9th Class Mathematics Polynomials Question Bank

done Polynomials Total Questions - 40

• question_answer1)
  If \[\mathbf{x=(}\sqrt{\mathbf{2}}\mathbf{+1}{{\mathbf{)}}^{\mathbf{-}\frac{\mathbf{1}}{\mathbf{3}}}}\]the value of \[\left( {{\mathbf{x}}^{\mathbf{3}}}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{3}}}} \right)\]  is
  A)
   0                                 done clear
  B)
   \[-\sqrt{2}\] done clear
  C)
   \[2\sqrt{2}\] done clear
  D)
   \[3\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer2)
  If \[{{\left( \mathbf{3a+1} \right)}^{\mathbf{2}}}\mathbf{+}{{\left( \mathbf{b-1} \right)}^{\mathbf{2}}}\mathbf{+}{{\left( \mathbf{2c-3} \right)}^{\mathbf{2}}}\mathbf{=0,}\] than value of \[\left( \mathbf{3a+b+2c} \right)\]is equal to:  
  A)
   3     done clear
  B)
   -1 done clear
  C)
   2                                 done clear
  D)
   5 done clear
  View Solution play_arrow

• question_answer3)
  If\[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{2}}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{y}}^{\mathbf{2}}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{z}}^{\mathbf{2}}}}\mathbf{=6}\], then  the valve of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{2}}}\]is
  A)
   3  done clear
  B)
   4 done clear
  C)
   8                                 done clear
  D)
   16 done clear
  View Solution play_arrow

• question_answer4)
  If \[\mathbf{x+y+z}=0\] then \[\mathbf{3}\left[ \frac{{{\mathbf{x}}^{\mathbf{2}}}}{\mathbf{yz}}\mathbf{+}\frac{{{\mathbf{y}}^{\mathbf{2}}}}{\mathbf{zx}}\mathbf{+}\frac{{{\mathbf{z}}^{\mathbf{2}}}}{\mathbf{xy}} \right]\mathbf{=?}\]
  A)
   \[{{\left( xyz \right)}^{2}}\]                   done clear
  B)
   \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}\] done clear
  C)
   9  done clear
  D)
   3 done clear
  View Solution play_arrow

• question_answer5)
  If \[\mathbf{x=3+2}\sqrt{\mathbf{2}}\] and \[\mathbf{xy=1}\], then the value of \[\frac{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-3xy+}{{\mathbf{y}}^{\mathbf{2}}}}{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3xy+}{{\mathbf{y}}^{\mathbf{2}}}}\] 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
  View Solution play_arrow

• question_answer6)
  If \[\mathbf{x=}\sqrt{\mathbf{3}}\mathbf{+}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\]and \[\mathbf{y=}\sqrt{\mathbf{3}}\mathbf{-}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}\], then the value of \[\frac{{{\mathbf{x}}^{\mathbf{2}}}}{\mathbf{y}}\mathbf{+}\frac{{{\mathbf{y}}^{\mathbf{2}}}}{\mathbf{x}}\]is
  A)
   \[\sqrt{3}\]                                done clear
  B)
   \[3\sqrt{3}\] done clear
  C)
   \[16\sqrt{3}\]                done clear
  D)
   \[2\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer7)
  If \[\mathbf{a=}\frac{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}\]and \[\mathbf{b=}\frac{\sqrt{\mathbf{5}}\mathbf{+}\sqrt{\mathbf{3}}}{\sqrt{\mathbf{5}}\mathbf{-}\sqrt{\mathbf{3}}}\] then the value of \[\frac{{{\mathbf{a}}^{\mathbf{2}}}\mathbf{-ab+}{{\mathbf{b}}^{\mathbf{2}}}}{{{\mathbf{a}}^{\mathbf{2}}}\mathbf{+ab+}{{\mathbf{b}}^{\mathbf{2}}}}\mathbf{=?}\]
  A)
   \[\frac{63}{61}\]           done clear
  B)
   \[\frac{67}{65}\] done clear
  C)
   \[\frac{65}{63}\]                                   done clear
  D)
   \[\frac{69}{67}\] done clear
  View Solution play_arrow

• question_answer8)
  if \[~{{a}^{4}}+{{b}^{4}}={{x}^{2}}{{y}^{2}}\], then \[\left( {{\mathbf{a}}^{\mathbf{6}}}+{{\mathbf{b}}^{\mathbf{6}}} \right)\] equals
  A)
   0      done clear
  B)
   1 done clear
  C)
   \[{{x}^{2}}+{{y}^{2}}\]                     done clear
  D)
   \[{{a}^{2}}{{b}^{4}}+{{a}^{2}}{{b}^{2}}\] done clear
  View Solution play_arrow

