**VINAYAK JTUDY JUNCTION, BEAWAR**

**Weakly test paper**

**Class 10 ^{th} Maths Real Numbers Time 1 hour MM 20**

- The product of three integer p,q,r is 72 where p, q, rare positive integers. HCF of p and q is 2. HCF of p and r is 1. Find the LCM of p,q,r2. Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.
3. Find the LCM and HCF of 6 and 20 by the prime factorization method.

4. State whether13/3125 will have a terminating decimal expansion or a non-terminating repeating decimal.

5. State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal.

6. Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.

7. Use Euclid’s division algorithm to find the HCF of 135 and 225

8. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m

9. Prove that √3 is irrational.

10. Show that 5 – √3 is irrational

11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

12. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

13. Express 156 as a product of its prime factors.

14. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.

15. Find the HCF and LCM of 12, 36 and 160, using the prime factorization method.

16. State whether 6/15 will have a terminating decimal expansion or a non-terminating repeating decimal.

17. State whether35/50 will have a terminating decimal expansion or a non-terminating repeatingdecimal.

18. Find the LCM and HCF of 192 and 8 and verify that LCM × HCF = product of the two numbers.

19. Use Euclid’s algorithm to find the HCF of 4052 and 12576.

20. Show that any positive odd integer is of the form of 4q + 1 or 4q + 3, where q is some integer.