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REAL NUMBERS

1) State Euclid’s division lemma.

2) Find the greatest number which divides 615 and 963 leaving remainder 6 in eah case.

3) What is the HCF of 84 and 270.

4) Prove that 523 is an irrational number.

5) If the HCF of 60 and 168 is 12, what is the LCM of 60 and 168?

6) If the HCF and LCM of the numbers 12 and 180 respectively and one of the numbers is 36, then what is the other

number?

7) Why the number 4n, where n is a natural number, can not end with 0?

8) Prove that 43 is an irrational number.

9) Why 5 x 7 x 11 + 7 is a composite number?

10) Why 13/120 is a non terminating rational number?

11) State whether the following real numbers are rational or not:

a) 6. 43

b) 47.5369821

c) 3.2010010001…

12) Prove that 3 is an irrational number.

13) Find the HCF and LCM of 90 and 144 by the prime factorization method.

14) Use Euclids’s division algorithm to find the HCF of

a) 196 and 38220

b) 867 and 255

15) Explain why 7 x 11 x 13+ 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.

16) Check whether 6n can end with the digit 0 for any natural number n.

17) Prove that 35 is an irrational number.

18) Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively.

19) A merchant has 120 litres of oil of one kind, 180 litres of another kind and 40 litres of third kind. He wants to sell the

oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

20) If the HCF of 408 and 1032 is expressible in the form 1032m – 408 x 5, find m.