9th Class Mathematics Number System and its Operations Question Bank

done Number Systems Total Questions - 45

• question_answer1)
  Which of the following is not a rational number?
  A)
  \[\sqrt{2}\]                                 done clear
  B)
  \[\sqrt{4}\]         done clear
  C)
  \[\sqrt{9}\]                     done clear
  D)
         \[\sqrt{16}\]                   done clear
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• question_answer2)
  Of which of the following is the set of natural numbers a subset?
  A)
   The set of even numbers. done clear
  B)
   The set of odd numbers. done clear
  C)
   The set of composite numbers. done clear
  D)
   The set of real numbers. done clear
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• question_answer3)
  Which is an irrational number between \[\sqrt{2}\]and\[\sqrt{3}\]?
  A)
  \[{{2}^{\frac{1}{2}}}\]                        done clear
  B)
         \[{{3}^{\frac{1}{4}}}\]                        done clear
  C)
  \[{{6}^{\frac{1}{4}}}\]                        done clear
  D)
         \[{{6}^{\frac{1}{8}}}\] done clear
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• question_answer4)
  What type of a number is\[\left( 6+\sqrt{2} \right)\left( 6-\sqrt{2} \right)\]?
  A)
   Rational number            done clear
  B)
   Irrational number done clear
  C)
          Prime number done clear
  D)
          Negative Integer done clear
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• question_answer5)
  What type of a number is\[{{\left( \sqrt{2}+\sqrt{3} \right)}^{2}}\]?
  A)
   A rational number done clear
  B)
   An irrational number done clear
  C)
   A fraction done clear
  D)
   A decimal number done clear
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• question_answer6)
  Given \[X\]: Every fraction is a rational number and \[Y\]: Every rational number is a fraction. Which of the following is correct?
  A)
   \[X\] is False and \[Y\] is True. done clear
  B)
   \[X\] is True and \[Y\] is False. done clear
  C)
   Both \[X\] and \[Y\] are True. done clear
  D)
   Both \[X\] and \[Y\] are False. done clear
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• question_answer7)
  What is the rationalizing factor of\[\left( 2\sqrt[3]{5} \right)\]?
  A)
  \[\sqrt[3]{5}\]                             done clear
  B)
  \[\sqrt[3]{{{5}^{2}}}\]  done clear
  C)
  \[{{5}^{2}}\]               done clear
  D)
         \[{{5}^{3}}\]               done clear
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• question_answer8)
  What is the rationalizing factor of\[\sqrt[5]{{{a}^{2}}{{b}^{3}}{{c}^{4}}}\]?
  A)
  \[\sqrt[5]{{{a}^{3}}{{b}^{2}}c}\]       done clear
  B)
         \[\sqrt[4]{{{a}^{3}}{{b}^{2}}c}\]       done clear
  C)
         \[\sqrt[3]{{{a}^{3}}{{b}^{2}}c}\]       done clear
  D)
         \[\sqrt{{{a}^{3}}{{b}^{2}}c}\] done clear
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• question_answer9)
  What is the rational denominator of\[\frac{2\sqrt[3]{5}}{\sqrt[3]{9}}\]?
  A)
  \[1\]                              done clear
  B)
  \[2\]      done clear
  C)
  \[3\]                  done clear
  D)
         \[4\] done clear
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• question_answer10)
  Find the value of\[{{\left( \sqrt[6]{27}-\sqrt{6\frac{3}{4}} \right)}^{2}}\]
  A)
  \[\frac{\sqrt{3}}{2}\]                  done clear
  B)
         \[\frac{3}{2}\]   done clear
  C)
  \[\frac{\sqrt{3}}{4}\]                  done clear
  D)
         \[\frac{3}{4}\]               done clear
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• question_answer11)
  What is the product of\[\sqrt[3]{4}\]and\[\sqrt[3]{22}\]?
