8th Class Mental Ability Algebraic Expressions Question Bank

done Algebraic Identities Total Questions - 38

• question_answer1)
  Identify the expression equivalent to \[\left( \frac{1}{3y}+\frac{1}{4x} \right)\left( \frac{1}{3y}-\frac{1}{4x} \right).\]                                               
  A)
  \[\frac{1}{3{{y}^{2}}}-\frac{1}{4{{x}^{2}}}\]             done clear
  B)
   \[\frac{1}{3{{y}^{2}}}+\frac{1}{4{{x}^{2}}}\]          done clear
  C)
   \[\frac{1}{4{{x}^{2}}}-\frac{1}{3{{y}^{2}}}\] done clear
  D)
   \[\frac{1}{9{{y}^{2}}}-\frac{1}{16{{x}^{2}}}\] done clear
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• question_answer2)
  Which of the following is the expansion of \[{{\left( \frac{3}{7}x-\frac{1}{2}y \right)}^{2}}?\]
  A)
   \[\frac{3}{7}{{x}^{2}}-\frac{1}{2}{{y}^{2}}+\frac{3}{7}xy\] done clear
  B)
        \[\frac{3}{7}{{x}^{2}}+\frac{3}{7}xy+\frac{1}{4}{{y}^{2}}\] done clear
  C)
        \[\frac{9}{49}{{x}^{2}}-\frac{3}{7}xy+\frac{1}{4}{{y}^{2}}\] done clear
  D)
        \[\frac{9}{49}{{x}^{2}}+\frac{3}{7}xy+\frac{1}{4}{{y}^{2}}\] done clear
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• question_answer3)
  Which of the following identities is applicable to find the value of \[{{(99)}^{2}}.\]
  A)
   \[{{a}^{2}}-{{b}^{2}}=(a+b)(a-b)\] done clear
  B)
  \[{{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\] done clear
  C)
   \[{{(a+b)}^{3}}={{a}^{3}}+3{{a}^{2}}b+3a{{b}^{2}}+{{b}^{3}}\] done clear
  D)
  \[{{(a-b)}^{3}}={{a}^{3}}-3{{a}^{2}}b+3a{{b}^{2}}-{{b}^{3}}\] done clear
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• question_answer4)
  If a + b = 7 and \[{{a}^{2}}+{{b}^{2}}=25,\]find the value of ab.
  A)
   26                   done clear
  B)
        24                   done clear
  C)
   13      done clear
  D)
        12 done clear
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• question_answer5)
  If\[x=0.1,\]find the value of\[~100-10x.\]
  A)
   100                 done clear
  B)
        99      done clear
  C)
   90      done clear
  D)
        110                 done clear
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• question_answer6)
  Find the value of \[100\frac{1}{2}\times 99\frac{1}{2}.\]
  A)
   \[9999\frac{1}{4}\]    done clear
  B)
       \[9999\frac{7}{4}\]     done clear
  C)
  \[9999\frac{3}{4}\]     done clear
  D)
        \[9999\frac{5}{4}\] done clear
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• question_answer7)
  Which of the following is the simplest form of \[\frac{{{(4x+2m)}^{2}}(-4{{m}^{2}}+16{{x}^{2}})}{(4{{m}^{2}}+16{{x}^{2}}+16mx)(-2m+4x)}\]
  A)
  \[~4m+2x\]            done clear
  B)
       \[~4x-2m\]      done clear
  C)
  \[~4m+16x\]           done clear
  D)
       \[4x+2m\]                    done clear
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• question_answer8)
  Identify the expression equivalent to the expansion of \[{{(2a+b-c)}^{2}}.\]
  A)
  \[2{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-2ab-2bc-2ca\] done clear
  B)
   \[4{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-4ab+4bc+4ca\] done clear
  C)
  \[4{{a}^{2}}-{{b}^{2}}+{{c}^{2}}-4ab-4bc-4ca\] done clear
  D)
   \[4{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+4ab-2bc-4ac\] done clear
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• question_answer9)
  Which of the following products is equal to\[25{{x}^{2}}-30xy+9{{y}^{2}}?\]
  A)
  \[\text{(}5x+3y\text{)(}5x+3y\text{)}\] done clear
  B)
       \[\text{(}5x-3y\text{)(}5x-3y\text{)}\] done clear
  C)
       \[\text{(}3x-5y\text{)(}3x-5y\text{)}\] done clear
  D)
      \[\text{(}3x+5y\text{)(}3x+5y\text{)}\]                      done clear
