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Show that cube of any positive integer i...

Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3, for some integer m.

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The correct Answer is:
`4q+3`
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CBSE COMPLEMENTARY MATERIAL-REAL NUMBERS-SHORT ANSWER TYPE QUESTION-II
  1. Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3...

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  2. Prove that sqrt(3) is an irrational number.

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  3. State fundamental theorem of arithmetic and hence find the unique fact...

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

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  5. Prove that 5-3/7 sqrt(3) is an irrational number.

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  6. Prove that 1/(2-sqrt(5)) is an irrational number.

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  7. Find HCF and LCM of 56 and 112 by prime factorization method.

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  8. Explain why: 7xx11xx13xx15+15 is a composite number.

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  9. Explain why: 11xx13xx17+17 is a composite number.

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  10. Explain why: 1xx2xx3xx5xx7+3xx7 is a composite number.

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  11. In a morning walk, three persons step off together and their steps mea...

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  12. During a sale, colour pencils were being sold in packs of 24 each a...

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  13. Find the largest number that divides 32 and 99 having leaving remaind...

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  14. The HCF of 65 and 117 is expressible in the form 65m-117. Find the val...

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  15. Using Euclid's division algorithm, find the largest number that divide...

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  16. Show that the square of any odd integer is of the form 4m+1, for some ...

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  17. Find the HCF of 180, 252 and 324 by Euclid's Division algorithm.

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  18. Find the greatest number of six digits exactly divisible by 18, 24 and...

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  19. Three bells toll at intervals of 9, 12, 15 minutes. If they start toll...

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  20. Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, whe...

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