Real Numbers Book Back Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  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. An irrational number between 2 and 2.5 is

    (a)

    \(\sqrt { 11 } \)

    (b)

    \(\sqrt { 5 } \)

    (c)

    \(\sqrt { 2.5 } \)

    (d)

    \(\sqrt { 8 } \)

  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. 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. Find the odd one out of the following

    (a)

    \(\sqrt { 32 } \times \sqrt { 2 } \)

    (b)

    \(\frac { \sqrt { 27 } }{ \sqrt { 3 } } \)

    (c)

    \(\sqrt { 72 } \times \sqrt { 8 } \)

    (d)

    \(\frac { \sqrt { 54 } }{ \sqrt { 18 } } \)

  6. 3 x 2 = 6
  7. Represent the following as decimal form 
    (i) \(\frac { -4 }{ 11 } \)
    (ii) \(\frac { 11 }{ 75 } \)

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

  9. Can we write 0.25 as 0.250000 ...? Can a terminating decimal be written as a recurring decimal?

  10. 3 x 3 = 9
  11. Express the following decimal expression into rational numbers. 0.86

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

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

  14. 2 x 5 = 10
  15. Find any two irrational numbers between \(\sqrt { 2 } \) and \(\sqrt { 3 } \)

  16. Express \(\frac { 1 }{ 33 } \)the rational number in recurring decimal form by using the recurring decimal expansion of \(\frac { 1 }{ 11 } \). Hence write in recurring decimal form

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