  A)
  \[2\sqrt[3]{11}\]              done clear
  B)
  \[\left( 3\sqrt{11} \right)\] done clear
  C)
         \[4\sqrt{11}\]     done clear
  D)
         \[8\sqrt[3]{11}\]              done clear
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• question_answer12)
  What is the quotient when \[\sqrt[6]{12}\] is divided by\[\sqrt{3}\sqrt[3]{2}\]?
  A)
  \[\frac{1}{\sqrt[2]{3}}\]              done clear
  B)
         \[\frac{1}{\sqrt[3]{3}}\]              done clear
  C)
  \[\frac{1}{\sqrt[4]{3}}\]              done clear
  D)
         \[\frac{1}{\sqrt[5]{3}}\]              done clear
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• question_answer13)
  If\[\frac{-4}{7}=\frac{-32}{x}\], what is the value of\[x\]?
  A)
  \[-56\]                done clear
  B)
         \[56\]                 done clear
  C)
  \[-65\]                done clear
  D)
         \[65\]                 done clear
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• question_answer14)
  Find the value of \[x-{{y}^{x-y}}\] when \[x=2\] and\[y=-2\].
  A)
  \[18\]                 done clear
  B)
         \[-18\]                done clear
  C)
  \[14\]                 done clear
  D)
         \[-14\]                done clear
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• question_answer15)
  If\[{{9}^{x+2}}=240+{{9}^{x}}\], find\[x\].
  A)
  \[0.5\]                done clear
  B)
         \[0.2\]                done clear
  C)
  \[0.4\]                done clear
  D)
         \[0.1\]                done clear
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• question_answer16)
  Which expression is equal to\[{{({{x}^{-1}}+{{y}^{-1}})}^{1}}\]?
  A)
  \[xy\]                 done clear
  B)
         \[x+y\]  done clear
  C)
  \[\frac{xy}{x+y}\]         done clear
  D)
         \[\frac{x+y}{xy}\]                     done clear
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• question_answer17)
  If\[{{10}^{x}}=64\], what is the value of\[{{10}^{\frac{x}{2}+1}}\]?
  A)
   \[18\]                            done clear
  B)
   \[42\]                done clear
  C)
          \[80\]                done clear
  D)
          \[81\]                done clear
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• question_answer18)
  If \[\frac{x}{{{x}^{1.5}}}=8{{x}^{-1}}\]and\[x>0\], find\[x\].
  A)
  \[\frac{\sqrt{2}}{4}\]                  done clear
  B)
         \[2\sqrt{2}\]                   done clear
  C)
  \[4\]                  done clear
  D)
         \[125\]               done clear
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• question_answer19)
  If\[{{4}^{x}}-{{4}^{x-1}}=24\], what is the value of\[{{(2x)}^{x}}\]?
  A)
  \[5\sqrt{5}\]                   done clear
  B)
         \[\sqrt{5}\]                     done clear
  C)
  \[25\sqrt{5}\]     done clear
  D)
         \[125\]               done clear
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• question_answer20)
  If\[x=\sqrt{5}+2\], find the value of\[x-\frac{1}{x}\].
  A)
  \[2\sqrt{5}\]                   done clear
  B)
         \[4\]                  done clear
  C)
  \[2\]                  done clear
  D)
         \[\sqrt{5}\]         done clear
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• question_answer21)
  If\[x=\frac{2}{3-\sqrt{7}}\], find the value of\[{{(x-3)}^{2}}\].
  A)
  \[1\]                  done clear
  B)
         \[3\]                  done clear
  C)
  \[6\]                  done clear
  D)
         \[7\]                  done clear
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• question_answer22)
  If\[x=7+4\sqrt{3}\]and\[xy=1\], what is the value of\[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}\]?
  A)
  \[64\]                             done clear
  B)
  \[134\]               done clear
  C)
  \[194\]               done clear
  D)
         \[1/49\]              done clear
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• question_answer23)
  If\[\sqrt{5}=2.236\]and\[\sqrt{3}=1.732\], find the value of\[\frac{1}{\sqrt{5}-\sqrt{3}}\].
