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Euclid Division lemma

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Using Eulids division lemma, show that the cube of any positive integer is of the form 9m , or ( 9m+1) or ( 9m+8) for some integer m.

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Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

RD SHARMA-REAL NUMBERS-All Questions
  1. Write whether (2sqrt(45)+3sqrt(20))/(2sqrt(5)) on simplification gives...

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  2. What is an algorithm?

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  3. Euclid Division lemma

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  4. If a and b are relatively prime numbers, then what is their HCF?

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  5. If p and q are two prime numbers, then what is their LCM?

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  6. What is the total number of factors of a prime number?

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  7. What is a composite number?

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  8. What is the HCF of the smallest composite number and the smallest p...

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  9. HCF of two numbers is always a factor of their LCM (True/false).

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  10. pi is an irrational number (True/false).

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  11. The sum of two prime numbers is always a prime number (True/false).

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  12. The product of any three consecutive natural numbers is divisible b...

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  13. Every even integer is of the form 2m , where m is an integer (True/...

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  14. Every odd integer is of the form 2m-1 , where m is an integer (True...

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  15. The product of two irrational numbers is an irrational number (True...

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  16. The sum of two irrational numbers is an irrational number (True/fal...

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  17. For what value of n ,\ 2^nxx5^n ends in 5.

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  18. If a and b are relatively prime numbers, then what is their HCF?

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  19. If a and b are relatively prime numbers, then what is their LCM?

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  20. Two numbers have 12 as their HCF and 350 as their LCM (True/false).

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