## Friday, May 06, 2011

### Real Number

MATHEMATICS (Class-10)
Chapter 1. Real Numbers
1. Express 3825 as a product of its prime factors.
2. Find the LCM and HCF of 8, 9 and 25 by the prime factorization method.
3. Find the HCF and LCM of 6, 72 and 120, using the prime factorization method.
4. State whether 29/343  will have a terminating decimal expansion or a non-terminating repeating decimal.
5. State whether 23/ 23 52will have a terminating decimal expansion or a non-terminating repeating decimal
6. Find the LCM and HCF of 336 and 54 and verify that LCM × HCF = product of the two numbers
7. Use Euclid’s division algorithm to find the HCF of 867 and 255
8. Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2+ 1, where is some integer.
9. Use Euclid’s division lemma to show that the cube of any positive integer is of the form 9m,9lm + 1 or 9m + 8.
10. Prove that 7 √5 is irrational.
11. Prove that √5 is irrational.
12. 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?