SELF TEST:
1. Use Euclid’s division algorithm to find the HCF of (i) 768 and 468 (2 mk)
2. Show that any positive odd integer is of the form 10q + 1, or 10q + 3, or 10q + 5, where q is some integer. (2 mk)
3. Karan has 180 apples and 150 guavas. He wants to pack them into packets containing equal number of fruits. What is the maximum number of fruits that each packet can hold? (2 mk)
4. Prove that n2 is even for every positive integer n. (2 mk)
5. Using Euclid’s Division Algorithm, find the HCF of 480 and 210 (2 mk)
6. Two tankers contain 540 litres and 300 litres of petrol respectively. A container with maximum capacity is used which can measure the petrol of either tanker in exact number of litres. How many containers of petrol are there in the first tanker. (2 mk)
7. Three people go for a morning walk together. Their steps measure 70 cm, 84 cm and 105 cm respectively. What is the minimum distance travelled when their steps will exactly match after starting the walk assuming that their walking speed is same. (3 mk)
8. In a seminar, the number of participants speaking in German, English and French are 207, 135 and 117 respectively. Find the numbers of rooms required to house them if in each room, the same number of participants are to be accommodated and all of them must belong to the same language. (2 mk)
9. Prove that 3 3√7 is an irrational number. (2 mk)
10. Find the LCM of 1824 and 1080. (2 mk)