8th Class Mathematics Algebraic Expressions Question Bank

done Algebra Total Questions - 40

• question_answer1)
  Add the following algebraic expression: \[5{{x}^{2}}-\frac{3}{5}x+\frac{3}{2},-\frac{7}{8}{{x}^{2}}+\frac{5}{4}x-\frac{1}{4}\,and\,-\frac{3}{4}{{x}^{2}}+\frac{1}{8}x-\frac{3}{16}\]
  A)
  \[\frac{1}{80}\left[ 135{{x}^{2}}+62x+35 \right]\]           done clear
  B)
  \[\frac{1}{40}\left[ 135{{x}^{2}}+31x+42 \right]\] done clear
  C)
  \[\frac{1}{80}\left[ 270{{x}^{2}}+62x+85 \right]\] done clear
  D)
  \[\frac{1}{40}\left[ 125{{x}^{2}}+62x+38 \right]\] done clear
  E)
  None of these done clear
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• question_answer2)

  Subtract the sum of A and B from C

  Where   \[A=\frac{3}{7}{{p}^{2}}{{q}^{2}}r-\frac{4}{5}pq{{r}^{2}}+\frac{3}{2}pqr+\frac{1}{21}{{p}^{2}}qr\]

  \[B=\frac{1}{14}pq{{r}^{2}}+\frac{2}{7}{{p}^{2}}qr-\frac{3}{5}{{p}^{2}}{{q}^{2}}r+pqr\]

  And \[c=\frac{3}{10}pqr-\frac{4}{7}r{{p}^{2}}q+\frac{2}{7}pq{{r}^{2}}-\frac{4}{5}{{p}^{2}}r{{q}^{2}}\]

  A)
  \[\frac{1}{105}[-66{{p}^{2}}{{q}^{2}}r+112pq{{r}^{2}}+162pqr+170{{p}^{2}}qr]\] done clear
  B)
  \[\frac{1}{210}[-132{{p}^{2}}{{q}^{2}}r+213pq{{r}^{2}}-462pqr-190{{p}^{2}}qr]\] done clear
  C)
  \[\frac{1}{210}[-232{{p}^{2}}{{q}^{2}}r+203pq{{r}^{2}}+362pqr+170{{p}^{2}}qr]\] done clear
  D)
  \[\frac{1}{105}[-166{{p}^{2}}{{q}^{2}}r-112pq{{r}^{2}}+462pqr-171{{p}^{2}}qr]\] done clear
  E)
  None of these done clear
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• question_answer3)
  Find the product of \[\left\{ 3{{x}^{2}}yz\times \frac{4}{5}(x+y)z \right\}\times \left\{ -\frac{3}{17}{{x}^{3}}y{{z}^{4}}(x+y+3z) \right\}\]
  A)
  \[\frac{-36}{85}{{x}^{5}}{{y}^{2}}{{z}^{6}}\left[ {{x}^{2}}+\text{ }2xy\text{ }+\text{ }{{y}^{2}}\,\,+\text{ }3xz\text{ }+\text{ }3yz \right]\] done clear
  B)
  \[\frac{36}{85}{{x}^{5}}y{{z}^{5}}\left[ {{x}^{2}}+\text{ 3}xy\text{ }+\text{ }{{y}^{3}}\,\,+\text{ }3xz\text{ }+\text{ }3yz \right]\] done clear
  C)
  \[\frac{36}{85}{{x}^{5}}{{y}^{2}}{{z}^{5}}\left[ {{x}^{2}}+\text{ 2}xy\text{ }+\text{ }{{y}^{2}}\,\,+\text{ 2}xz\text{ }+\text{ }3yz \right]\] done clear
  D)
  \[\frac{-36}{85}{{x}^{5}}y{{z}^{6}}\left[ {{x}^{2}}+\text{ 2}x{{y}^{2}}\text{ }+\text{ }y\,\,+\text{ 3}xz\text{ }+\text{ }3yz \right]\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer4)
  If\[\left( a+\frac{1}{a} \right)=5\], then find the value of \[{{a}^{4}}+\frac{1}{{{a}^{4}}}\].
  A)
  527    done clear
  B)
                  625 done clear
  C)
  627                               done clear
  D)
  425 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer5)
  Find the product of \[\left( a+\frac{1}{a} \right)\left( {{a}^{2}}+\frac{1}{{{a}^{2}}} \right)\left( {{a}^{4}}+\frac{1}{{{a}^{4}}} \right)\left( {{a}^{8}}+\frac{1}{{{a}^{8}}} \right)\left( a-\frac{1}{a} \right)\]
  A)
  \[{{a}^{16}}+\frac{1}{{{a}^{16}}}\] done clear
  B)
                   \[{{a}^{16}}-\frac{1}{{{a}^{16}}}\] done clear
  C)
  \[{{a}^{16}}+\frac{1}{{{a}^{16}}}+\frac{3}{8}{{a}^{8}}+\frac{1}{4{{a}^{8}}}\]           done clear
  D)
  \[{{a}^{16}}+\frac{1}{{{a}^{16}}}+\frac{3}{8}{{a}^{8}}-\frac{1}{8{{a}^{8}}}\] done clear
  E)
  None of these done clear
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• question_answer6)

