CBSE 10 Mathematics Real Numbers Practice Paper 01
1. The decimal expansion of the rational number \(\frac{43}{2^4 5^3}\) will terminate after how many places of decimals?
2. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.
3. Find LCM of numbers whose prime factorisation are expressible as 3 × 52 and 32 × 72.
4. Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.
5. Explain why (17 × 5 × 11 × 3 × 2 + 2 × 11) is a composite number?
6. Prove that 3 + 2√3 is an irrational number.
7. Three bells rings at intervals of 12, 18, 21 minutes respectively. If they start ringing together, after what time will they next ring together?
8. Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times.
9. Find the HCF of 255 and 867 by Euclid’s division algorithm.
10. Show that any positive odd integer is of the form 4q + 1 or 4q + 3 where q is a positive integer.
11. Prove that √3 is an irrational number.
12. Prove that \(\frac{1}{\sqrt3}\) is an irrational number.
13. Show that any positive even integer is of the form of 6m or 6m+2 where m is some integer.
14. Find the largest number which divides 28 and 32 leaving remainder 8 and 12 respectively.
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