8th Class Mathematics Algebraic Expressions Question Bank

done Algebraic Expressions & Identities Total Questions - 40

• question_answer1)
  \[{{\left( 3a-2b+5c \right)}^{2}}\]
  A)
   \[9{{a}^{2}}+4{{b}^{2}}+25{{c}^{2}}-12\,ab-20\,bc+30\,ac\] done clear
  B)
   \[9{{a}^{2}}-4{{b}^{2}}-5{{c}^{2}}+12\,ab-20\,bc-30\,ac\] done clear
  C)
   \[9{{a}^{2}}+4{{b}^{2}}-5{{c}^{2}}-12\,ab-20\,bc+30\,ac\] done clear
  D)
   \[3{{a}^{2}}+4{{b}^{2}}-5{{c}^{2}}-12\,ab-20\,bc-30\,ac\] done clear
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• question_answer2)
  If \[\mathbf{x}+\frac{1}{x}=\mathbf{4}\], find the value of \[{{\mathbf{x}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{2}}}}\]
  A)
   16                                done clear
  B)
   18              done clear
  C)
   14      done clear
  D)
   12 done clear
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• question_answer3)
  If \[{{\mathbf{a}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{a}}^{\mathbf{2}}}}=\mathbf{14}\]find the value of \[{{x}^{\mathbf{2}}}+\frac{1}{{{x}^{\mathbf{2}}}}\]
  A)
   2                                 done clear
  B)
   4               done clear
  C)
   \[2\sqrt{3}\]   done clear
  D)
  \[\sqrt{3}\] done clear
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• question_answer4)
  If \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})=125\] and \[\left( \mathbf{ab}+\mathbf{b}c+\mathbf{ca} \right)=\mathbf{50}\] find the value of \[\left( \mathbf{a}+\mathbf{b}+\mathbf{c} \right)\]
  A)
   10                                done clear
  B)
   15    done clear
  C)
   \[\sqrt{15}\]                              done clear
  D)
   12 done clear
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• question_answer5)
  Simplify\[\frac{6}{m}-\frac{(3-n)}{2mn}\]
  A)
   \[\frac{11n-3}{2mn}\]             done clear
  B)
   \[\frac{13n-3}{2{{m}^{2}}n}\]          done clear
  C)
   \[\frac{11n-3}{2{{m}^{2}}n}\]        done clear
  D)
   \[\frac{13n-3}{2mn}\] done clear
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• question_answer6)
  Simplify: \[\frac{3{{p}^{2}}-15{{p}^{3}}q}{12{{p}^{2}}q}\]
  A)
   \[\frac{1-5q}{40q}\]                  done clear
  B)
   \[\frac{1-5q}{4q}\]           done clear
  C)
   \[\frac{1-5pq}{4q}\]  done clear
  D)
   \[\frac{1-5pq}{4{{p}^{2}}q}\] done clear
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• question_answer7)
  If \[x+\frac{1}{x}=\sqrt{5}\], then the value of \[{{\mathbf{x}}^{\mathbf{3}}}+\frac{1}{{{x}^{3}}}\]
  A)
   \[8\sqrt{5}\]                  done clear
  B)
   \[2\sqrt{5}\]  done clear
  C)
   \[5\sqrt{5}\]                  done clear
  D)
   \[7\sqrt{5}\] done clear
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• question_answer8)
  If \[\mathbf{a}+\frac{1}{a}=\frac{17}{4}\]then the value of \[\mathbf{a}-\frac{1}{a}\]is
  A)
   4                                 done clear
  B)
   13/4              done clear
  C)
   17/4                             done clear
  D)
   15/4 done clear
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• question_answer9)
  If \[\left( \mathbf{a}+\mathbf{b} \right)=\mathbf{2}\] and \[\left( \mathbf{a}-\mathbf{b} \right)=\mathbf{10}.\] Find the value of \[\left( {{a}^{2}}+{{b}^{2}} \right)=10.\]
  A)
   40                                done clear
  B)
   52    done clear
  C)
   38                                done clear
  D)
   42 done clear
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• question_answer10)
  If \[{{\mathbf{x}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{2}}}}=\mathbf{7}\], find the value of \[\left( x+\frac{1}{x} \right)\]
  A)
   6                                 done clear
  B)
   9                done clear
  C)
   3        done clear
  D)
   4 done clear
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• question_answer11)
  If \[\left( \mathbf{3a}+\mathbf{4b} \right)=\mathbf{16}\] and \[\mathbf{ab}=\mathbf{4}.\]Find the value of \[\left( \mathbf{9}{{\mathbf{a}}^{\mathbf{2}}}+\mathbf{16}{{\mathbf{b}}^{\mathbf{2}}} \right)\]
  A)
   160   done clear
  B)
   100             done clear
  C)
   120                              done clear
  D)
   140 done clear
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• question_answer12)
  If \[\left( \mathbf{a}+\mathbf{b}+\mathbf{c} \right)=\mathbf{15}\] and \[(ab+bc+ca)=74,\] find the value of \[\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}} \right)\]
  A)
   67                                done clear
  B)
   77               done clear
  C)
   57                                done clear
  D)
   37 done clear
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• question_answer13)
  If \[\left( 3x-2y \right)=5\] and \[\mathbf{xy}=\mathbf{6}.\]Find the value of \[~27{{x}^{3}}-8{{y}^{3}}\]
  A)
   550                              done clear
  B)
   625             done clear
  C)
   665  done clear
  D)
   675 done clear
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• question_answer14)
  If \[{{\left( x+\frac{1}{x} \right)}^{2}}=3\] find the value of \[{{x}^{3}}+\frac{1}{{{x}^{3}}}\]
  A)
   1                                 done clear
  B)
   0    done clear
  C)
   \[-1\]                            done clear
  D)
   2 done clear
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• question_answer15)
  If \[{{\mathbf{a}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{a}}^{\mathbf{2}}}}=27\] find the value of \[\left( {{a}^{3}}-\frac{1}{{{a}^{3}}} \right)\]
  A)
   120                              done clear
  B)
   140    done clear
  C)
   100                              done clear
  D)
   110 done clear
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• question_answer16)
  If \[\mathbf{x}+\frac{1}{\mathbf{x}}=\mathbf{4}\] then, what is the value of \[{{\mathbf{x}}^{4}}+\frac{1}{{{\mathbf{x}}^{4}}}\]
  A)
   191                              done clear
  B)
   192             done clear
  C)
   193                              done clear
  D)
   194 done clear
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• question_answer17)
  If \[\mathbf{a}+\mathbf{b}=\mathbf{7}\]and \[\mathbf{ab}=\mathbf{12}\] then what is the value of \[{{\mathbf{a}}^{\mathbf{2}}}-\mathbf{ab}-{{\mathbf{b}}^{\mathbf{2}}}\]
  A)
   12                                done clear
  B)
   13              done clear
  C)
   14                                done clear
  D)
   \[-\]5 done clear
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• question_answer18)
  If \[{{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}+{{\mathbf{c}}^{\mathbf{2}}}=\mathbf{20},\text{ }\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\] find\[\mathbf{ab}+\mathbf{b}c+\mathbf{ca}\]
  A)
   10                                done clear
  B)
   \[-\]10 done clear
  C)
   20                                done clear
  D)
  \[-\]20 done clear
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• question_answer19)
  If \[x-\frac{1}{x}=3\] then find \[\frac{x}{{{x}^{2}}+1}\] is
  A)
   9                                 done clear
  B)
   \[\frac{1}{3}\]              done clear
  C)
   13                                done clear
  D)
   \[\frac{1}{\sqrt{13}}\] done clear
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• question_answer20)
  If \[\mathbf{ab}=\mathbf{6}\]and \[\mathbf{a}+\mathbf{b}=\mathbf{5}\], then the value of \[{{\mathbf{a}}^{\mathbf{2}}}+{{\mathbf{b}}^{\mathbf{2}}}\]is
  A)
   11                                done clear
  B)
   12              done clear
  C)
   13  done clear
  D)
   16 done clear
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• question_answer21)
  If \[\mathbf{x}+\frac{1}{\mathbf{x}}=\mathbf{5}\], then the value of \[{{\mathbf{x}}^{2}}+\frac{1}{{{\mathbf{x}}^{2}}}=\]
  A)
   21                                done clear
  B)
   22             done clear
  C)
   23    done clear
  D)
   24 done clear
