| NCERT EXERCISE 1.1 – REAL NUMBERS |
| [A] Write the answer of the following questions |
| 1. Express number as a product of its prime factors : 140 |
| 2. Express number as a product of its prime factors : 156 |
| 3. Express number as a product of its prime factors : 3825 |
| 4. Express number as a product of its prime factors : 5005 |
| 5. Express number as a product of its prime factors : 7429 |
| 6. Find the LCM and HCF of the given integers by applying the prime factorisation method : 12, 15 and 21 |
| 7. Find the LCM and HCF of the given integers by applying the prime factorisation method : 17, 23 and 29 |
| 8. Find the LCM and HCF of the given integers by applying the prime factorisation method : 8, 9 and 25 |
| 9. Check whether $$6^n$$ can end with the digit 0 for any natural number $$n$$. |
| [B] Write the answer of the following questions |
| 10. Find the LCM and HCF of 26 and 91 and verify that LCM × HCF $$=$$ product of the two numbers. |
| 11. Find the LCM and HCF of 510 and 92 and verify that LCM × HCF $$=$$ product of the two numbers. |
| 12. Find the LCM and HCF of 336 and 54 and verify that LCM × HCF $$=$$ product of the two numbers. |
| 13. Given that $${HCF}(306,657)=9$$, find $${LCM}(306,657)$$. |
| 14. Explain why $$7 \times 11 \times 13 + 13$$ and $$7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$$ are composite numbers. |
| 15. Sonia takes 18 minutes and Ravi takes 12 minutes to complete one round of a circular field. After how many minutes will they meet again at the starting point? |
| NCERT EXERCISE 1.2 – IRRATIONAL NUMBERS |
| 16. Prove that the given is irrational : $$7\sqrt{5}$$ |
| 17. Prove that the given is irrational : $$6+\sqrt{2}$$ |
| [C] Write the answer of the following questions |
| 18. Prove that $$\sqrt{5}$$ is irrational. |
| 19. Prove that $$3+2\sqrt{5}$$ is irrational. |
| 20. Prove that the given is irrational : $$\frac{1}{\sqrt{2}}$$ |
| [D] Write the answer of the following questions |
| 21. Prove that the following are irrationals: (i) $$\frac{1}{\sqrt{2}}$$ |
