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The product of two consecutive integers ...

The product of two consecutive integers is divisible by 2. Is this statement true or false. Give Reason?

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Yes, two consecutive integers can be `n(n+1)`. So, one number of these two must be divisible by 2. Hence, product of number is divisiblw by 2.
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NCERT EXEMPLAR-REAL NUMBERS-Real Numbers
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  2. Write whether every positive integer can be of the form 4q+2 where q i...

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  3. The product of two consecutive integers is divisible by 2. Is this sta...

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

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  5. Write whether the square of any positive integer can be of the form 3m...

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  6. A positive integer is the form of 3q+1 q, being a natural number. Can ...

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  7. The number 525 and 3000 are both divisible only 3,5,15,25,75. What is ...

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  8. Explain why 3 xx 5 xx 7 +7 is a composite number.

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  9. Can two number have 18 as their HCF and 380 as their LCM? Give reason

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  10. Without actually performing the long divison, find if (987)/(10500) wi...

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  11. A rational number in its decimal expansion is 327.7081. What can you s...

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  12. Prove that the square of any positive integer is of the form 4q or ...

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

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  14. Show that the square of any positive integer cannot of the form 5q+2 o...

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  15. Show that the square of any positive integer cannot be of the form 6m+...

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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. If n is an odd positive integer, show that (n^2-1) is divisible by 8.

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  18. Prove that if xa n dy are odd positive integers, then x^2+y^2 is even ...

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  19. Use Euclid division algorithm to find the HCF of 441, 567 and 693.

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