# Class 10 – Real Numbers – Previous Years Questions

Real Numbers – Previous Years Questions

1. What is the HCF of smallest prime number and the smallest composite number ? [CBSE 2018] [1 Mark]
2. Find after how many places of decimal the decimal form of the number $\frac{27}{{2^{3}}.5^{4}.3^{2}}$ will terminate. [CBSE 2019] [1 Mark]
3. Express 429 as a product of its prime factors. [CBSE 2019] [1 Mark]
4. $\frac{2+\sqrt{5}}{3}$ is __________ number. [CBSE 2020] [1 Mark]
5. Given that HCF (135, 225) = 45, find the LCM (135, 225). [CBSE 2020] [1 Mark]
6. After how many decimal places will the decimal representation of the rational number $\frac{229}{2^{2}\times&space;5^{7}}$ terminate? [CBSE 2020] [1 Mark]
7. Given that  2 is irrational, prove that (5+3 2) is an irrational number. [CBSE 2018] [2 Marks]
8. If HCF of 65 and 117 is expressible in the form 65n – 117, then find the value of n. [CBSE 2019] [2 Marks]
9. On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm, and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? [CBSE 2019] [2 Marks]
10. Find HCF and LCM of 404 and 96 and verify that HCF x LCM = Product of the two given numbers. [CBSE 2018] [3 Marks]
11. Prove that 3 is an irrational number. [CBSE 2019] [3 Marks]
12. Find the largest number which on dividing 1251, 9377, and 15628 leaves remainders 1, 2 and 3 respectively. [CBSE 2019] [3 Marks]
13. Prove that 5 is an irrational number. [CBSE 2020] [3 Marks]