  What must be added to the following expression to make it a perfect square?

  \[\frac{3{{x}^{2}}}{64}-5\frac{\sqrt{21x}}{12}+\frac{157}{9}\]

   
  A)
  \[\frac{21}{9}\] done clear
  B)
  1 done clear
  C)
  2   done clear
  D)
  \[\frac{33}{9}\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  Factorize: \[-2xy\text{ }+\text{ }1\text{ }-\text{ }{{y}^{2}}-\text{ }{{x}^{2}}\]
  A)
  \[\left( 1\text{ }+\text{ }x\text{ }-\text{ }y \right)\left( 1\text{ }\text{ }x\text{ }+\text{ }y \right)~\] done clear
  B)
           \[\left( 1\text{ }+\text{ }x\text{ }+\text{ }y \right)\left( 1\text{ }\text{ }x\text{ }-\text{ }y \right)\] done clear
  C)
  \[\left( 1\text{ }+\text{ }xy \right)\left( x\text{ }+\text{ }y\text{ }+\text{ }l \right)~\] done clear
  D)
             \[\left( 1\text{ }-\text{ }xy \right)\left( 1+\text{ }x\text{ }+\text{ }y \right)\] done clear
  E)
  None of these done clear
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• question_answer8)
  Factorize the following expression:\[{{(2a+3b+c)}^{2}}-20a10c-30b+21\].
  A)
  \[\left( 2a+3b+c-7 \right)\left( 2a+3b+c-3 \right)\] done clear
  B)
  \[\left( 2a3b+c+7 \right)\left( 2a3b+c-3 \right)\] done clear
  C)
  \[\left( 2a+3bc-7 \right)\left( 2a+3b+c-7 \right)\] done clear
  D)
  \[\left( a+3b+c-7 \right)\left( a+3b+c-3 \right)\] done clear
  E)
  None of these done clear
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• question_answer9)
  One of the factors of \[6\text{ }-\text{ }m\text{ }-\text{ }2{{m}^{2}}\] is _____
  A)
  \[\left( m+6 \right)\]                     done clear
  B)
  \[\left( 2m+3 \right)\] done clear
  C)
  \[\left( -2m+3 \right)\]       done clear
  D)
  \[\left( -2m+6 \right)\] done clear
  E)
  None of these done clear
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• question_answer10)
  Solve :\[\frac{6{{m}^{2}}+\text{ }13m\text{ }-4}{2m+5}\], \[\frac{12{{m}^{2}}+\text{ 5}m\text{ +}4}{4m+5}\]
  A)
  m = 2       done clear
  B)
         m = -2       done clear
  C)
  m = l                            done clear
  D)
  m = -3 done clear
  E)
  None of these done clear
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• question_answer11)
  Which among the following is a factor of\[~6{{m}^{5}}+15{{m}^{4}}+16{{m}^{3}}+4{{m}^{2}}+10m-35\]?
  A)
  \[3{{m}^{2}}+\text{ }4\]                     done clear
  B)
  \[2{{m}^{2}}+5\] done clear
  C)
  \[2{{m}^{3}}+\text{ }5{{m}^{2}}+\text{ }2m-6\]      done clear
  D)
  \[3{{m}^{2}}+5\] done clear
  E)
  None of these done clear
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• question_answer12)
  If \[15{{a}^{4}}-\text{ }16{{a}^{3}}+\text{ }9{{a}^{2}}-\text{ }\frac{10}{3}a\text{ }+\text{ }6\] is divided by 3a - 2 then quotient and remainder are respectively _
  A)
  \[5{{a}^{3}}-\text{ }2{{a}^{2}}+\text{ }5a\text{ }and\text{ }5\]         done clear
  B)
  \[5{{a}^{3}}-\text{ }2{{a}^{2}}+\text{ }\frac{5}{3}a\text{ }and\text{ }5\] done clear
  C)
  \[6{{a}^{3}}-\text{ }2{{a}^{2}}+\text{ }\frac{3}{5}a\text{ }and\text{ 6}\]          done clear
  D)
  \[5{{a}^{3}}-\text{ }2{{a}^{2}}+\text{ }\frac{5}{3}a\text{ }and\text{ 6}\] done clear
  E)
  None of these done clear
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• question_answer13)
  What must be subtracted from \[34a-22{{a}^{3}}-\] \[12{{a}^{4}}-\]\[10{{a}^{2}}-\text{ }75\] so that the resulting polynomial is exactly divisible by\[-4{{a}^{3}}+\text{ }2{{a}^{2}}-\text{ }8a\text{ }+\text{ }30\]?
  A)
  215                               done clear
  B)
  -215         done clear
  C)
  285                               done clear
  D)
  -285 done clear
  E)
  None of these done clear
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• question_answer14)
  Find the product of\[\left( p\text{ }+\text{ }q\text{ }+\text{ }r \right)\text{ }[\text{ }{{\left( p\text{ }-\text{ }q \right)}^{2}}+{{\left( q\text{ }-\text{ }r \right)}^{2}}+\text{ }{{\left( r\text{ }-\text{ }p \right)}^{2}}]\].
  A)
  \[{{p}^{3}}+{{q}^{3}}+{{r}^{3}}\]                       done clear
  B)
  \[{{p}^{3}}\text{ }+\text{ }{{q}^{3}}\text{ }+\text{ }{{r}^{3}}\text{ }\,3pqr\] done clear
  C)
  \[2\text{ }\left( {{p}^{3}}\text{ }+\text{ }{{q}^{3}}+{{r}^{3}}\text{ }-\text{ }3pqr \right)\]        done clear
  D)
  \[{{p}^{3}}\text{ }+\text{ }{{q}^{3}}+\,\,{{r}^{3}}+\,\,2\text{ }\left( pq\,\,+\,\,qr\,\,+\,\,rp \right)\] done clear
  E)
  None of these done clear
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• question_answer15)
  If \[\left( x-p+y-q \right)=8\]and \[\left( x\text{ }p+x\text{ }q+y\text{ }p+y\text{ }q \right)=16,\]then find the value of\[{{\left( x+y \right)}^{2}}+\]\[{{\left( p+q \right)}^{2}}\].
  A)
  96                     done clear
  B)
  64           done clear
  C)
  48                                 done clear
  D)
  80 done clear
  E)
  None of these done clear
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• question_answer16)
  If \[\frac{1}{p}-\frac{1}{q}-\frac{1}{r}=\frac{1}{18}\] and \[pq\text{ }+\text{ }qr\text{ }=\text{ }pr\]then find the value of r.
  A)
  0                                  done clear
  B)
  1            done clear
  C)
  18                                 done clear
  D)
  -36 done clear
  E)
  None of these done clear
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• question_answer17)
  Which one among the following statements is correct?
  A)
  An equation is not true for all the values of the variables used in it done clear
  B)
  An identity is true for only some certain values of the variable. done clear
  C)
  Polynomial is an algebraic expression containing one or more terms with non zero coefficients and the variables used in it have integer exponents done clear
  D)
  All the above done clear
  E)
  None of these done clear
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• question_answer18)
  If \[\frac{1}{m}+\frac{1}{n}=-3\] and\[mn=-\frac{1}{54}\], then find the value of\[\frac{1}{{{m}^{3}}}+\frac{1}{{{n}^{3}}}\].
  A)
  \[\frac{1}{212}\]       done clear
  B)
                    -513         done clear
  C)
  \[-\frac{1}{219}\]                       done clear
  D)
  517 done clear
  E)
  None of these done clear
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• question_answer19)
  Find the LCM of the polynomial \[{{\left( 3x+\text{ }y \right)}^{2}}-{{\left( 2x\text{ }-\text{ }y \right)}^{2}}and\text{ }{{\left( 7x\text{ }+\text{ }3y \right)}^{2}}-\text{ }{{\left( 6x\text{ }+\text{ }y \right)}^{2}}\]
  A)
  \[5x\text{ }\left( x\text{ }+\text{ }2y \right)\text{ }\left( 13x\text{ }+\text{ }4y \right)\]            done clear
  B)
  \[\left( 7x\text{ }+\text{ }3y \right)\text{ }\left( 2x\text{ }+\text{ }y \right)\text{ }\left( 3x\text{ }+\text{ }y \right)\] done clear
  C)
  \[6x\text{ }\left( 3x\text{ }+\text{ }y \right)\text{ }\left( 7x\text{ }+\text{ }3y \right)\]             done clear
  D)
  \[\left( 3x\text{ }+\text{ }5y \right)\text{ }\left( 2x\text{ }+\text{ }3y \right)\text{ }7x\] done clear
  E)
  None of these done clear
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• question_answer20)
  Find the HCF of the polynomials \[{{x}^{2}}\text{ }+\text{ }5x\text{ }+\text{ }6\]and\[{{\left( x\text{ }+\text{ }2 \right)}^{2}}-\text{ }4x\text{ }-\text{ }8\].
  A)
  \[\left( x+3 \right)\]          done clear
  B)
  \[\left( x+1 \right)\]         done clear
  C)
  \[\left( x+2 \right)\]                      done clear
  D)
  \[\left( x-2 \right)\] done clear
  E)
  None of these done clear
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• question_answer21)
  The Polynomial, \[{{p}^{2}}+\text{ }2q\text{ }-\text{ }{{q}^{2}}+\text{ }{{r}^{2}}-\text{ }1\text{ }-\text{ }2\]pr on factorization gives _____
  A)
  \[\left( p\text{ }+\text{ }1\text{ }+\text{ }q \right)\text{ }\left( p\text{ }+\text{ }q\text{ }\text{ }r\text{ }-\text{ }1 \right)\] done clear
  B)
  \[\left( p\text{ }\text{ }1\text{ }+\text{ }q\text{ }-\text{ }r \right)\text{ }\left( p\text{ }+\text{ }1\text{ }\text{ }q\text{ }-\text{ }r \right)\] done clear
  C)
  \[\left( p\text{ }+\text{ }q\text{ }+\text{ }r\text{ }-1 \right)\text{ }\left( p\text{ }+\text{ }1\text{ }\text{ }q\text{ }+\text{ }r \right)\] done clear
