9th Class Mathematics Number System and its Operations Question Bank

done Number System Total Questions - 40

• question_answer1)
  If \[\mathbf{x=}\frac{\mathbf{1}}{\mathbf{2-}\sqrt{\mathbf{3}}}\], what is the value of \[{{\mathbf{x}}^{\mathbf{3}}}-\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{7x}+\mathbf{5}\]
  A)
   2                                 done clear
  B)
   3 done clear
  C)
   5                                 done clear
  D)
   9 done clear
  View Solution play_arrow

• question_answer2)
  What is the value of \[\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}\], is being given that \[\sqrt{\mathbf{5}}=\mathbf{2}.\mathbf{236}\] and \[\sqrt{10}=3.1\mathbf{6}2\]
  A)
   5.398     done clear
  B)
   4.258 done clear
  C)
   5.355                           done clear
  D)
   3.855 done clear
  View Solution play_arrow

• question_answer3)
  If the sum of five consecutive integers is S, then the largest of those integers in terms of S is
  A)
   \[\frac{S-10}{5}\]                      done clear
  B)
   \[\frac{S-4}{4}\] done clear
  C)
   \[\frac{S+5}{4}\]                                  done clear
  D)
   \[\frac{S+10}{5}\] done clear
  View Solution play_arrow

• question_answer4)
  If \[x=\sqrt[3]{2+\sqrt{3}}\],then \[{{\mathbf{x}}^{\mathbf{3}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{3}}}},=\]
  A)
   2                                 done clear
  B)
   4 done clear
  C)
   8                                 done clear
  D)
   9 done clear
  View Solution play_arrow

• question_answer5)
  \[({{5}^{61}}+{{5}^{62}}+{{5}^{63}})\]is divisible by
  A)
   31        done clear
  B)
   11 done clear
  C)
   13                                done clear
  D)
   17 done clear
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• question_answer6)
  The value of: \[\sqrt{-\sqrt{3}+\sqrt{3+8\sqrt{7+4\sqrt{3}}}}\]is
  A)
   1                                 done clear
  B)
   2 done clear
  C)
   3                                 done clear
  D)
   8 done clear
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• question_answer7)
  The value of\[\frac{1}{\sqrt{6.25}+\sqrt{5.25}}+\frac{1}{\sqrt{4.25}+\sqrt{3.25}}+\frac{1}{\sqrt{5.25}+\sqrt{4.25}}+\frac{1}{\sqrt{3.25}+\sqrt{2.25}}\]is
  A)
   1.00  done clear
  B)
   1.25 done clear
  C)
   1.50                          done clear
  D)
   2.25 done clear
  View Solution play_arrow

• question_answer8)
  \[\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}=\]
  A)
   5      done clear
  B)
   4 done clear
  C)
   3                                 done clear
  D)
   2 done clear
  View Solution play_arrow

• question_answer9)
  The value of\[\sqrt{4\sqrt[3]{16\sqrt{4\sqrt[3]{16}\sqrt{4\sqrt[3]{16}}}}}......\]is
  A)
   2                                 done clear
  B)
   \[{{2}^{2}}\] done clear
  C)
   23                                done clear
  D)
   \[{{2}^{5}}\] done clear
  View Solution play_arrow

• question_answer10)
  If \[m=\sqrt{3+\sqrt{3+\sqrt{3+.....}}}\] \[n=\sqrt{3-\sqrt{3-\sqrt{3-.........}}}\] Then among the following the relation between m and n holds is
  A)
   \[m-n+1=0\]                 done clear
  B)
   \[~m+n-1=0\] done clear
  C)
   \[m+n+1=0\]            done clear
  D)
   \[m-n-1=0\] done clear
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• question_answer11)
  If \[\mathbf{x}=\frac{\sqrt{3}}{2}\], then the value of \[\sqrt{\mathbf{l}+\mathbf{a}}+\sqrt{\mathbf{l}-\mathbf{a}}\] is
  A)
   \[\sqrt{3}\]      done clear
  B)
   \[\frac{\sqrt{3}}{2}\] done clear
  C)
   \[2+\sqrt{3}\]                      done clear
  D)
   \[2-\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer12)
  A rational numbers between \[-\,\mathbf{3}\] and 4.
  A)
   - 4.5                             done clear
  B)
   -3.5             done clear
  C)
   \[\frac{13}{2}\]                                     done clear
  D)
   \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer13)
  The decimal representation of \[\frac{-26}{45}\] is
  A)
   \[.3\overline{5}\]                       done clear
  B)
   \[-1\overline{55}\]             done clear
  C)
   \[-.3\overline{55}\]                     done clear
  D)
   \[-\,0.5\overline{7}\] done clear
  View Solution play_arrow

