Olympiad – Class IX – Mathematics - Number Systems

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Question - 1

Which of the following is not a rational number?

  • A \(\sqrt { 2 } \)
  • B \(\sqrt { 4 } \)
  • C \(\sqrt { 9 } \)
  • D \(\sqrt { 16 } \)

Question - 2

Of which of the following is the set of natural numbers a subset?

  • A The set of even numbers.
  • B The set of odd numbers.
  • C The set of composite numbers.
  • D The set of real numbers.

Question - 3

Which is an irrational number between \(\sqrt { 2 } \ and\ \sqrt { 3 } \)?

  • A \({ 2 }^{ \frac { 1 }{ 2 } }\)
  • B \({ 3 }^{ \frac { 1 }{ 4 } }\)
  • C \({ 6 }^{ \frac { 1 }{ 4 } }\)
  • D \({ 6 }^{ \frac { 1 }{ 8 } }\)

Question - 4

What type of a number is \(\left( 6+\sqrt { 2 } \right) \left( 6-\sqrt { 2 } \right) \)?

  • A Rational number
  • B Irrational number
  • C Prime number
  • D Negative Integer

Question - 5

What type of a number is \(\left( \sqrt { 2 } +{ \sqrt { 3 } } \right) ^{ 2 }\)?

  • A A rational number
  • B An irrational number
  • C A fraction
  • D A decimal number

Question - 6

Given X : Every fraction is a rational number. and
Y: Every rational number isafraction.
Which of the following is correct?

  • A X is False and Y is True.
  • B X is True and Y is False
  • C Both X and Yare True.
  • D Both X and Yare False.

Question - 7

What is the rationalizing factor of \(\left( 2\sqrt [ 3 ]{ 5 } \right) \)?

  • A \(\sqrt [ 3 ]{ 5 } \)
  • B \(\sqrt [ 3 ]{ { 5 }^{ 2 } } \)
  • C 52
  • D 53

Question - 8

What is the rationalizing factor of \(\sqrt [ 5 ]{ { a }^{ 2 }{ b }^{ 3 }{ c }^{ 4 } } \)?

  • A \(\sqrt [ 5 ]{ { a }^{ 3 }{ b }^{ 2 }{ c } } \)
  • B \(\sqrt [ 4 ]{ { a }^{ 3 }{ b }^{ 2 }c } \)
  • C \(\sqrt [ 3 ]{ { a }^{ 2 }{ b }^{ 2 }c } \)
  • D \(\sqrt { { a }^{ 3 }{ b }^{ 2 }c } \)

Question - 9

What is the rational denominator of \(\frac { 2\sqrt [ 3 ]{ 5 } }{ \sqrt [ 3 ]{ 9 } } \)?

  • A 1
  • B 2
  • C 3
  • D 4

Question - 10

Find the value of \({ \left( \sqrt [ 6 ]{ 27 } -\sqrt { 6\frac { 3 }{ 4 } } \right) }^{ 2 }\)

  • A \(\frac { \sqrt { 3 } }{ 2 } \)
  • B \(\frac { 3 }{ 2 } \)
  • C \(\frac { \sqrt { 3 } }{ 4 } \)
  • D \(\frac { 3 }{ 4 } \)
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