  D)
  \[\left( p\text{ }\text{ }1\text{ }+\text{ }r\text{ }\text{ }q \right)\text{ }\left( q\text{ }+\text{ }p\text{ }\text{ }1\text{ }-r \right)\] done clear
  E)
  None of these done clear
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• question_answer22)
  The dimensions of a rectangular box are represented as \[\left( a\text{ }+\text{ }2b \right)\text{ }\left( {{a}^{2}}+\text{ }4{{b}^{2}} \right)\] and (a - 2b) then what will be the volume of the rectangular box?
  A)
  \[{{a}^{2}}\,8{{b}^{4}}\,+\,6\text{ }{{a}^{2}}{{b}^{2}}\]            done clear
  B)
  \[{{a}^{4}}\,+16{{b}^{4}}\,-\,8{{a}^{2}}{{b}^{2}}\] done clear
  C)
  \[{{a}^{4}}\,-\,16{{b}^{2}}\]                         done clear
  D)
  \[{{a}^{4}}\,+8{{b}^{4}}\,+\,12{{a}^{2}}{{b}^{2}}\] done clear
  E)
  None of these done clear
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• question_answer23)
  Solve: \[\frac{3m-2}{4}+m=\frac{2}{3}+\frac{2m+3}{3}\]
  A)
   \[m=-1\]                       done clear
  B)
  \[m=-2\]        done clear
  C)
  \[m=2\]             done clear
  D)
  \[m=1\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  Find the Value of t if \[\frac{1}{t+1}+\frac{1}{t+2}+\frac{2}{t+10}\].
  A)
  \[t=\frac{-26}{17}\]       done clear
  B)
  \[t=\frac{-17}{8}\]      done clear
  C)
  t = 2                             done clear
  D)
  t = ­­-3 done clear
  E)
  None of these done clear
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• question_answer25)
  Divide 84 into two parts such that \[{{\left( \frac{4}{17} \right)}^{th}}\]of one part is equal to other part. Find the product of both the parts.
  A)
  1078                      done clear
  B)
  1088 done clear
  C)
  2032                       done clear
  D)
  3076 done clear
  E)
  None of these done clear
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• question_answer26)
  In a fraction, if both the numerator and denominator are decreased by thrice, it is equal to\[\frac{2}{5}\]. If the numerator is increased by 3 and denominator is increased by 2, the fraction becomes\[\frac{2}{3}\]. Find the fraction.
  A)
  \[\frac{5}{8}\]                           done clear
  B)
  \[\frac{7}{13}\] done clear
  C)
  \[\frac{8}{13}\]                          done clear
  D)
  \[\frac{8}{11}\] done clear
  E)
  None of these done clear
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• question_answer27)
  The sum of the digits of a two digit number is 9. If 27 is subtracted from the number, the resultant number becomes the number obtained on reversing the digits of the original number Find the original number.
  A)
  54                           done clear
  B)
  45 done clear
  C)
  63         done clear
  D)
  81 done clear
  E)
  None of these done clear
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• question_answer28)
  The sum of three consecutive even numbers is 330, then find \[\frac{3}{4}\]th of the greatest number
  A)
  72                                 done clear
  B)
  84 done clear
  C)
  112                               done clear
  D)
  140 done clear
  E)
  None of these done clear
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• question_answer29)
  If the side of a chess board is smaller than its perimeter by 42 cm then find the area of the chess board.
  A)
  \[100c{{m}^{2}}\]       done clear
  B)
  \[144c{{m}^{2}}\] done clear
  C)
  \[196c{{m}^{2}}\]               done clear
  D)
  \[180m\,c{{m}^{2}}\] done clear
  E)
  None of these done clear
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• question_answer30)
  Cost of two chairs and three tables is Rs 3320, while the cost of one chair and two tables is Rs Rs 2020. Find the cost of each chair.
  A)
  Rs 780                        done clear
  B)
  Rs 620 done clear
  C)
  Rs 580          done clear
  D)
  Rs 720 done clear
  E)
  None of these done clear
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• question_answer31)
  A number is 20 less than ten times of the average of its fifth, quarter and one-fourteenth. Find \[\frac{2}{9}\] of the number.
  A)
  380                       done clear
  B)
  440 done clear
  C)
  320             done clear
  D)
  480 done clear
  E)
  None of these done clear
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• question_answer32)
  A number is such that it is as much greater than 560 as it is less than 894.  Find \[\frac{3}{7}\] of the number.
  A)
  222                               done clear
  B)
  432          done clear
  C)
  363                               done clear
  D)
  333 done clear
  E)
  None of these done clear
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• question_answer33)
  Three prizes are to be distributed in a quiz programme. The price-value of the second prize is seven-eighths of the price value of the first prize and the price value of the third prize is five-sixths of the second prize. If the total price value of three prizes is Rs 18,000, then find the price value of third price.
  A)
  Rs 6008                         done clear
  B)
  Rs 6048 done clear
  C)
  Rs 5040   done clear
  D)
  Rs 6912 done clear
  E)
  None of these done clear
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• question_answer34)
  Runs scored by Rahul in a match are 38 more than the balls faced by Virat. The number of balls faced by Rahul is 8 less than the runs scored by virat. If together they have scored 144 runs and the balls faced by Rahul are 18 more than those faced by virat. Find the number of runs scored by Rahul.
  A)
  68                             done clear
  B)
  72 done clear
  C)
  78       done clear
  D)
  66 done clear
  E)
  None of these done clear
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• question_answer35)
  Find the solution set of \[8m+16\le -\,\,48\] and\[11\,m\ +\,27\le \,\,-28\].
  A)
  \[-8\le ,\text{ }m\le ,\,8\]              done clear
  B)
  \[-6\le \,m<5\] done clear
  C)
  \[-8\le ,m\le ,\,\,5\]          done clear
  D)
  \[-6\le \,m\le -5\] done clear
  E)
  None of these done clear
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• question_answer36)
  The number of positive integral solutions of the in equation \[\frac{x+5}{x+8}>1\]is _______
  A)
  6                                  done clear
  B)
  8 done clear
  C)
  1                                  done clear
  D)
  0 done clear
  E)
  None of these done clear
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• question_answer37)
  There are 62 questions in a test. Each correct answer gives 2 marks and for each wrong answer 1 mark is deducted. A student scored 34 marks and he attempted all the questions, then find the number of questions answered incorrectly
  A)
  34                                 done clear
  B)
  28 done clear
  C)
  33                                 done clear
  D)
  32 done clear
  E)
  None of these done clear
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• question_answer38)
  In 1 hour, Ratish walks twice the distance that Sumit walks in the same period. In 8 hours, Ratish walks 6 miles more than what sumit walks in 10 hours. How many miles does sumit walk in 5 hours?
  A)
  3                                  done clear
  B)
  4 done clear
  C)
  5         done clear
  D)
  6 done clear
  E)
  None of these done clear
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• question_answer39)
  How much pure alchohal be added to 600 ml of a 20 % solution to make its strength 36%?
  A)
  100ml                       done clear
  B)
  120ml done clear
  C)
  140ml                           done clear
  D)
  150ml done clear
  E)
  None of these done clear
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• question_answer40)
  Yashika has Rs 108 in Rs 5, Rs 2, Rs 1, coins. She has twice as many Rs 2 coins as she has Rs 5 coins. Find the total number of coins she has.
  A)
  24 Coins              done clear
  B)
  36 Coins done clear
  C)
  42 Coins                done clear
  D)
  38 Coins done clear
  E)
  None of these done clear
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