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. |

## Monday, 19 September 2011

### CBSE :10th Real Numbers Extra score Test paper

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