Real Numbers Important Questions

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    6 x 1 = 6
  1. If n is a natural number then \(\sqrt { n } \) is

    (a)

    always a natural number

    (b)

    always an irrational number

    (c)

    always a rational number

    (d)

    may be rational or irrational

  2. Which one of the following, regarding sum of two irrational numbers, is true?

    (a)

    always an irrational number

    (b)

    may be a rational or irrational number

    (c)

    always a rational number

    (d)

    always an integer.

  3. An irrational number between 2 and 2.5 is

    (a)

    \(\sqrt { 11 } \)

    (b)

    \(\sqrt { 5 } \)

    (c)

    \(\sqrt { 2.5 } \)

    (d)

    \(\sqrt { 8 } \)

  4. The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is 

    (a)

    \(0.\bar { 43 } \)

    (b)

    0.45

    (c)

    \(0.4\bar { 5 } \)

    (d)

    \(0.\bar { 45 } \)

  5. \(0.\overline { 34 } +0.3\bar { 4 } \) = 

    (a)

    \(0.6\overline { 87 } \)

    (b)

    \(0.\overline { 68 } \)

    (c)

    \(0.6\bar { 8 } \)

    (d)

    \(0.68\bar { 7 } \)

  6. The decimal form of -\(\frac { 3 }{ 4 } \) is_______________

    (a)

    - 0.75

    (b)

    - 0.50

    (c)

    -0.25

    (d)

    - 0.125

  7. 5 x 1 = 5
  8. The value of \(3\sqrt { 3 } +\sqrt { 3 } \) is ______________.

    ()

    \(4\sqrt { 3 } \)

  9. The value of \(\left[ \sqrt { { x }^{ 3 } } \right] ^{2/3}\) is

    ()

    x

  10. If \(\sqrt { 10 } \)= 3.1622, then the value of is \(\frac { 1 }{ \sqrt { 10 } } \) is_________.

    ()

    0.31623

  11. The rational number equivalent to \(\frac { 5 }{ 9 } \) such that its numerator is 25 is____________ .

    ()

    \(\frac { 25 }{ 45 } \)

  12. Divide \(15\sqrt { 12 } \) by \(3\sqrt { 3 } \)the result is ___________.

    ()

    10

  13. 10 x 2 = 20
  14. Express the following in the form \({p\over q},\) where p and q are integers and q \(\ne\) 0.
    \(0.\overline {47}\)

  15. Find three different irrational numbers between the rational numbers  \(\frac { 5 }{ 7 } \) and \(\frac { 9 }{ 11 } \)

  16. Evaluate : 10 -4

  17. Find the value of  \({ 625 }^{ \frac { 3 }{ 4 } }\)

  18. Find any three rational numbers between \(\frac { -7 }{ 11 } \)and \(\frac { 2 }{ 11 } \)

  19. Represent the following as decimal form 
    (i) \(\frac { -4 }{ 11 } \)
    (ii) \(\frac { 11 }{ 75 } \)

  20. Convert the following decimal numbers in the form of \(\frac { p }{ q } (p,q\in Z\quad and\quad q\neq 0)\)
    (i) \(0.\overline { 3 } \)
    (ii) \(2.12\overline { 4 } \)
    (iii) \(0.4\overline { 5 } \)
    (iv) \(0.\overline { 568 } \)

  21. Convert the following rational numbers into decimal
    (i) \(2\over 3\)
    (ii) \(47\over 99\)
    (iii) \(-{16\over 45}\)

  22. We used to write \(\pi\) as \(\frac{22}{7}.\) Can we say \(\pi\) is a rational number?

  23. Find any 4 irrational numbers between \(\frac { 1 }{ 4 } \) and \(\frac { 1 }{ 3 } \)

  24. 3 x 3 = 9
  25. Represent \(\sqrt { 9.3 } \) on a number line

  26. Find the decimal expansion of \(\sqrt { 3 } \)

  27. Sho that \(\sqrt [ 3 ]{ 2 } >\sqrt [ 5 ]{ 3 } \)

  28. 2 x 5 = 10
  29. Find any two irrational numbers between\(\frac { 6 }{ 7 } \) and \(\frac { 12 }{ 13 } \)

  30. Find any three rational numbers between \(\frac { 1 }{ 2 } \) and \(\frac { 1 }{ 5 } \)

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