• question_answer9)
  If \[\mathbf{xy}\left( \mathbf{x}-\mathbf{y} \right)=\mathbf{1}\], then the value of \[\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{3}}}{{\mathbf{y}}^{\mathbf{3}}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{3}}}\]is:
  A)
   0                                 done clear
  B)
   1 done clear
  C)
   3    done clear
  D)
   -3 done clear
  View Solution play_arrow

• question_answer10)
  If \[{{\left( \mathbf{a+}\frac{\mathbf{1}}{\mathbf{a}}\mathbf{~} \right)}^{\mathbf{2}}}\mathbf{=3}\], then the value of \[{{\mathbf{a}}^{\mathbf{206}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{200}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{90}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{84}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{18}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{12}}}\mathbf{+}{{\mathbf{a}}^{\mathbf{6}}}\mathbf{+1}\]is
  A)
   0              done clear
  B)
   1 done clear
  C)
   84                                done clear
  D)
   206 done clear
  View Solution play_arrow

• question_answer11)
  If \[\mathbf{x+}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{=3}\], then the value of \[\frac{{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+3}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+5}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x+1}}{{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+1}}\]
  A)
   3     done clear
  B)
   5 done clear
  C)
   7                             done clear
  D)
   9 done clear
  View Solution play_arrow

• question_answer12)
  If \[\mathbf{x+y+z=6}\], then the value of \[{{\left( \mathbf{x-1} \right)}^{\mathbf{3}}}\mathbf{+}{{\left( \mathbf{y-2} \right)}^{\mathbf{3}}}\mathbf{+}{{\left( \mathbf{z-3} \right)}^{\mathbf{3}}}\] is
  A)
   \[3\left( x-1 \right)\left( y+2 \right)\left( z-3 \right)\]            done clear
  B)
   \[3\left( x+1 \right)\left( y-2 \right)\left( z-3 \right)\] done clear
  C)
   \[3\left( x-1 \right)\left( y-2 \right)\left( z+3 \right)\]            done clear
  D)
   \[3\left( x-1 \right)\left( y-2 \right)\left( z-3 \right)\] done clear
  View Solution play_arrow

• question_answer13)
  If \[\mathbf{x}=\mathbf{999}\], then the value of \[\sqrt[\mathbf{3}]{\mathbf{x}\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x+3} \right)\mathbf{+1}}\]is
  A)
   1000 done clear
  B)
   999 done clear
  C)
   998                              done clear
  D)
   1002 done clear
  View Solution play_arrow

• question_answer14)
  The degree of the polynomial \[\frac{{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+}{{\mathbf{x}}^{\mathbf{5}}}\mathbf{-}{{\mathbf{x}}^{\mathbf{8}}}}{{{\mathbf{x}}^{\mathbf{3}}}}\] is
  A)
   2                     done clear
  B)
   3              done clear
  C)
   4                                 done clear
  D)
   5 done clear
  View Solution play_arrow

• question_answer15)
  What is the remainder when \[\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{3x}+\mathbf{5}\] is divided by\[\mathbf{2x}-1\]?
  A)
   2                     done clear
  B)
   3                done clear
  C)
   4   done clear
  D)
   5 done clear
  View Solution play_arrow

• question_answer16)
  2 is a root of \[\mathbf{k}{{\mathbf{x}}^{\mathbf{4}}}-\mathbf{13}{{\mathbf{x}}^{\mathbf{3}}}+\mathbf{k}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{12x}.\]What is the value of k?
  A)
   \[k=1\]                         done clear
  B)
   \[k=2\]          done clear
  C)
   \[k=3\]                         done clear
  D)
   \[k=4\] done clear
  View Solution play_arrow

• question_answer17)
  If \[\mathbf{x}+\mathbf{1}\text{ }\mathbf{and}\text{ }\mathbf{x}-\mathbf{1}\] are factors of \[\mathbf{f}\left( \mathbf{x} \right)\mathbf{=}{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+3ax+b,}\] then the value of \[\mathbf{3a}+\mathbf{2b}\] is
  A)
   5                                 done clear
  B)
   -1   done clear
  C)
   4                                 done clear
  D)
   -6 done clear
  View Solution play_arrow

• question_answer18)
  If the area of rectangle is 3x2 + 6xy + 3y2 and its breadth is \[\mathbf{x+y,}\]then its length is
  A)
   \[x-2y\]                         done clear
  B)
   \[-x+2y\]          done clear
  C)
   \[3x+3y\]    done clear
  D)
   \[x+y\] done clear
  View Solution play_arrow

• question_answer19)
  If \[\mathbf{(x+2)}\] and \[\left( \mathbf{x+3} \right)\] are two factors of \[{{\mathbf{x}}^{\mathbf{3}}}+\mathbf{9}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{26x}+\mathbf{24},\]then the third factor is
  A)
   \[x+7\]                         done clear
  B)
   \[x+9\]           done clear
  C)
   \[x+4\]       done clear
  D)
   \[~x+8\] done clear
  View Solution play_arrow

