2750
1. If HCF of 124 and 148 is 4 , then its LCM is:
2746
2. The relation between HCF and LCM of 12 and 20 will be:
2741
3. Express 0.375 in the form $\frac{p}{q}$.
2763
4. If two positive integers $a$ and $b$ can be expressed as $a=x^{3} y^{2}$ and $b=x y^{3} ; x, y$ being prime numbers, then $\operatorname{HCF}(a, b)$ is:
2747
5. If $\boldsymbol{a}$ and $\boldsymbol{b}$ are two positive integers, then the relation between their LCM and HCF will be:
2759
6. Which of the following is rational number?
2748
7. The relation between their LCM and HCF, if numbers are positive integer.
2752
8. . If $H C F$ of 35 and 84 is 7 , then find its LCM:
2754
9. The LCM of 12,15 and 21 will be:
2743
10. Explain 0.0875 in the form $\frac{p}{q}$.
2751
11. Which of the following number will be terminating?
2756
12. The HCF of 36 and 78 will be:
2757
13. The LCM of 26 and 91 will be:
2760
14. For some integer $m$, every even integer is of the form
2764
15. The HCF of 870 and 225 will be:
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: