Number Systems CBSE Questions & Answers

Number Systems

This is Mathematics Class 09 Number Systems CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(x = 2 + \sqrt 3 \), then \(x + {1 \over x}\) =
  • A
    4
    Correct
  • B
    5
  • C
    -4
  • D
    -5
2
The decimal form of \({2 \over {11}}\) is
  • A
    0.18
  • B
    \(0.0\overline {18} \)
  • C
    \(0.\overline {18} \)
    Correct
  • D
    0.018
3
The simplest form of \(0.\overline {36} \) is
  • A
    none of these
  • B
    \({{36} \over {100}}\)
  • C
    \({4 \over {11}}\)
    Correct
  • D
    \({4 \over 9}\)
4
The simplest form of \(0.5\overline 7 \) is
  • A
    \({{57} \over {100}}\)
  • B
    none of these
  • C
    \({{57} \over {99}}\)
  • D
    \({{26} \over {45}}\)
    Correct
5
A number which can neither be expressed as a terminating decimal nor as a repeating decimal is called
  • A
    a whole number
  • B
    a rational number
  • C
    an irrational number
    Correct
  • D
    an integer
6
The decimal form of \({1 \over {999}}\) is
  • A
    \(0.00\overline 1 \)
  • B
    0.999
  • C
    \(0.0\overline {01} \)
  • D
    \(0.\overline {001} \)
    Correct
7
If ‘m’ is a positive integer which is not a perfect square, then \(\sqrt m \) is
  • A
    a rational number
  • B
    an integer
  • C
    a natural number
  • D
    an irrational number
    Correct
8
If ‘m’ is a positive integer which is not a perfect cube, then \(\root 3 \of m \) is
  • A
    an integer
  • B
    a natural number
  • C
    an irrational number
    Correct
  • D
    a rational number
9
Every real number is
  • A
    neither rational nor irrational
  • B
    irrational
  • C
    rational
  • D
    either rational or irrational
    Correct
10
Which of the following statement is true?
  • A
    \(\sqrt {a - b} = \sqrt a - \sqrt b \)
  • B
    \(\sqrt {ab} = \sqrt a \times \sqrt b \)
    Correct
  • C
    \(\root 3 \of {ab} = \sqrt a \times \sqrt b \)
  • D
    \(\sqrt {a + b} = \sqrt a + \sqrt b \)
11
The value of \(15\sqrt {15} \div 3\sqrt 5 \) is
  • A
    5
  • B
    3
  • C
    \(5\sqrt 3 \)
    Correct
  • D
    \(3\sqrt 5 \)
12
The value of \({2 \over {\sqrt 5 - \sqrt 3 }}\) is
  • A
    \(\sqrt 5 - \sqrt 3 \)
  • B
    \(\sqrt 5 + \sqrt 3 \)
    Correct
  • C
    \({1 \over {\sqrt 5 - \sqrt 3 }}\)
  • D
    \({1 \over {\sqrt 5 + \sqrt 3 }}\)
13
If \({{2 + \sqrt 3 } \over {2 - \sqrt 3 }} = a + b\sqrt 3 \), then
  • A
    a = -7 and b = -4
  • B
    a = 7 and b = -4
  • C
    a = 7 and b = 4
    Correct
  • D
    a = -7 and b = 4
14
If \(x = 3 + \sqrt 8 \) , then the value of \(\left( {{x^2} + {1 \over {{x^2}}}} \right)\) is
  • A
    32
  • B
    34
    Correct
  • C
    12
  • D
    6
15
If \(x = 4 - \sqrt {15} \), then the value of \(\left( {x + {1 \over x}} \right)\) is
  • A
    7
  • B
    10
  • C
    8
    Correct
  • D
    6