• question_answer20)
  If \[\mathbf{x}=\mathbf{2},\] \[\mathbf{y}=\mathbf{3}\] and \[\mathbf{z}=-\mathbf{5},\] then \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{z}}^{\mathbf{3}}}\mathbf{=}\]
  A)
   90                                done clear
  B)
   -90          done clear
  C)
   0                                 done clear
  D)
   368 done clear
  View Solution play_arrow

• question_answer21)
  If \[\mathbf{3x}+\frac{1}{\mathbf{3x}}=\mathbf{3}\], then the value of \[27{{x}^{3}}+\frac{1}{27{{x}^{3}}}\] is
  A)
   -52                   done clear
  B)
   52              done clear
  C)
   18          done clear
  D)
   -18 done clear
  View Solution play_arrow

• question_answer22)
  If\[\left( x+\frac{1}{x} \right)=4,\]then\[\left( x-\frac{1}{x} \right)\]is
  A)
   \[2\sqrt{2}\]                              done clear
  B)
   \[\sqrt{6}\]            done clear
  C)
   \[2\sqrt{3}\]    done clear
  D)
   \[3\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer23)
  The factorization of \[\mathbf{4}{{\mathbf{a}}^{\mathbf{2}}}-\mathbf{4a}+\mathbf{1}\] is
  A)
   \[\left( 2a-1 \right)\left( 2a+1 \right)\]        done clear
  B)
   \[\left( 2a-1 \right)\left( 1-2a \right)\]   done clear
  C)
   \[\left( 2a+1 \right)\left( 2a+1 \right)\]       done clear
  D)
   \[\left( 2a- \right)\left( 2a-1 \right)\] done clear
  View Solution play_arrow

• question_answer24)
  The factors of the expression \[{{\mathbf{x}}^{\mathbf{2}}}\text{-}\frac{{{y}^{2}}}{100}\]is
  A)
   \[\left( x-\frac{y}{10} \right)\left( x-\frac{y}{10} \right)\]    done clear
  B)
   \[\left( x+\frac{y}{10} \right)\left( x+\frac{y}{10} \right)\] done clear
  C)
   \[\left( y+\frac{x}{10} \right)\left( y+\frac{x}{10} \right)\] done clear
  D)
   \[\left( x+\frac{y}{10} \right)\left( x-\frac{y}{10} \right)\] done clear
  View Solution play_arrow

• question_answer25)
  The value of \[{{\left( \mathbf{-a+b+c} \right)}^{\mathbf{2}}}\] is
  A)
   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-2ab+2bc-2ca\]    done clear
  B)
   \[~{{a}^{2}}-{{b}^{2}}-{{c}^{2}}-2ab+2bc-2ca\] done clear
  C)
   \[{{x}^{2}}-{{y}^{2}}+{{z}^{2}}-2xy+3yz-4xz\]      done clear
  D)
   \[{{a}^{2}}+{{b}^{2}}-{{c}^{2}}-2ab-2bc-2ac\] done clear
  View Solution play_arrow

• question_answer26)
  If \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{12}\]and a2 + b2 + c2 = 50, then the value of \[\mathbf{ab}+\mathbf{be}+\mathbf{ca},\]is
  A)
   44                                done clear
  B)
   22              done clear
  C)
   23                                done clear
  D)
   47 done clear
  View Solution play_arrow

• question_answer27)
  The factors of the expression \[{{\mathbf{x}}^{\mathbf{4}}}+{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{1}\]is
  A)
   \[\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}-1+x \right)\]           done clear
  B)
   \[\left( {{x}^{2}}-1-x \right)\left( {{x}^{2}}-1-x \right)\] done clear
  C)
   \[\left( {{x}^{2}}+1-x \right)\left( {{x}^{2}}-1-x \right)\]           done clear
  D)
   \[({{x}^{2}}+1-x)({{x}^{2}}+1+x)\] done clear
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• question_answer28)
  The product of \[\left( \mathbf{x-}\frac{\mathbf{1}}{\mathbf{x}} \right)\left( \mathbf{x+}\frac{\mathbf{1}}{\mathbf{x}} \right)\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{2}}}} \right)\left( {{\mathbf{x}}^{\mathbf{4}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{4}}}} \right)\]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
  View Solution play_arrow

• question_answer29)
    If \[\mathbf{x+}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{=3}\], then the value of \[{{\mathbf{x}}^{\mathbf{4}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{4}}}}\]is
  A)
   56                    done clear
  B)
   74             done clear
  C)
   47        done clear
  D)
   60 done clear
  View Solution play_arrow

