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For any positive integer n, prove that n...

For any positive integer n, prove that `n^(3) - n` is divisible by 6.

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KUMAR PRAKASHAN-REAL NUMBERS -TEST YOUR SKILLS
  1. Using Euclid’s division algorithm, find the HCF of 5404 and 4800

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  2. Using Euclid’s division algorithm, find the HCF of 1620, 1725 and 255.

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  3. For any positive integer n, prove that n^(3) - n is divisible by 6.

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  4. Find the missing numbers a, b, c and d in the following factor tree

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  5. Find the HCF of 525 and 1120 by the prime factorisation method. Then, ...

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  6. The HCF of 128 and 68 is expressible in ? the form 128 m - 1 5 x 6 8 ....

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  7. Explain why 5 x 7 x 13 + 13 is a composite number

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  8. The HCF of two numbers is 145 and their LCM is 2175. If one of the nu...

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  9. Find the HCF and LCM of 510 and 92 and also verify that HCF x LCM = th...

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  10. Find the HCF and LCM of 60, 120 and 288.

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  11. Prove that 3 +2 sqrt(5) is irrational.

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  12. Prove that sqrt(3) + sqrt(5) is irrational.

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  13. Prove that sqrt(11) is irrational.

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  14. Prove that 5sqrt(7) is irrational.

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  15. Prove that (2)/sqrt(3) is irrational.

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  16. Prove that sqrt(p) + sqrt(q) is irrational, where p and q are primes.

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  17. Prove that there is no rational number whose square is 6.

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  18. Without actually performing the long division, , state whether the fol...

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  19. Express 0.bar43 in the (p)/(q) form

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  20. Write down the decimal expansions of the following rational numbers wi...

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