  A)
  \[3.968\]            done clear
  B)
         \[\frac{1}{3.968}\]         done clear
  C)
  \[1.984\]            done clear
  D)
         \[\sqrt{0.504}\]   done clear
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• question_answer24)
  Identify a rational number between \[-5\] and\[5\].
  A)
   \[0\]                 done clear
  B)
  \[-7.3\]               done clear
  C)
          \[-5.7\]  done clear
  D)
         \[1.101100110001\]. done clear
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• question_answer25)
  The sum of the digits of a number is subtracted from the number, the resulting number is always divisible by which of the following numbers?
  A)
   \[2\]                             done clear
  B)
   \[5\]                 done clear
  C)
   \[8\]                 done clear
  D)
          \[9\]     done clear
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• question_answer26)
  Find the difference between \[1.\overline{4}\] and\[0.\overline{2}\].
  A)
  \[0.\overline{2}\]            done clear
  B)
         \[1.\overline{3}\] done clear
  C)
  \[\frac{11}{9}\] done clear
  D)
  \[\frac{12}{9}\] done clear
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• question_answer27)
  If \[\sqrt{a}\] is an irrational number, what is\[a\]?
  A)
   Rational            done clear
  B)
          Irrational           done clear
  C)
          0                                 done clear
  D)
   Real                 done clear
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• question_answer28)
  Which of the following is an irrational number?
  A)
  \[\sqrt{9}\]                     done clear
  B)
         \[\pi \]                done clear
  C)
  \[\frac{22}{7}\]              done clear
  D)
         \[2.5151515...\]              done clear
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• question_answer29)
              Which of the following numbers is an irrational number?
  A)
  \[\sqrt{16}-4\]    done clear
  B)
         \[\left( 3-\sqrt{3} \right)\left( 3+\sqrt{3} \right)\] done clear
  C)
                     \[\sqrt{5}+3\]    done clear
  D)
         \[-\sqrt{25}\] done clear
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• question_answer30)
  If\[x=2+{{2}^{1/3}}+{{2}^{2/3}}\], find the value of\[({{x}^{3}}-6{{x}^{2}}+6x)\].
  A)
  \[2\]                  done clear
  B)
          \[4\]                 done clear
  C)
   \[8\]                 done clear
  D)
          \[6\]                 done clear
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• question_answer31)
  If\[x=\frac{1}{2-\sqrt{3}}\], find the value of\[{{x}^{3}}-2{{x}^{2}}-7x+10\].
  A)
   \[14\]                done clear
  B)
          \[8\]                 done clear
  C)
   \[4\]                 done clear
  D)
          \[16\]                done clear
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• question_answer32)
  If\[a=3\]and\[b=5\], find the value of\[{{a}^{a}}+{{b}^{b}}\].
  A)
   \[512\]              done clear
  B)
          \[251\]              done clear
  C)
   \[513\]              done clear
  D)
          \[152\]              done clear
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• question_answer33)
  If\[p=3\]and\[q=5\], find the value of\[{{\left( \frac{1}{p}+\frac{1}{q} \right)}^{p}}\].
  A)
   \[\frac{3375}{512}\]      done clear
  B)
          \[\frac{512}{3375}\]      done clear
  C)
          \[\frac{512}{225}\]                   done clear
  D)
          \[\frac{64}{225}\]                     done clear
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• question_answer34)
  Find the value of\[\frac{1}{\sqrt{5}-\sqrt{4}}\].
  A)
   \[\sqrt{5}-\sqrt{4}\]        done clear
  B)
          \[\sqrt{5}+\sqrt{4}\]      done clear
  C)
   \[\frac{\sqrt{5}+\sqrt{4}}{9}\]   done clear
  D)
          \[\sqrt{4}-\sqrt{5}\]        done clear
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• question_answer35)
  Find the rational number for\[0.\overline{5}\].
  A)
  \[\frac{9}{5}\]               done clear
  B)
         \[\frac{5}{10}\]  done clear
  C)
  \[\frac{5}{9}\]               done clear
  D)
         \[\frac{10}{5}\]              done clear
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• question_answer36)
  Identify the simplest form of\[\frac{5\sqrt{3}+3\sqrt{5}}{5\sqrt{3}-3\sqrt{5}}\].
  A)
  \[6+\sqrt{15}\]               done clear
  B)
  \[4+\sqrt{15}\]   done clear
  C)
  \[4+\sqrt{3}\]    done clear
  D)
         \[6+\sqrt{5}\]                done clear
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• question_answer37)
  Find the value of\[\frac{{{(0.6)}^{0}}-{{(0.1)}^{-1}}}{{{\left( \frac{3}{8} \right)}^{-1}}{{\left( \frac{3}{2} \right)}^{3}}+{{\left( \frac{-1}{3} \right)}^{-1}}}\].
  A)
  \[\frac{-2}{3}\]              done clear
  B)
         \[\frac{3}{2}\]               done clear
  C)
  \[-\frac{3}{2}\]              done clear
  D)
         \[\frac{2}{3}\]   done clear
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• question_answer38)
  \[m\] and \[n\] are integers and\[\sqrt{mn}=10\]. Which of the following cannot be a value of\[m+n\]?
  A)
  \[25\]                             done clear
  B)
  \[52\]                 done clear
  C)
  \[101\]               done clear
  D)
         \[50\]                 done clear
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• question_answer39)
  If\[2.5252525...=\frac{p}{q}\](in the lowest form) what is the value of\[\frac{q}{p}\]?
  A)
  \[0.4\]                done clear
  B)
         \[0.42525\]         done clear
  C)
  \[0.0396\]          done clear
  D)
         \[0.396\]                        done clear
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• question_answer40)
  If\[{{x}^{x\sqrt{x}}}={{\left( x\sqrt{x} \right)}^{x}}\], find the value of\[x\].
  A)
  \[\frac{3}{2}\]                           done clear
  B)
  \[\frac{2}{9}\]               done clear
  C)
  \[\frac{9}{4}\]                           done clear
  D)
  \[\frac{4}{9}\] done clear
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• question_answer41)
  Simplify\[\frac{{{a}^{\frac{1}{2}}}+{{a}^{-\frac{1}{2}}}}{1-a}+\frac{1-{{a}^{-\frac{1}{2}}}}{1+\sqrt{a}}\].
  A)
   \[1\]                 done clear
  B)
          \[0\]     done clear
  C)
   \[\frac{2}{1-a}\]            done clear
  D)
          \[1+a\] done clear
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• question_answer42)
  Which symbol is used to denote a collection of all positive integers?
  A)
   \[N\]                 done clear
  B)
          \[W\]                done clear
  C)
          \[Z\]                             done clear
  D)
   \[Q\]                 done clear
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• question_answer43)
  Find the value of \[0.9999.......\] in the form of\[\frac{p}{q}\](\[p,\,\,q\in Z\]and\[q\ne 0\])
  A)
  \[\frac{1}{9}\]               done clear
  B)
         \[\frac{2}{9}\]   done clear
  C)
  \[\frac{9}{10}\]              done clear
  D)
  \[1\]                  done clear
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• question_answer44)
  If\[x=\sqrt[3]{2+\sqrt{3}}\], find the value of\[{{x}^{3}}+\frac{1}{{{x}^{3}}}\].
  A)
   \[2\]                 done clear
  B)
          \[4\]                 done clear
  C)
   \[8\]                 done clear
  D)
          \[9\]                             done clear
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• question_answer45)
  Find the simplest rationalising factor of\[{{5}^{1/3}}+{{5}^{-1/3}}\]
  A)
  \[{{5}^{2/3}}+1+{{5}^{-2/3}}\]        done clear
  B)
  \[{{5}^{1/3}}-{{5}^{-1/3}}\]  done clear
  C)
         \[{{5}^{2/3}}-1+{{5}^{-2/3}}\]          done clear
  D)
         \[{{5}^{2/3}}+1-{{5}^{-2/3}}\]                      done clear
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