REAL NUMBER CLASS X

10th Real Numbers test paper 2012

1. Express 140 as a product of its prime factors

2. 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.

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

22. Prove that 3√2 5 is irrational.

23. Prove that 1/√2 is irrational. (3 marks)

24. In a school there are tow sections- section A and Section B of class X. There are 32 students in section A and 36 students in section B. Determine the minimum number of books required for their class library so that they can be distributed equally among students of section A or section B.

25. Express 3825 as a product of its prime factors.

26. Find the LCM and HCF of 8, 9 and 25 by the prime factorization method.

27. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.

28. State whether 29/343 will have a terminating decimal expansion or a non-terminating repeating decimal.

29. State whether 23/ 23 52 will have a terminating decimal expansion or a non-terminating repeating decimal

30. Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

31. 6. Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers

32. Use Euclid’s division algorithm to find the HCF of 867 and 255

33. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.

34. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m, 9lm + 1 or 9m + 8.

35. Prove that 7 √5 is irrational.

36. Prove that √5 is irrational.

37. There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

38. Express 5005 as a product of its prime factors.

39. Find the LCM and HCF of 24, 36 and 72 by the prime factorization method.