6. If a and b are two odd prime numbers, show that a - b is composite.
7. A merchant has 120 litres of oil of one kind, 180 litres of oil of another kind. He wants to sell the
oil by filling the two kinds of oil in tins of equal capacity. Find the greatest capacity of such a tin
8. Write the prime factorisation of:
(i) 72
(ii) 5005
9. In a seminar, the number of participants in Hindi, English and Mathematics are 60, 84 and 108
respectively. Find the minimum number of rooms required, if in each room the same number of
participants are to be seated and all of them being in the same subject.
10. Prove that 3 - 15 is an irrational number.
11. Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m
9m + 1 or 9m + 8.
12. Find the LCM and HCF of the following integers by applying the prime factorisation method :
(i) 12, 15 and 21
(i) 17, 23 and 29
(iii) 8, 9 and 25
13. Check whether 6" can end with the digit 0 for any natural number n.
14. There is a circular nath
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Ones digit of cube of 29
The digit 23
We know that
23³= 23×23×23
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