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
The value of \({{3\sqrt {12} } \over {6\sqrt {27} }}\) is
  • A
    \({1 \over 3}\)
    Correct
  • B
    \(\sqrt 3 \)
  • C
    \(\sqrt 2 \)
  • D
    \({1 \over 2}\)
2
\((5 + \sqrt 8 ) + (3 - \sqrt 2 )(\sqrt 2 - 6)\) is
  • A
    positive and irrational
  • B
    positive and rational
    Correct
  • C
    negative and rational
  • D
    negative and irrational
3
\(8\sqrt {15} \div 2\sqrt 3 \)
  • A
    \(4\sqrt 5 \)
    Correct
  • B
    \(4\sqrt {15} \)
  • C
    none of these
  • D
    \(2\sqrt 5 \)
4
If \({x^{{1 \over {12}}}} = {49^{{1 \over {24}}}}\), then the value of ‘x’ is
  • A
    49
  • B
    7
    Correct
  • C
    2
  • D
    12
5
Which of the following is a rational number?
  • A
    \(\pi \)
  • B
    0
    Correct
  • C
    \(2\sqrt 3 \)
  • D
    \(1 + \sqrt 3 \)
6
The simplest form of \({25^{{1 \over 3}}} \times {5^{{1 \over 3}}}\) is
  • A
    125
  • B
    25
  • C
    5
    Correct
  • D
    none of these
7
The rational number not lying between \({{ - 1} \over 5}\) and \({{ - 2} \over 5}\) is
  • A
    \({{ - 1} \over 4}\)
  • B
    0
    Correct
  • C
    \({{ - 3} \over {10}}\)
  • D
    \({{ - 7} \over {25}}\)
8
If \(\sqrt 3 = 1.732\) and \(\sqrt 2 = 1.414\), then the value of \({1 \over {\sqrt 3 - \sqrt 2 }}\) is
  • A
    \({1 \over {\sqrt {1.732} - \sqrt {1.414} }}\)
  • B
    0.318
  • C
    \({1 \over {3.146}}\)
  • D
    3.146
    Correct
9
The simplified form of \({16^{{{ - 1} \over 4}}} \times \root 4 \of {16} \) is
  • A
    16
  • B
    4
  • C
    1
    Correct
  • D
    6
10
\({2^{{4 \over 3}}}\) is same as
  • A
    none of these
  • B
    \(\root 4 \of {{2^3}} \)
  • C
    \(\root 3 \of 4 \)
  • D
    \(\root 3 \of {{2^4}} \)
    Correct
11
The value of ‘x’ in \(3 + {2^x} = {(64)^{{1 \over 2}}} + {(27)^{{1 \over 3}}}\) is
  • A
    14
  • B
    8
  • C
    5
  • D
    3
    Correct
12
The value of \({x^{a - b}} \times {x^{b - c}} \times {x^{c - a}}\) is
  • A
    1
    Correct
  • B
    2
  • C
    x
  • D
    0
13
If \(a = - 2,b = - 1\), then \({a^b} - {b^a}\) is equal to
  • A
    -2
  • B
    0
  • C
    -3
    Correct
  • D
    -1
14
If \({{3 - \sqrt 5 } \over {3 + 2\sqrt 5 }} = a\sqrt 5 - {{19} \over {11}}b\) , then the value of ‘b’ is
  • A
    3
  • B
    2
  • C
    1
    Correct
  • D
    a
15
The value of \({\left( {{{81} \over {16}}} \right)^{{{ - 3} \over 4}}} \times \left\{ {{{\left( {{{25} \over 9}} \right)}^{{{ - 3} \over 2}}} \div {{\left( {{5 \over 2}} \right)}^{ - 3}}} \right\}\) is
  • A
    4
  • B
    1
    Correct
  • C
    3
  • D
    2