Number Systems CBSE Questions & Answers

Number Systems

This is Mathematics Class 09 Number Systems CBSE Questions & Answers. There are 14 questions in this test with each question having around four answer choices.

Questions & Answers

1
\({{\sqrt 3 + \sqrt 2 } \over {\sqrt 3 - \sqrt 2 }} + {{\sqrt 3 - \sqrt 2 } \over {\sqrt 3 + \sqrt 2 }}\) =
  • A
    10
    Correct
  • B
    8
  • C
    -8
  • D
    -10
2
\({{\sqrt {32} + \sqrt {48} } \over {\sqrt 8 + \sqrt {12} }}\) =
  • A
    2
    Correct
  • B
    6
  • C
    4
  • D
    8
3
\({\left( {{{125} \over {216}}} \right)^{{{ - 1} \over 3}}}\) =
  • A
    216
  • B
    \({5 \over 6}\)
  • C
    125
  • D
    \({6 \over 5}\)
    Correct
4
If \({3^x} + 64 = {2^6} + {(\sqrt 3 )^8}\) , then the value of ‘x’ is
  • A
    3
  • B
    2
  • C
    1
  • D
    4
    Correct
5
The value of \(\root 4 \of {{{(64)}^{ - 2}}} \) is
  • A
    \({1 \over 2}\)
  • B
    \({1 \over 8}\)
    Correct
  • C
    \({1 \over {16}}\)
  • D
    \({1 \over 4}\)
6
On simplification \((3 + \sqrt 3 )(3 - \sqrt 3 )\) give
  • A
    \( - 2\sqrt 3 \)
  • B
    0
  • C
    6
    Correct
  • D
    16
7
The value of \({1 \over {\sqrt 8 - 3\sqrt 2 }}\) is
  • A
    \( - \sqrt 2 \)
  • B
    \({1 \over {\sqrt 2 }}\)
  • C
    \(\sqrt 2 \)
  • D
    \( - {1 \over {\sqrt 2 }}\)
    Correct
8
The \({p \over q}\) form of \(1.\overline {27} \), where ‘p’ and ‘q’ are integers and \(q \ne 0\) is
  • A
    \({{11} \over {14}}\)
  • B
    \({{17} \over {14}}\)
  • C
    \({{14} \over {11}}\)
    Correct
  • D
    \({{14} \over {15}}\)
9
The value of \(\root 4 \of {\root 3 \of {{2^2}} } \) is
  • A
    \({2^{{1 \over 6}}}\)
    Correct
  • B
    \({2^{{{ - 1} \over 6}}}\)
  • C
    \({2^6}\)
  • D
    \({2^{ - 6}}\)
10
The value of 1.9999………………. in the form \({p \over q}\), where ‘p’ and ‘q’ are integers and q \( \ne \) 0, is
  • A
    2
    Correct
  • B
    \({{19} \over {10}}\)
  • C
    \({{1999} \over {1000}}\)
  • D
    \({1 \over 9}\)
11
\(2\sqrt 3 + \sqrt 3 \) is equal to
  • A
    \(3\sqrt 3 \)
    Correct
  • B
    3
  • C
    \(2\sqrt 6 \)
  • D
    \(3\sqrt 6 \)
12
Which of the following is equal to ‘x’?
  • A
    \({x^{{{12} \over 7}}} \times {x^{{7 \over {12}}}}\)
  • B
    \({x^{{{12} \over 7}}} - {x^{{5 \over 7}}}\)
  • C
    \(\root {12} \of {{{\left( {{x^4}} \right)}^{{1 \over 3}}}} \)
  • D
    \({\left( {\sqrt {{x^3}} } \right)^{{2 \over 3}}}\)
    Correct
13
A rational number equivalent to a rational number \({7 \over {19}}\) is
  • A
    \({{14} \over {57}}\)
  • B
    \({{17} \over {119}}\)
  • C
    \({{21} \over {38}}\)
  • D
    \({{21} \over {57}}\)
    Correct
14
If \(\sqrt {10} = 3.162\) , then the value of \({1 \over {\sqrt {10} }}\) is
  • A
    31.62
  • B
    0.003162
  • C
    0.3162
    Correct
  • D
    3.162