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# Maths, X

1. Show that every positive even integer is of the from 2m, and that every positive odd integer is of the form 2m + 1, where m is some integer
2. Show that any positive integer is of the form 3q or 3q + 1 or 3q + 2 for some integer
3. Use Euclid’s Lemma to show that square of any positive integer is of form 4m or 4m+1 for some integer m.
4. Find the HCF of 1656 and 4025 by Euclid’s method.
5. Find the LCM of 2520 and 2268 by prime factorization
6. Find the LCM of 336 and 54 by prime factorisation method.
7. Find the HCF and LCM of 306 and 54. Verify that HCF × LCM = Product of the two numbers.
8. A baker has 444 sweet biscuits and 276 salty biscuits. He wants to stack them in such a way that each stack has the same number and same type of biscuits and they take up the least area of the tray. What is the number of biscuits that can be placed in each stack for this purpose?
9. 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?
10. Two tankers contain 850 litres and 680 litres of petrol respectively. Find the maximum capacity of a container which can measure the petrol of either tanker in exact number of times.