8th Class Mental Ability Algebraic Expressions Question Bank

done Algebra Total Questions - 20

• question_answer1)
  Find the solution of \[\frac{\mathbf{4y+1}}{\mathbf{3}}\mathbf{+}\frac{\mathbf{2y-1}}{\mathbf{2}}\mathbf{-}\frac{\mathbf{3y-7}}{\mathbf{5}}\mathbf{=6}\mathbf{.}\]
  A)
  1    done clear
  B)
                                 \[-2\frac{11}{4}\] done clear
  C)
  \[-\frac{11}{4}\]                    done clear
  D)
         \[2\frac{3}{4}\] done clear
  E)
  None of these done clear
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• question_answer2)
  If \[\mathbf{6}\mathbf{.5n+}\frac{\mathbf{19}\mathbf{.5n-32}\mathbf{.5}}{\mathbf{2}}\mathbf{=6}\mathbf{.5n-13-}\left( \frac{\mathbf{13n-26}}{\mathbf{2}} \right)\] , then find the value of n.
  A)
  0                          done clear
  B)
         5 done clear
  C)
  2                           done clear
  D)
         1 done clear
  E)
  None of these done clear
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• question_answer3)
  The distance between two milestones is 230 km and two cars start simultaneously from the milestones in opposite directions and the distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/h, find the speed of each car.
  A)
  25 km/h, 40 km/h done clear
  B)
                     40 km/h, 50 km/h done clear
  C)
  20 km/h, 40 km/h done clear
  D)
                     30 km/h/40 km/h done clear
  E)
  None of these done clear
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• question_answer4)
  A store has provision which would last for a certain number of men for 21 days. For one seventh of the men it will last for how many days?
  A)
  147       done clear
  B)
         158 done clear
  C)
  129                      done clear
  D)
         174 done clear
  E)
  None of these done clear
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• question_answer5)
  Factorise the given polynomial \[\frac{\mathbf{9}}{\mathbf{16}}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}\frac{\mathbf{4}}{\mathbf{9}}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+4}{{\mathbf{z}}^{\mathbf{2}}}\mathbf{-xy-}\frac{\mathbf{8}}{\mathbf{3}}\mathbf{yz+3zx}\mathbf{.}\]
  A)
  \[{{\left( \frac{3}{4}x-\frac{2}{3}y+2z \right)}^{2}}\] done clear
  B)
                     \[{{\left( \frac{3}{4}x+\frac{2}{3}y+2z \right)}^{2}}\] done clear
  C)
  \[{{\left( \frac{3}{4}x+\frac{2}{3}y-2z \right)}^{2}}\] done clear
  D)
         \[{{\left( \frac{3}{4}x-\frac{2}{3}y-2z \right)}^{2}}\] done clear
  E)
  None of these done clear
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• question_answer6)
  Simplify the given expression: \[\frac{\mathbf{0}\mathbf{.86\times 0}\mathbf{.86\times 0}\mathbf{.86+0}\mathbf{.14\times 0}\mathbf{.14\times 0}\mathbf{.14}}{\mathbf{0}\mathbf{.86\times 0}\mathbf{.86-0}\mathbf{.86\times 0}\mathbf{.14+0}\mathbf{.14\times 0}\mathbf{.14}}\].
  A)
  1         done clear
  B)
         0 done clear
  C)
  2                          done clear
  D)
         -1 done clear
  E)
  None of these done clear
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• question_answer7)
  The value of \[\left( \mathbf{x-y} \right)\left( \mathbf{x+y} \right)\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}} \right)\mathbf{\{}{{\left( {{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}} \right)}^{\mathbf{2}}}\mathbf{-2}{{\mathbf{x}}^{\mathbf{2}}}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{\}}\] is:
  A)
  \[{{x}^{8}}-{{y}^{8}}\]    done clear
  B)
        \[{{x}^{8}}+{{y}^{8}}\] done clear
  C)
  \[{{x}^{6}}-{{y}^{6}}\]                done clear
  D)
         \[{{x}^{6}}+{{y}^{6}}\] done clear
  E)
  None of these done clear
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• question_answer8)
  The product of \[\left( \mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+}{{\mathbf{y}}^{\mathbf{2}}} \right)\] and \[\left( \mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+3}{{\mathbf{y}}^{\mathbf{2}}} \right)\] 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)
  \[6{{x}^{5}}+10{{x}^{2}}{{y}^{3}}+3{{y}^{4}}\]           done clear
  D)
  \[6{{x}^{4}}+11{{x}^{2}}{{y}^{2}}+3{{y}^{4}}\] done clear
  E)
  None of these done clear
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• question_answer9)
  Find the quotient of polynomial if \[{{\mathbf{y}}^{\mathbf{3}}}\mathbf{-6}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{+9y-2}\] is divided by \[\mathbf{y}-\mathbf{2}.\]
  A)
  \[{{y}^{2}}+4y+1\]          done clear
  B)
         \[{{y}^{2}}-4y+1\] done clear
  C)
  \[{{y}^{2}}+4y-1\]          done clear
  D)
        \[{{y}^{2}}-4y-1\] done clear
  E)
  None of these done clear
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• question_answer10)
  Find the remainder when \[\mathbf{5}{{\mathbf{m}}^{\mathbf{3}}}\mathbf{-13}{{\mathbf{m}}^{\mathbf{2}}}\mathbf{+15m+7}\] is divided by \[\mathbf{4-3m+}{{\mathbf{m}}^{\mathbf{2}}}\mathbf{.}\]
  A)
  m - 1       done clear
  B)
                     m + 1                                       done clear
  C)
                     2m + 1                done clear
  D)
         2m ? l done clear
  E)
  None of these done clear
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• question_answer11)
  If \[\mathbf{x+}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{=6}\], then the value of \[{{\mathbf{x}}^{\mathbf{4}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{4}}}}\mathbf{=}\]
  A)
  526                      done clear
  B)
                     1154 done clear
  C)
                     1528                    done clear
  D)
         529 done clear
  E)
  None of these done clear
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• question_answer12)
  What must be subtracted from \[\mathbf{4p}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-2pq-v+5}\,\,\mathbf{to}\,\,\mathbf{get}\,\,\mathbf{-}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{+pq-8}{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-2v+6}\]?
  A)
  \[4p{{x}^{2}}+3{{q}^{2}}-3pq+v-1\] done clear
  B)
  \[5{{q}^{2}}-3pq+8pq+2{{q}^{2}}+v-1\] done clear
  C)
  \[-5\,{{p}^{2}}+3pq-2{{q}^{2}}-v+1\]           done clear
  D)
  \[-3{{p}^{2}}+p\,q+14{{q}^{2}}+3v-11\] done clear
  E)
  None of these done clear
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• question_answer13)
  Divide \[\left( \mathbf{2}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-5}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+8x-5} \right)\,\,\mathbf{by}\,\,\left( \mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-3x+5} \right)\] and find the quotient.
  A)
  \[x+5\]                  done clear
  B)
                     \[x+4\]                                      done clear
  C)
                     \[x-1\]    done clear
  D)
         \[x+2\] done clear
  E)
  None of these done clear
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• question_answer14)
  Which one of the following expressions is equal to \[\mathbf{64}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+9}{{\mathbf{y}}^{\mathbf{2}}}\mathbf{-48xy}\]?
  A)
  \[{{\left( 8x+3y \right)}^{2}}\]          done clear
  B)
                     \[{{\left( 5x-y \right)}^{2}}\] done clear
  C)
  \[{{\left( 8x-3y \right)}^{2}}\]    done clear
  D)
         \[{{\left( 5x-2y \right)}^{2}}\] done clear
  E)
  None of these done clear
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• question_answer15)
  Evaluate \[{{\left( \frac{\mathbf{-1728}}{\mathbf{2744}} \right)}^{\frac{\mathbf{2}}{\mathbf{3}}}}{{\left( \frac{\mathbf{4096}}{\mathbf{9216}} \right)}^{\frac{\mathbf{1}}{\mathbf{2}}}}\mathbf{-}{{\left( \frac{\mathbf{729}}{\mathbf{343}} \right)}^{\frac{\mathbf{2}}{\mathbf{3}}}}\]
  A)
  0                          done clear
  B)
         \[\frac{4208}{2152}\] done clear
  C)
  \[-\frac{57}{49}\]     done clear
  D)
         \[\frac{2152}{4208}\] done clear
  E)
  None of these done clear
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• question_answer16)
  Evaluate \[{{\left[ {{\left( \sqrt{\frac{\mathbf{2}}{\mathbf{3}}} \right)}^{\mathbf{2}}}\mathbf{-}\sqrt[\mathbf{3}]{\frac{\mathbf{8}}{\mathbf{27}}} \right]}^{\mathbf{1000}}}\]
  A)
  0         done clear
  B)
         1                      done clear
  C)
  2                          done clear
  D)
         -1 done clear
  E)
  None of these done clear
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• question_answer17)
  There are two neighbours, one has 6 oxen and other has 8 cows, and they have common field for the grazing of the cattle. They use the field for their cattle turn wise for feeding them. The 6 oxen or the 8 cows can graze the field in 25 days. In how much time will 1 ox and 2 cows graze the same field if left together?
  A)
  40 days               done clear
  B)
         60 days done clear
  C)
         50 days                done clear
  D)
         55 days done clear
  E)
  None of these done clear
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• question_answer18)
  Thomas needs some money for the construction work of his house and he does not have enough money for this work. He decides to lend the money from the money lender. He borrows Rs 2750 at the rate of 12% and lend the same amount to his friend at the rate of 18% per annum as he decides to postpone his work for some time because his friend needs the amount urgently. His friend pays him back the amount after two years and he returns the due amount to the money lender. The amount of money he earns from this transaction is:
  A)
  Rs. 250                done clear
  B)
                     Rs. 330 done clear
  C)
                     Rs. 450                done clear
  D)
         Rs. 340 done clear
  E)
  None of these done clear
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• question_answer19)
  A publishing house recruit 6 typists to type the manuscript of a book. If all the typists work for 5 hours a day, they take 16 days to complete the work. Due to some reason two typists leave the work before it starts and hence the company is left with only 4 typists to complete the work. In how many days will 4 typists complete the same job working 6 hour a day?
  A)
  20 days     done clear
  B)
                     15 days                                     done clear
  C)
                     10 days                done clear
  D)
         12 days done clear
  E)
  None of these done clear
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• question_answer20)
  In an army of 1000 soldiers there is a provision of food for 48 days when they are in remote areas for their duty or on the war. Due to infiltration of enemy 600 more soldiers are inducted in the group so that they can fight with the situation of urgency. For how many days will the given food last in the canteen?
  A)
  12 days               done clear
  B)
         30 days done clear
  C)
         45 days                done clear
  D)
         60 days done clear
  E)
  None of these done clear
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