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If n is an odd integer then show that ...

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

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VK GLOBAL PUBLICATION-REAL NUMBERS-Proficiency Exercise (Short Answer Questions-II)
  1. Show that 12^n cannot end with the digits 0 or 5 for any natural numbe...

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

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  3. Find the HCF (210, 55) by Euclid's Division algorithm

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  4. Find the greatest number that will divide 445, 572 and 699 leaving ...

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  5. Write the denominator of the rational number 257/5000 in the form 2^m ...

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  6. Using prime factorisation method, find the LCM or 21, 28, 36, 45.

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  7. Prove that 1/ sqrt3 is irrational.

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  8. Use Euclid's division algorithm to find the HCF of: (i) 4052 and 12576...

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  9. Find the greatest number of 6 digits exactly divisible by 24, 15 an...

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  10. express the given decimal expansion in the form of p/q 0.2bar26

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  11. Show that 9^n cannot end with the digit 2 for any n in N.

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  12. Express 3825 as product of its prime factors using factor tree.

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  13. Find the HCF of 306 and 657 by the prime factorisation method. Hence f...

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

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  15. Show that 2sqrt3 is an irrational number.

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  16. The length, breadth and height of a room are 8m and 25cm, 6m and 75m ...

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

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  18. Find the LCM and HCF of the following pairs of integers and verify th...

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  19. Find the largest number which divides 318 and 739 leaving remainder 3 ...

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