• question_answer30)
  If \[{{\mathbf{x}}^{\mathbf{2}}}+\frac{1}{{{\mathbf{x}}^{\mathbf{2}}}}=\mathbf{123}.\]Then the value of \[{{\mathbf{x}}^{3}}-\frac{1}{{{\mathbf{x}}^{3}}}\] is
  A)
   1340                            done clear
  B)
   1364    done clear
  C)
   1358                            done clear
  D)
   1360 done clear
  View Solution play_arrow

• question_answer31)
  The value of \[\frac{{{\left( {{a}^{2}}-{{b}^{2}} \right)}^{3}}{{\left( {{b}^{2}}-{{c}^{2}} \right)}^{3}}+{{\left( {{c}^{2}}-{{a}^{2}} \right)}^{3}}}{{{\left( a-b \right)}^{3}}+{{\left( b-c \right)}^{3}}+{{\left( c-a \right)}^{3}}}\]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)
   \[(a-b)\left( b-c \right)\left( c-a \right)\]              done clear
  D)
   \[\left( a+b \right)\left( b+c \right)\left( c+a \right)\] done clear
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• question_answer32)
  If \[\mathbf{p=2-a,}\] then the value of \[{{\mathbf{a}}^{\mathbf{3}}}\mathbf{+6ap+}{{\mathbf{p}}^{\mathbf{3}}}\mathbf{-8}\] is
  A)
   1                                 done clear
  B)
   0        done clear
  C)
   3                                 done clear
  D)
   -1 done clear
  View Solution play_arrow

• question_answer33)
  he factors of the expression \[\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+4xy+}{{\mathbf{y}}^{\mathbf{2}}}\] is
  A)
   \[\left( 2x+y \right)\left( 2x+y \right)\]  done clear
  B)
   \[\left( 2x+y \right)\left( 2x-y \right)\] done clear
  C)
   \[\left( 2x-y \right)(2x-y)\]            done clear
  D)
   \[\left( 2x+x \right)\left( 2y+x \right)\] done clear
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• question_answer34)
  When the polynomial \[\mathbf{f(x)=}{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+3}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+x-1}\] is divided by \[\left( \mathbf{x-2} \right)\] what will be the remainder?
  A)
   17                   done clear
  B)
   33          done clear
  C)
   23                                done clear
  D)
   29 done clear
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• question_answer35)
  If polynomials \[\mathbf{2}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+a}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x-5}\] and \[{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-2x+a}\] are divided by\[\left( \mathbf{x-2} \right)\], the same remainders are obtained. Find the value of a.
  A)
   -3     done clear
  B)
   3              done clear
  C)
   -4                                done clear
  D)
   -9 done clear
  View Solution play_arrow

• question_answer36)
  For what value of k, \[\mathbf{3}{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+2}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{+3k}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+2x+6}\] is exactly divisible by \[\mathbf{(x-2)?}\]
  A)
   1                                 done clear
  B)
   2               done clear
  C)
   -2                                done clear
  D)
   \[-\frac{8}{3}\] done clear
  View Solution play_arrow

• question_answer37)
  What is the LCM of \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-1,}\]\[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-4x+3}\] and \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3x+2?}\]
  A)
   \[\left( x+3 \right)\left( x+1 \right)\]          done clear
  B)
   \[\left( {{x}^{2}}-1 \right)\left( x+2 \right)\left( x-3 \right)\] done clear
  C)
   \[\left( x-1 \right)\left( x-2 \right)\left( x-3 \right)\]             done clear
  D)
   \[\left( {{x}^{2}}-1 \right)\left( x+2 \right)\left( x+3 \right)\] done clear
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• question_answer38)
  What is the HCF of \[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{5x}+\mathbf{6},\]\[{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{7x}+\mathbf{12}\] and \[{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{9x}+\mathbf{20}\]
  A)
   1         done clear
  B)
   \[\left( x-3 \right)\]          done clear
  C)
   \[\left( 2x-5 \right)\]                     done clear
  D)
   \[x-4\] done clear
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• question_answer39)
  If the LCM and HCF of two quadratic polynomials are \[{{\mathbf{x}}^{\mathbf{3}}}-\mathbf{7x}+\mathbf{6}\] and \[\left( \mathbf{x}-\mathbf{1} \right)\] respectively, find the polynomials.
  A)
   \[\left( {{x}^{2}}-3x+2 \right),\left( {{x}^{2}}+2x+3 \right)\]        done clear
  B)
   \[\left( {{x}^{2}}+3x-2 \right),\left( {{x}^{2}}-2x+3 \right)\] done clear
  C)
   \[\left( {{x}^{2}}-3x+2 \right),\left( {{x}^{2}}+2x-3 \right)\]        done clear
  D)
   \[\left( {{x}^{2}}+3x+2 \right),\left( {{x}^{2}}+2x+3 \right)\] 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 \[{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{=?}\]
  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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