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• question_answer22)
  What must be subtracted from \[3{{a}^{2}}-6ab-3{{b}^{2}}-1\] to get \[4{{a}^{2}}-7ab-4{{b}^{2}}+1?\]
  A)
   \[-{{a}^{2}}+ab+{{b}^{2}}-2\]        done clear
  B)
   \[{{a}^{2}}+ab+{{b}^{2}}+2\] done clear
  C)
   \[{{a}^{2}}-ab-{{b}^{2}}+2\]      done clear
  D)
   \[{{a}^{2}}-ab-4{{b}^{2}}-2\] done clear
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• question_answer23)
  Find the sum of the given expression \[-5{{x}^{2}}+3x-8,4x+7-2{{x}^{2}}\]and \[\mathbf{6}-\mathbf{2x}+\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}\]
  A)
   \[2x+3y+z\]                 done clear
  B)
   \[x+2y+3z\] done clear
  C)
   \[9x+6y+4z\]                done clear
  D)
   \[-5{{x}^{2}}+5x+5\] done clear
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• question_answer24)
  Simplify : \[\left( 4x+5y \right)\left( 4x-5y \right)\]
  A)
   \[16{{x}^{2}}-25xy\]              done clear
  B)
   \[16{{x}^{2}}-5{{y}^{2}}\] done clear
  C)
   \[16{{x}^{2}}-5{{y}^{2}}\] done clear
  D)
   \[16{{x}^{2}}-{{y}^{2}}\] done clear
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• question_answer25)
  Solve the expression \[\left( x-\frac{3}{x} \right)\left( x-\frac{3}{x} \right)=\]
  A)
   \[{{x}^{2}}+\frac{9}{{{x}^{2}}}-18\]          done clear
  B)
   \[{{x}^{3}}+\frac{9}{{{x}^{3}}}-6\] done clear
  C)
   \[{{x}^{2}}+\frac{9}{{{x}^{2}}}-6\]     done clear
  D)
   \[{{x}^{2}}+\frac{1}{{{x}^{2}}}-6\] done clear
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• question_answer26)
  Solve \[(4{{x}^{2}}+5)(4{{x}^{2}}+5)\]
  A)
   \[16{{x}^{4}}+25+40{{x}^{2}}\]     done clear
  B)
   \[16{{x}^{4}}+28+30{{x}^{2}}\] done clear
  C)
   \[16{{x}^{4}}+30+20{{x}^{2}}\]   done clear
  D)
   \[16{{x}^{4}}+8+25{{x}^{2}}\] done clear
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• question_answer27)
  Multiply \[\left( 3x+2y \right)\left( 3x+2y \right)\]
  A)
   \[9{{x}^{2}}+4{{y}^{2}}+12xy\] done clear
  B)
   \[18{{x}^{2}}+2{{y}^{2}}+10xy\] done clear
  C)
   \[9{{x}^{2}}+4{{y}^{2}}+8xy\]                      done clear
  D)
   \[9{{x}^{2}}+6{{y}^{3}}+12xy\] done clear
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• question_answer28)
  The product of \[(3{{x}^{2}}+{{\mathbf{y}}^{\mathbf{2}}})\]and \[\left( 2{{x}^{2}}+3{{y}^{2}} \right)\] is
  A)
   \[{{x}^{3}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]           done clear
  B)
   \[3{{x}^{2}}+5{{x}^{5}}{{y}^{2}}+3{{y}^{4}}\] done clear
  C)
   \[6{{x}^{2}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]                    done clear
  D)
   \[6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}\] done clear
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• question_answer29)
  The product of \[(-3{{x}^{2}}y)+(4{{x}^{2}}y-3x{{y}^{2}}+4x-5y)\]  is
  A)
   \[12{{x}^{3}}{{y}^{2}}+9{{x}^{2}}{{y}^{2}}-12{{x}^{4}}y+15{{x}^{3}}{{y}^{3}}\] done clear
  B)
   \[-12{{x}^{4}}{{y}^{2}}+9{{x}^{3}}{{y}^{3}}-12{{x}^{3}}y+15{{x}^{2}}{{y}^{2}}\] done clear
  C)
   \[-12x{{y}^{2}}+9{{x}^{3}}{{y}^{2}}-12{{x}^{3}}y+15xy\]   done clear
  D)
   \[-12x{{y}^{3}}+9xy-12x{{y}^{2}}+15{{x}^{2}}y\] done clear
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• question_answer30)
  \[(4x-7y)(4x-7y)\]equal 10
  A)
   \[16{{x}^{2}}+56xy+49{{y}^{2}}\] done clear
  B)
   \[16{{x}^{2}}-8xy+49{{y}^{2}}\] done clear
  C)
   \[16{{x}^{2}}-56xy-49{{y}^{2}}\]                done clear
  D)
   \[16{{x}^{2}}-56xy+49{{y}^{2}}\] done clear
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• question_answer31)
  If\[{{(3a+1)}^{2}}+{{(b-1)}^{2}}+{{(2c-3)}^{3}}=0\], then the value of (3a+b+2c) is equal to:
  A)
   3      done clear
  B)
   -1 done clear
  C)
   2                                 done clear
  D)
   5 done clear
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• question_answer32)
  If \[x+y+z=0,\] then \[3\left[ \frac{{{x}^{2}}}{yz}+\frac{{{y}^{2}}}{zx}+\frac{{{z}^{2}}}{xy} \right]\]=?