• question_answer14)
  \[\mathbf{1}.\mathbf{272727}=\mathbf{1}.\overline{\mathbf{27}}\]can be expressed in the form \[\frac{p}{q}\], where p and q are integers an\[\mathbf{q}\ne 0\] than it is equal to
  A)
   \[\frac{106}{99}\]                     done clear
  B)
   \[\frac{127}{99}\]            done clear
  C)
   \[\frac{14}{11}\]    done clear
  D)
   \[\frac{27}{99}\] done clear
  View Solution play_arrow

• question_answer15)
  If \[\mathbf{A}={{\mathbf{2}}^{x}},\mathbf{B}={{\mathbf{4}}^{\mathbf{y}}},\mathbf{C}={{\mathbf{8}}^{z}}\], where \[\mathbf{x}=0.\overline{1},\mathbf{y}=\mathbf{0}.\overline{\mathbf{4}},\mathbf{z}=\mathbf{0}.\overline{\mathbf{6}}\], then \[\mathbf{A}\times \mathbf{B}\times \mathbf{C}\]is
  A)
   8        done clear
  B)
   2              done clear
  C)
   16                                done clear
  D)
   4 done clear
  View Solution play_arrow

• question_answer16)
  If\[x=2.\overline{3}-0.\overline{9},\,y=2.\overline{5}-0.\overline{5},\]then \[{{x}^{2}}+{{y}^{2}}-2xy\] is
  A)
   \[\frac{1}{4}\]  done clear
  B)
   \[\frac{1}{3}\] done clear
  C)
   \[\frac{1}{2}\]                          done clear
  D)
   \[\frac{1}{5}\] done clear
  View Solution play_arrow

• question_answer17)
  If \[{{\left( 3 \right)}^{0.\overline{4}+0.\overline{5}}}=x,{{\left( 27 \right)}^{0.\overline{21}+0.\overline{12}}}\] then \[x\times y\] is
  A)
   \[{{3}^{4}}\]                          done clear
  B)
   \[{{3}^{3}}\]              done clear
  C)
   32           done clear
  D)
   \[{{3}^{5}}\] done clear
  View Solution play_arrow

• question_answer18)
  If \[\mathbf{x=}\frac{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{1}}}{\sqrt{\mathbf{2}}\mathbf{-}\sqrt{\mathbf{1}}}\] and \[y\mathbf{=}\frac{\sqrt{\mathbf{2}}-\sqrt{\mathbf{1}}}{\sqrt{\mathbf{2}}+\sqrt{\mathbf{1}}}\], find the value of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{y}}^{\mathbf{2}}}\]
  A)
   96                                done clear
  B)
   34    done clear
  C)
   10                                done clear
  D)
   \[2\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer19)
  If \[\mathbf{a=3+2}\sqrt{\mathbf{2}}\]and \[\mathbf{b=}\frac{\mathbf{1}}{\mathbf{a}}\], then \[{{\mathbf{a}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{b}}^{\mathbf{2}}}\mathbf{=}\]
  A)
   49                                done clear
  B)
   34    done clear
  C)
   100                              done clear
  D)
   102 done clear
  View Solution play_arrow

• question_answer20)
  \[\frac{{{\mathbf{4}}^{\mathbf{-}}}^{\mathbf{3}}\mathbf{\times }{{\mathbf{a}}^{\mathbf{-}}}^{\mathbf{5}}\mathbf{\times }{{\mathbf{b}}^{\mathbf{4}}}}{{{\mathbf{4}}^{\mathbf{-}}}^{5}\mathbf{\times }{{\mathbf{a}}^{\mathbf{-}}}^{8}\mathbf{\times }{{\mathbf{b}}^{3}}}=\]
  A)
   \[\frac{16{{a}^{3}}}{{{b}^{7}}}\]   done clear
  B)
   \[8\frac{{{a}^{2}}}{{{b}^{-7}}}\]           done clear
  C)
   \[2\frac{{{a}^{-13}}}{{{b}^{-7}}}\]                          done clear
  D)
   \[\frac{{{a}^{8}}}{{{b}^{-1}}}\] done clear
  View Solution play_arrow

• question_answer21)
  if \[2\sqrt[3]{189}+3\sqrt[3]{448}-7\sqrt[3]{56}\] is simplified, then the resultant answer is
  A)
   \[8\sqrt[3]{7}\]                          done clear
  B)
   \[6\sqrt[3]{7}\]            done clear
  C)
   \[4\sqrt[3]{7}\]    done clear
  D)
   \[9\sqrt[3]{7}\] done clear
  View Solution play_arrow

• question_answer22)
  If \[7\sqrt[4]{162}-5\sqrt[4]{32}+\sqrt[4]{1250}\] is simplified, then the resultant value is
  A)
   \[6\sqrt[3]{2}\]                          done clear
  B)
   \[6\sqrt[4]{2}\]           done clear
  C)
   \[6\sqrt[5]{2}\]                          done clear
  D)
   \[16\sqrt[4]{2}\] done clear
  View Solution play_arrow

• question_answer23)
  The two irrational numbers lying between \[\sqrt{\mathbf{3}}\]and \[\sqrt{5}\] are
  A)
   \[{{15}^{\frac{1}{4}}},\frac{{{3}^{\frac{1}{4}}}}{1}\times {{15}^{\frac{1}{8}}}\]       done clear
  B)
   \[{{6}^{\frac{1}{2}}},{{2}^{\frac{1}{8}}}\times {{6}^{\frac{1}{4}}}\] done clear
  C)
   \[{{6}^{\frac{1}{8}}},{{2}^{\frac{1}{6}}}\times {{6}^{\frac{1}{6}}}\]        done clear
  D)
   \[{{3}^{\frac{1}{8}}},{{2}^{\frac{1}{8}}}\times {{6}^{\frac{1}{8}}}\] done clear
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• question_answer24)
  If \[x=\frac{1}{2+\sqrt{3}}\], then the value of \[{{x}^{3}}-2{{x}^{2}}-7x+5\]is
  A)
   1                     done clear
  B)
   2             done clear
  C)
   3       done clear
  D)
   4 done clear
  View Solution play_arrow

• question_answer25)
  If \[x=2-\sqrt{3}\], then the value of \[~{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{4x}+\mathbf{4}\] is.
  A)
   \[12+2\sqrt{3}\]                        done clear
  B)
   \[19+8\sqrt{3}\]          done clear
  C)
   \[12+2\sqrt{3}\]            done clear
  D)
   \[19-8\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer26)
  The value of x, when \[{{\mathbf{2}}^{x+4}}{{.3}^{x+\mathbf{l}}}=\mathbf{288}\]
  A)
   1                     done clear
  B)
   -1             done clear
  C)
   0                                 done clear
  D)
   2 done clear
  View Solution play_arrow

• question_answer27)
  Which of the following is the value of a in \[\frac{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}\mathbf{=a+b}\sqrt{\mathbf{15}}\]
  A)
   2                                 done clear
  B)
   -1             done clear
  C)
   -3                                done clear
  D)
   4 done clear
  View Solution play_arrow

• question_answer28)
  The square root of \[\mathbf{0}.\overline{\mathbf{4}}\] is
  A)
   \[0.\overline{6}\]       done clear
  B)
   \[0.\overline{7}\]              done clear
  C)
   \[0.\overline{8}\]                                   done clear
  D)
   \[0.\overline{9}\] done clear
  View Solution play_arrow

• question_answer29)
  If \[\sqrt{\mathbf{18225}}=\mathbf{135}\], then the value of \[\sqrt{182.25}+\sqrt{1.8225}+\sqrt{0.018225}+\sqrt{0.00018225}\] is
  A)
   1.49985                        done clear
  B)
   14.9985       done clear
  C)
   149.985            done clear
  D)
   1499.85 done clear
  View Solution play_arrow

• question_answer30)
  If\[{{\mathbf{2}}^{\mathbf{x-1}}}\mathbf{+}{{\mathbf{2}}^{\mathbf{x+1}}}\mathbf{=640}\], the value of x is
  A)
   7                     done clear
  B)
   8      done clear
  C)
   9                                 done clear
  D)
   6 done clear
  View Solution play_arrow

• question_answer31)
  The product of \[\left( 0.\overline{\mathbf{09}}\times \mathbf{7}.\overline{\mathbf{3}} \right)\] is equal to
  A)
   1                                 done clear
  B)
   0               done clear
  C)
   0           done clear
  D)
   \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer32)
  \[\mathbf{0}.\mathbf{142857}-\mathbf{0}.\mathbf{285714}\]is equal to
  A)
   2                                 done clear
  B)
   1               done clear
  C)
   0                                 done clear
  D)
   \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer33)
  \[\frac{\mathbf{1}}{\mathbf{1+}{{\mathbf{2}}^{\mathbf{x-y}}}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{1+}{{\mathbf{2}}^{\mathbf{y-x}}}}\mathbf{=?}\]
  A)
   \[x\]                             done clear
  B)
   \[x-y\]          done clear
  C)
   1    done clear
  D)
   0 done clear
  View Solution play_arrow

• question_answer34)
  If \[x+\sqrt{7}=7+\sqrt{y},x+\sqrt{7}=7+\sqrt{y}\], and x, y are positive integers, then the value of \[\frac{\sqrt{x}+y}{x+\sqrt{y}}\]is.
  A)
   0                     done clear
  B)
   2              done clear
  C)
   \[\frac{1}{2}\]                          done clear
  D)
   1 done clear
  View Solution play_arrow

• question_answer35)
  The largest among the numbers \[{{\mathbf{2}}^{\mathbf{250}}}\mathbf{,}{{\mathbf{3}}^{\mathbf{150}}}\mathbf{,}{{\mathbf{5}}^{\mathbf{100}}}\] and \[{{\mathbf{4}}^{\mathbf{200}}}\] is
  A)
   \[{{4}^{200}}\]       done clear
  B)
   5100               done clear
  C)
   2250                              done clear
  D)
   2150 done clear
  View Solution play_arrow

• question_answer36)
  \[\frac{{{\mathbf{a}}^{\mathbf{-1}}}}{{{\mathbf{a}}^{\mathbf{-1}}}\mathbf{+}{{\mathbf{b}}^{\mathbf{-1}}}}\mathbf{+}\frac{{{\mathbf{a}}^{\mathbf{-1}}}}{{{\mathbf{a}}^{\mathbf{-1}}}\mathbf{-}{{\mathbf{b}}^{\mathbf{-1}}}}\mathbf{=?}\]
  A)
   0                                 done clear
  B)
   1               done clear
  C)
   \[\frac{2{{b}^{2}}}{{{b}^{2}}-{{a}^{2}}}\]     done clear
  D)
   \[\frac{2{{b}^{2}}}{{{b}^{2}}+{{a}^{2}}}\] done clear
  View Solution play_arrow

• question_answer37)
   \[\frac{{{\mathbf{x}}^{\mathbf{-1}}}}{{{\mathbf{x}}^{\mathbf{-1}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{-1}}}}\mathbf{+}\frac{{{\mathbf{x}}^{\mathbf{-1}}}}{{{\mathbf{x}}^{\mathbf{-1}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{-1}}}}\mathbf{=?}\]
  A)
   \[\frac{2{{y}^{2}}}{{{y}^{2}}-{{x}^{2}}}\]    done clear
  B)
   \[\frac{2{{x}^{2}}}{{{y}^{2}}-{{x}^{2}}}\]         done clear
  C)
   \[\frac{2{{y}^{2}}}{{{y}^{2}}+{{z}^{2}}}\]         done clear
  D)
   \[\frac{2{{x}^{2}}}{{{y}^{2}}+{{x}^{2}}}\] done clear
  View Solution play_arrow

• question_answer38)
  \[\frac{{{\left( {{\mathbf{a}}^{\mathbf{x+y}}} \right)}^{\mathbf{2}}}{{\left( {{\mathbf{a}}^{\mathbf{y+z}}} \right)}^{\mathbf{2}}}{{\left( {{\mathbf{a}}^{\mathbf{z+x+}}} \right)}^{\mathbf{2}}}}{\left( {{\mathbf{a}}^{\mathbf{4x}}}\mathbf{.}{{\mathbf{a}}^{\mathbf{4y}}}\mathbf{.}{{\mathbf{a}}^{\mathbf{4z}}} \right)}\mathbf{=?}\]
  A)
   2a                                done clear
  B)
   \[x+y+z\]         done clear
  C)
   1         done clear
  D)
   0 done clear
  View Solution play_arrow

• question_answer39)
  The greatest among \[\sqrt{\mathbf{11}}\mathbf{-}\sqrt{\mathbf{9}}\mathbf{,}\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}\mathbf{,}\sqrt{\mathbf{7}}\mathbf{-}\sqrt{\mathbf{5}}\mathbf{,}\sqrt{\mathbf{13}}\mathbf{-}\sqrt{\mathbf{11}}\]is
  A)
   \[\sqrt{11}-\sqrt{9}\]           done clear
  B)
   \[\sqrt{5}-\sqrt{3}\]      done clear
  C)
   \[\sqrt{7}-\sqrt{5}\]       done clear
  D)
   \[\sqrt{13}-\sqrt{11}\] done clear
  View Solution play_arrow

• question_answer40)
  The smallest of \[\sqrt{6}+\sqrt{3},\] \[\sqrt{7}+\sqrt{2},\]\[\sqrt{8}+\sqrt{1},\] \[\sqrt{5}+\sqrt{4}\] is
  A)
   \[\sqrt{6}+\sqrt{3}\]                  done clear
  B)
   \[\sqrt{7}+\sqrt{2}\]         done clear
  C)
   \[\sqrt{8}+\sqrt{1}\]   done clear
  D)
   \[\sqrt{5}+\sqrt{4}\] done clear
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