repeating decimals. Integers are the set of whole numbers and their negative counterparts. Whole Numbers are the set of natural numbers and zero.
| 3. What is the significance of the Euclid's Division Lemma in Real Numbers? | |
Ans. Euclid's Division Lemma is a fundamental concept in Number Theory and is significant in Real Numbers as well. It states that for any two positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. This lemma is used to prove various theorems in Number Theory, like Fundamental Theorem of Arithmetic, HCF and LCM of two numbers, and many more.
| 4. How can Real Numbers be represented on a number line? | |
Ans. Real Numbers can be represented on a number line, where each point on the line corresponds to a unique Real Number. The number line is drawn horizontally, with zero at the center, and positive numbers to the right, and negative numbers to the left. The distance between any two points on the line is proportional to the difference between the corresponding Real Numbers. Irrational numbers can also be represented on the number line, but they will have non-terminating and non-repeating decimals.
| 5. What are the applications of Real Numbers in real-life scenarios? | |
Ans. Real Numbers have various applications in real-life scenarios. They are used in measuring quantities, like length, weight, temperature, and many more. Real Numbers also play a crucial role in financial calculations, like interest rates, stock prices, and currency exchange rates. They are used in various scientific fields, like physics, chemistry, and engineering, to represent values and measurements.
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