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• question_answer10)
  Find the value of the expression\[\frac{{{(a-c)}^{2}}-{{(a+c)}^{2}}}{{{({{a}^{2}}+{{c}^{2}})}^{2}}-({{a}^{2}}-{{c}^{2}})},\]when \[a=\frac{1}{3}\]and \[c=\frac{1}{17}.\]
  A)
   -51                  done clear
  B)
        92                   done clear
  C)
        68                   done clear
  D)
        85                   done clear
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• question_answer11)
  If \[a+b=8\]and \[ab=12,\]find the value of \[{{a}^{4}}+{{b}^{4}}.\]
  A)
   1680               done clear
  B)
        1312               done clear
  C)
        1424               done clear
  D)
        2030               done clear
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• question_answer12)
  Find the value of the algebraic expression \[{{x}^{2}}y-3xy+5\]when \[x=4\]and \[y=1.\]
  A)
   6                     done clear
  B)
        7        done clear
  C)
        8        done clear
  D)
        9                                 done clear
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• question_answer13)
  Identify the product of \[({{x}^{3}}+15)\] and \[(2{{x}^{3}}-3).\]
  A)
  \[2{{x}^{6}}+{{x}^{3}}-54\]     done clear
  B)
         \[2{{x}^{6}}+27{{x}^{3}}-45\] done clear
  C)
       \[~2{{x}^{9}}-\text{ }{{x}^{6}}-45\]    done clear
  D)
         \[~2{{x}^{9}}+{{x}^{6}}-45\]   done clear
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• question_answer14)
  Find the value of \[1.8\times 1.8-2\text{ }\times \text{ }1.8\text{ }\times \text{ }1.2+\text{ }\]\[1.2\text{ }\times \text{ }1.2.\]
  A)
   0.60                done clear
  B)
        0.26                done clear
  C)
   0.16                done clear
  D)
        0.36    done clear
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• question_answer15)
  What must be added to \[{{x}^{2}}+10x\]to make it a perfect square?
  A)
   49                   done clear
  B)
        25      done clear
  C)
   100                 done clear
  D)
        36       done clear
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• question_answer16)
  Find the product of\[(12{{m}^{2}}n-3m{{n}^{2}}-1)\] and \[6{{m}^{2}}{{n}^{2}}.\]
  A)
  \[72{{m}^{4}}{{n}^{3}}-18{{m}^{3}}{{n}^{4}}-6{{m}^{2}}{{n}^{2}}\] done clear
  B)
  \[24{{m}^{4}}{{n}^{3}}-15{{m}^{3}}{{n}^{4}}-5{{m}^{2}}{{n}^{2}}\] done clear
  C)
  \[60{{m}^{4}}{{n}^{3}}-16{{m}^{3}}{{n}^{4}}-4{{m}^{2}}{{n}^{2}}\] done clear
  D)
   \[48{{m}^{4}}{{n}^{3}}-12{{m}^{3}}{{n}^{4}}-8{{m}^{2}}{{n}^{2}}\] done clear
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• question_answer17)
  If \[{{\left( 2a-\frac{1}{a} \right)}^{2}}=4{{a}^{2}}-x+\frac{1}{a},\]find the value of \['x'\]
  A)
   2                     done clear
  B)
        1         done clear
  C)
   4                     done clear
  D)
        -2                    done clear
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• question_answer18)
  Find the value of \[{{\left( 19\frac{1}{2} \right)}^{2}}.\]
  A)
   \[340\frac{1}{4}\]      done clear
  B)
        \[360\frac{1}{4}\]      done clear
  C)
        \[370\frac{1}{4}\]      done clear
  D)
        \[380\frac{1}{4}\]      done clear
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• question_answer19)
  If \[3y-\frac{1}{2y}=8,\] find the value of \[9{{y}^{2}}+\frac{1}{4{{y}^{2}}}.\]
  A)
   63                   done clear
  B)
        65      done clear
  C)
        67      done clear
  D)
        69       done clear
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• question_answer20)
  Which of the following expressions are perfect squares?

  \[9{{x}^{2}}-6x+9\]              \[{{x}^{2}}-7x+10\]

  \[49{{x}^{2}}+9{{y}^{2}}-42xy\]    \[16{{x}^{2}}+24x+9\]

  A)
                                 Only (i) and (ii)        done clear
  B)
   Only (ii) and (iii) done clear
  C)
                    Only (i) and (iv) done clear
  D)
                    Only (iii) and (iv)        done clear
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• question_answer21)
  Find the value of\[\frac{0.75\times 0.75-0.25\times 0.25}{0.5}\]
  A)
   0.50                done clear
  B)
        0.75                done clear
  C)
   0.25                done clear
  D)
        1.0                  done clear
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• question_answer22)
  Find the value of \[25{{x}^{2}}+10xy-{{y}^{2}},\] when \[x=4\]and \[y=1.\]
  A)
   400                 done clear
  B)
        440                 done clear
  C)
        439                 done clear
  D)
        441                 done clear
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• question_answer23)
  If \[\left( a-\frac{1}{a} \right)=4,\]find the value of \[{{a}^{2}}+\frac{1}{{{a}^{2}}}.\]
  A)
   16                   done clear
  B)
        18                   done clear
  C)
   14      done clear
  D)
        20                               done clear
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• question_answer24)
  Find the value of \[10.01\times 9.99.\]
  A)
   90.0099          done clear
  B)
        90.0099          done clear
  C)
        90.9900          done clear
  D)
        99.9999                      done clear
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• question_answer25)
  Find the product of \[\text{(}p+1\text{)(}p+2\text{)}\] and \[(p+3).\]
  A)
  \[{{p}^{3}}+4{{p}^{2}}+11p+8\] done clear
  B)
         \[{{p}^{3}}+6{{p}^{2}}+11p+6\] done clear
  C)
  \[{{p}^{3}}+6{{p}^{2}}+12p+14\] done clear
  D)
        \[~{{p}^{3}}+6{{p}^{2}}+12p+12\] done clear
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• question_answer26)
  Find the value of \[52\text{ }\times \text{ }52\text{ }+\text{ }2\text{ }\times \text{ }52\text{ }\times \text{ }48\text{ }+\text{ }48\text{ }\times \text{ }48.\]
  A)
   12148             done clear
  B)
        10000             done clear
  C)
        11234             done clear
  D)
        14136             done clear
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• question_answer27)
  Identify the middle term in the product of \[(2{{x}^{3}}-4)\] and \[(5{{x}^{3}}-3).\]
  A)
  \[-14{{x}^{3}}\]                   done clear
  B)
  \[-26{{x}^{3}}\]       done clear
  C)
       \[10{{x}^{6}}\]        done clear
  D)
        12                   done clear
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• question_answer28)
  Find the product of \[(a+\sqrt{2})(a-\sqrt{2})\] and \[({{a}^{2}}+2).\]
  A)
  \[{{a}^{4}}+4\]                               done clear
  B)
  \[~{{a}^{4}}+8\]               done clear
  C)
       \[~{{a}^{4}}-4\]     done clear
  D)
        \[{{a}^{4}}-8\]        done clear
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• question_answer29)
  Given \[v+\frac{1}{v}=7,\]find the value of \[{{v}^{4}}+\frac{1}{{{v}^{4}}}.\]
  A)
   2209               done clear
  B)
        2207               done clear
  C)
   2227               done clear
  D)
        2272   done clear
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• question_answer30)
  The perimeter of a triangle is\[10{{p}^{2}}-6p+9\] and two of its sides are \[2{{p}^{2}}-3p+1\] and \[5{{p}^{2}}-4p+4.\] Find third side of the triangle.
  A)
  \[3{{p}^{2}}-p+4\]    done clear
  B)
  \[3{{p}^{2}}+p-4\] done clear
  C)
  \[~3{{p}^{2}}+p+4\]        done clear
  D)
        \[~3{{p}^{2}}-p4\] done clear
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• question_answer31)
  If \[x-\frac{1}{x}=7,\]What is the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}?\]
  A)
   47                   done clear
  B)
        49                   done clear
  C)
   51                   done clear
  D)
        77                               done clear
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• question_answer32)
  Find the value of \[0.67\times 0.67-0.33\times 0.33.\]
  A)
   0.34    done clear
  B)
                    0.034 done clear
  C)
   3.4                  done clear
  D)
                    34 done clear
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• question_answer33)
  If \[t+\frac{1}{t}=2,\]find the value of \[t-\frac{1}{t}.\]
  A)
   0                     done clear
  B)
        4                     done clear
  C)
   -2                    done clear
  D)
         done clear
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• question_answer34)
  Find the product of \[(2x-3)\]and \[(x+2).\]
  A)
  \[2{{x}^{2}}-7x+6\]            done clear
  B)
                    \[2{{x}^{2}}-x-6\]   done clear
  C)
  \[2{{x}^{2}}+x-6\] done clear
  D)
        \[2{{x}^{2}}-7x-6\]             done clear
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• question_answer35)
  What is the value of \[\frac{{{(225+175)}^{2}}+{{(125-175)}^{2}}}{225\times 225+175\times 175}?\]
  A)
   0                     done clear
  B)
        400                 done clear
  C)
   2                     done clear
  D)
        50 done clear
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• question_answer36)
  Identify the expansion of \[{{\left( \frac{1}{4}+\frac{3}{4}b \right)}^{2}}.\]
  A)
   \[\frac{1}{16}+\frac{3}{16}b+\frac{{{b}^{2}}}{16}\] done clear
  B)
        \[\frac{1}{16}+\frac{3}{8}b+\frac{9}{16}{{b}^{2}}\] done clear
  C)
        \[\frac{3}{16}b+\frac{1}{64}+\frac{9}{16}{{b}^{2}}\]           done clear
  D)
   \[\frac{1}{4}+\frac{3}{4}b+\frac{9}{16}\]           done clear
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• question_answer37)
  If \[\frac{1}{a}=5\]and \[\frac{1}{b}=3,\]Find the value of \[\left( \frac{1}{a}+\frac{1}{b} \right)\]and \[\left( \frac{1}{a}-\frac{1}{b} \right).\]
  A)
   40                   done clear
  B)
        24                   done clear
  C)
   16                   done clear
  D)
        32                   done clear
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• question_answer38)
  If \[(-2x+3y)\]is a side of a square, find its area.
  A)
   \[4{{x}^{2}}+2xy+{{y}^{2}}\] done clear
  B)
        \[4{{x}^{2}}+4xy+9{{y}^{2}}\]            done clear
  C)
   \[4{{x}^{2}}-12xy+9{{y}^{2}}\]            done clear
  D)
   \[4{{x}^{2}}+12xy+9{{y}^{2}}\] done clear
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