Real Number System Important Questions

8th Standard

    Reg.No. :
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Maths

Time : 02:00:00 Hrs
Total Marks : 50
    10 x 1 = 10
  1. The additive inverse of \(\frac { -3 }{ 5 } \) is __________ .

    (a)

    \(\frac { -3 }{ 5 } \)

    (b)

    \(\frac { 5 }{ 3 } \)

    (c)

    \(\frac { 3 }{ 5 } \)

    (d)

    \(\frac { -5 }{ 3 } \)

  2. ________ has no reciprocal.

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    \(\frac {1}{4}\)

  3. The multiplicative inverse of 2-4 is

    (a)

    2

    (b)

    4

    (c)

    24

    (d)

    -4

  4. (-2)-2 is equal to

    (a)

    \(\frac{1}{2}\)

    (b)

    \(\frac{1}{4}\)

    (c)

    \(\frac{-1}{2}\)

    (d)

    \(\frac{-1}{4}\)

  5.  \(\frac { 2 }{ 5 } \times \frac { 4 }{ 7 } =\) ____________

    (a)

    \(\frac { 14 }{ 20 } \)

    (b)

    \(\frac { 8 }{ 35 } \)

    (c)

    \(\frac { 20 }{ 14 } \)

    (d)

    \(​​\frac { 35 }{ 8 } \)

  6. \(\left( 1-\frac { 1 }{ 2 } \right) +\left( \frac { 3 }{ 4 } -\frac { 1 }{ 4 } \right) \)

    (a)

    0

    (b)

    1

    (c)

    \(\frac { 1 }{ 2 } \)

    (d)

    \(\frac { 3 }{ 4 } \)

  7. Which of the following numbers is a perfect cube?

    (a)

    125

    (b)

    36

    (c)

    75

    (d)

    100

  8. The number of zeros at the end of the cube of 100 is

    (a)

    1

    (b)

    2

    (c)

    4

    (d)

    6

  9. Which of the following is false?

    (a)

    Cube of any odd number is odd.

    (b)

    A perfect cube does not end with two zeros.

    (c)

    The cube of a single digit number may be a single digit number.

    (d)

    There is no perfect cube which ends with 8.

  10. Find the smallest number by which the number 108 must be multiplied to obtain a perfect cube

    (a)

    2

    (b)

    3

    (c)

    4

    (d)

    5

  11. 10 x 2 = 20
  12. Simplify: \(\left( 1\frac { 1 }{ 3 } +\frac { 2 }{ 3 } \right) \times \frac { 8 }{ 15 } \)

  13. By observing the unit’s digits, which of the numbers 3136, 867 and 4413 can not be perfect squares?

  14. Simplify: \({ \left( \frac { 3 }{ 2 } \right) }^{ 5 }\)

  15. Find the value of the following:
    34 x 3-3

  16. Find the value of the following:
    \({ \left( \frac { 3 }{ 8 } \right) }^{ 5 }\times { \left( \frac { 3 }{ 8 } \right) }^{ 4 }\div { \left( \frac { 3 }{ 8 } \right) }^{ 9 }\)

  17. Find the square root of 529 using long division method.

  18. Simplify:
    \(\frac { { \left( { 2 }^{ 2 } \right) }^{ 3 } }{ { \left( { 3 }^{ 2 } \right) }^{ 2 } } \)

  19. Find the value of the following :
    (-4)3

  20. Find the cube root of 512.

  21. Is 250 a perfect cube? If not, then by which smallest natural number should 250 be divided so that the quotient is a perfect cube?

  22. 10 x 3 = 30
  23. Name the property under addition used in each of the following :
    \(\frac { 4 }{ 9 } +\left( \frac { 7 }{ 8 } +\frac { 1 }{ 2 } \right) =\left( \frac { 4 }{ 9 } +\frac { 7 }{ 8 } \right) +\frac { 1 }{ 2 } \).

  24. Name the property under multiplication used in each of the following:
    \(\frac { 2 }{ 7 } \times \left( \frac { 9 }{ 10 } +\frac { 2 }{ 5 } \right) =\frac { 2 }{ 7 } \times \frac { 9 }{ 10 } +\frac { 2 }{ 7 } \times \frac { 2 }{ 5 } \).

  25. Use distributive property of multiplication of rational numbers and simplify:
    \(\frac { -5 }{ 4 } \times \left( \frac { 8 }{ 9 } +\frac { 5 }{ 7 } \right) \)

  26. Find the value of m for which
    8m-3 = 1

  27. Simplify: \(\frac { 11 }{ 12 } \div \left( \frac { 5 }{ 9 } \times \frac { 18 }{ 25 } \right) \)

  28. Write down the unit digits of the following:
    (i) 782
    (ii) 272
    (iii) 412
    (iv) 352
    (v) 422

  29. Using the given pattern, find the missing numbers:
    12 + 22 + 2 2 = 32
    23 + 32 + 62 = 72
    32 + 42 + 122 = 132
    42 + 52 + ___ = 212
    52 + ___ + 302 = 312
    62 + 72 + ___ = ___

  30. Find the square root of the following :\(\frac{9}{64}\)

  31. Find the square root of the following numbers by the factorization method :
    5929

  32. Write the approximate value of the following numbers to the accuracy stated:
    3576274 to the nearest Lakhs.

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