  A)
   \[{{\left( xyz \right)}^{2}}\]                   done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] done clear
  C)
   9        done clear
  D)
   3 done clear
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• question_answer33)
  If \[x=3+2\sqrt{2}\]and \[\mathbf{xy}=\mathbf{1},\]then the value of \[\frac{{{x}^{2}}-3xy+{{y}^{2}}}{{{x}^{2}}+3xy+{{y}^{2}}}\]is
  A)
   \[\frac{30}{31}\]                                   done clear
  B)
   \[\frac{70}{31}\] done clear
  C)
   \[\frac{35}{31}\]                                   done clear
  D)
   \[\frac{31}{37}\] done clear
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• question_answer34)
  If \[a=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}\] and \[b=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}\] then the value of \[\frac{{{a}^{2}}-ab+{{b}^{2}}}{{{a}^{2}}+ab+{{b}^{2}}}\]=?
  A)
   \[\frac{61}{63}\]           done clear
  B)
   \[\frac{67}{65}\] done clear
  C)
   \[\frac{65}{63}\]                                   done clear
  D)
   \[\frac{69}{67}\] done clear
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• question_answer35)
  If \[\mathbf{xy}\left( \mathbf{x}-\mathbf{y} \right)=\mathbf{1}\], then the value of \[\frac{1}{{{x}^{3}}{{y}^{3}}}-{{\mathbf{x}}^{\mathbf{3}}}+{{\mathbf{y}}^{\mathbf{3}}}\]is :
  A)
   0                    done clear
  B)
   1 done clear
  C)
   3                                 done clear
  D)
   -3 done clear
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• question_answer36)
  If \[\left( \mathbf{a}+\mathbf{b} \right)=\mathbf{5},\] then find \[{{\mathbf{a}}^{\mathbf{2}}}-\mathbf{ab}+{{\mathbf{b}}^{\mathbf{2}}}\] (given \[{{\mathbf{a}}^{\mathbf{3}}}+{{\mathbf{b}}^{\mathbf{3}}}=\mathbf{8}\])
  A)
   1.6        done clear
  B)
   2 done clear
  C)
   3                                 done clear
  D)
   0 done clear
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• question_answer37)
  The factors of the expression \[{{x}^{2}}-\frac{{{y}^{2}}}{100}\] is
  A)
   \[\left( x-\frac{y}{100} \right)\left( x-\frac{y}{100} \right)\]               done clear
  B)
   \[\left( x+\frac{y}{100} \right)\left( x+\frac{y}{100} \right)\] done clear
  C)
   \[\left( y+\frac{x}{100} \right)\left( y+\frac{x}{100} \right)\] done clear
  D)
   \[\left( x+\frac{y}{100} \right)\left( x-\frac{y}{100} \right)\] done clear
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• question_answer38)
  The product of \[\left( x-\frac{1}{x} \right)\left( x+\frac{1}{x} \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}} \right)\left( {{x}^{4}}+\frac{1}{{{x}^{4}}} \right)\] is
  A)
   \[\left( {{x}^{8}}-\frac{1}{{{x}^{8}}} \right)\]                        done clear
  B)
   \[\left( {{x}^{4}}-\frac{1}{{{x}^{4}}} \right)\]       done clear
  C)
   \[\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)\]            done clear
  D)
   \[\left( {{x}^{8}}+\frac{1}{{{x}^{8}}} \right)\] done clear
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• question_answer39)
  The value of \[\frac{({{a}^{2}}-{{b}^{2}})({{b}^{2}}-{{c}^{2}})({{c}^{2}}-{{a}^{2}})}{{{(a-b)}^{3}}+{{(b-c)}^{3}}+{{(c-a)}^{2}}}\]is
  A)
   \[3\left( a+b \right)\left( b+c \right)\left( c+a \right)\]             done clear
  B)
   \[3\left( a-b \right)\left( b-c \right)\left( c-a \right)\] done clear
  C)
   \[\left( a-b \right)\left( b-c \right)\left( c-a \right)\]              done clear
  D)
   \[\left( a+b \right)\left( b+c \right)\left( c+a \right)\] done clear
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• question_answer40)
  If HCF and LCM of two terms a and b are x and y respectively and \[\mathbf{a}+\mathbf{b}=\mathbf{x}+\mathbf{y},\]then \[{{\mathbf{x}}^{\mathbf{2}}}+{{\mathbf{y}}^{\mathbf{2}}}\]= ?
  A)
   \[{{a}^{2}}-{{b}^{2}}\]                    done clear
  B)
   \[2{{a}^{2}}+{{b}^{2}}\]          done clear
  C)
   \[{{a}^{2}}+{{b}^{2}}\] done clear
  D)
   \[{{a}^{2}}+2{{b}^{2}}\] done clear
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