2746
1. The relation between HCF and LCM of 12 and 20 will be:
2747
2. If $\boldsymbol{a}$ and $\boldsymbol{b}$ are two positive integers, then the relation between their LCM and HCF will be:
2762
3. The decimal expansion of the rational number $\frac{7}{5}$ will terminate after:
2755
4. . The LCM of 8,9 and 25 will be:
2761
5. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :
2764
6. The HCF of 870 and 225 will be:
2743
7. Explain 0.0875 in the form $\frac{p}{q}$.
2753
8. The decimal expansion of $\frac{17}{8}$ will be:
2742
9. Express 0.104 in the form $\frac{p}{q}$.
2759
10. Which of the following is rational number?
2754
11. The LCM of 12,15 and 21 will be:
2751
12. Which of the following number will be terminating?
2756
13. The HCF of 36 and 78 will be:
2750
14. If HCF of 124 and 148 is 4 , then its LCM is:
2760
15. For some integer $m$, every even integer is of the form
Chapter 1 of Class 10 Maths, Real Numbers, forms the basis of advanced mathematics. Here are the key topics covered in this chapter:
The Fundamental Theorem of Arithmetic states that every composite number can be expressed (factorized) as a product of prime numbers in a unique way, except for the order of primes. For example:
Euclid's Division Lemma 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
Applications include finding the HCF of two numbers.
Proving that certain numbers, such as \( \sqrt{2} \), \( \sqrt{3} \), and \( \sqrt{5} \), are irrational involves using proof by contradiction and the properties of prime factorization.
Rational numbers have either a terminating or repeating decimal expansion. For example:
Understanding Real Numbers is crucial as it lays the foundation for higher-level mathematical concepts and problem-solving skills. The topics in this chapter are also frequently tested in board exams.
Looking for more practice? Check out these resources: