Real Numbers Model Question Paper

9th Standard

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Maths

Time : 01:30:00 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. The number \(0.\bar { 3 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

    (a)

    \(\frac { 33 }{ 100 } \)

    (b)

    \(\frac { 3 }{ 10 } \)

    (c)

    \(\frac { 1 }{ 3 } \)

    (d)

    \(\frac { 3 }{ 100 } \)

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

    (a)

    \(0.6\overline { 87 } \)

    (b)

    \(0.\overline { 68 } \)

    (c)

    \(0.6\bar { 8 } \)

    (d)

    \(0.68\bar { 7 } \)

  5. Which one of the following has terminating decimal expansion?

    (a)

    \(\frac { 7 }{ 9 } \)

    (b)

    \(\frac { 8 }{ 15 } \)

    (c)

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

    (d)

    \(\frac { 5 }{ 32 } \)

  6. The value of \(\bar { 0.03 } \) +\(\bar { 0.03 } \)  is ___________.

    (a)

    \(\bar { 0.09 } \)

    (b)

    \(\bar { 0.09 } \)

    (c)

    \(\bar { 0.09 } \)

    (d)

    0

  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. 7 x 2 = 14
  14. Find any three rational numbers between \(\frac { -7 }{ 11 } \)and \(\frac { 2 }{ 11 } \)

  15. Express the rational number \(\frac { 1 }{ 27 } \)  in recurring decimal form by using the recurring decimal expansion of \(1\over3\) . Hence write\(\frac { 59 }{ 27 } \) in recurring decimal form.

  16. 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) \(0.\overline { 568 } \)

  17. Verify that 1 = \(0.\overline { 9 } \)

  18. We used to write \(\sqrt{2}=1.414=\frac{1414}{1000}.\) Can we say  \(\sqrt{2}\)  is a rational number?

  19. Give any two rational numbers lying between 0.5151151115…. and 0.5353353335…

  20. Find any 4 irrational numbers between \(\frac { 1 }{ 2 } \) and \(\frac { 2 }{ 3 } \)

  21. 5 x 3 = 15
  22. Express the following decimal expression into rational numbers. \(0.\overline { 24 } \)

  23. Express the following decimal expression into rational numbers \(17.2\overline { 15 } \)

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

  25. Simplify;\(\sqrt { 44 } +\sqrt { 99 } -\sqrt { 275 } \)

  26. Write in scientific notation ;(60000000)3

  27. 2 x 5 = 10
  28. Find any two irrational numbers between\(\frac { 6 }{ 7 } \) and \(\frac { 12 }{ 13 } \)

  29. Represent the following numbers on the number line.
    (i) 5.348
    (ii) \(6.\bar { 4 } \) up to 3 decimal places
    (iii) \(4.\bar { 73 } \)  upto 4 decimal places

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