2763
1. 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:
2746
2. The relation between HCF and LCM of 12 and 20 will be:
2753
3. The decimal expansion of $\frac{17}{8}$ will be:
2759
4. Which of the following is rational number?
2748
5. The relation between their LCM and HCF, if numbers are positive integer.
2761
6. If HCF of 65 and 117 is expressible in the form $65 m-117$, then the value of $m$ is :
2741
7. Express 0.375 in the form $\frac{p}{q}$.
2758
8. The LCM of 45 and 75 will be:
2745
9. Express 15.75 in the form $\frac{p}{q}$.
2751
10. Which of the following number will be terminating?
2756
11. The HCF of 36 and 78 will be:
2754
12. The LCM of 12,15 and 21 will be:
2752
13. . If $H C F$ of 35 and 84 is 7 , then find its LCM:
2742
14. Express 0.104 in the form $\frac{p}{q}$.
2757
15. The LCM of 26 and 91 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: