CBSE Class 10 – Mathematics
Chapter 1: Real Numbers
Hard / Frequently Asked Questions

1. Using Euclid’s Division Lemma, find the HCF of 210 and 55, and show that it can be expressed as a linear combination of 210 and 55.

2. Prove that 5/√3 is an irrational number.

3. A sweet seller has 420 kaju barfis and 130 badam barfis. He wants to stack them in such a way that each stack has the same number of pieces and no piece is left over. What is the maximum number of pieces in each stack?

4. Show that the square of any positive integer is of the form 3m or 3m+1, where m is an integer.

5. Prove that there are infinitely many prime numbers of the form 6n + 5, where n is a natural number.

6. Find the HCF of 96 and 404 by Euclid’s Division Lemma method. Hence, find integers x and y such that
HCF(96, 404) = 96x + 404y.

7. Show that 7 + 5√2 is an irrational number.

8. Prove that √7 is irrational.

9. Find the HCF of 867 and 255, and express it as a linear combination of these numbers.

10. Show that one and only one of the numbers n, n+2, n+4 is divisible by 3, where n is any positive integer.