SSC Quantitative Aptitude Algebra Question Bank

done Elementary Algebra (I) Total Questions - 56

• question_answer1)
  If \[a+\frac{1}{b}=1\]and \[b+\frac{1}{c}=1,\]then the value of \[c+\frac{1}{a}\]is [SSC CGL Tier II, 2017]
  A)
  0 done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  3 done clear
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• question_answer2)
  If \[x=y+2,\]then \[{{x}^{3}}-{{y}^{3}}-{{z}^{3}}\]is [SSC CGL Tier II, 2017]
  A)
  \[0\] done clear
  B)
  \[3xy\] done clear
  C)
  \[-\,3xyz\] done clear
  D)
  \[1\] done clear
  View Solution play_arrow

• question_answer3)
  If \[a+b+c+d=4,\]then the value of \[\frac{1}{(1-a)(1-b)(1-a)}+\frac{1}{(1-b)(1-c)(1-d)}+\] \[\frac{1}{(1-c)(1-d)(1-a)}+\frac{1}{(1-d)(1-a)(1-b)}\]is [SSC CGL Tier II, 2017]
  A)
  0 done clear
  B)
  1 done clear
  C)
  4 done clear
  D)
  \[1+abcd\] done clear
  View Solution play_arrow

• question_answer4)
  If x = 11, the value of \[{{x}^{5}}-12{{x}^{4}}+12{{x}^{3}}-12{{x}^{2}}+12x-1\] is [SSC CGL Tier II, 2017]
  A)
  11 done clear
  B)
  10 done clear
  C)
  12 done clear
  D)
  -10 done clear
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• question_answer5)
  If \[a=\frac{1}{a-5}(a>0),\]then the value of \[a+\frac{1}{a}\] is [SSC CGL Tier II, 2017]
  A)
  \[\sqrt{29}\] done clear
  B)
  \[-\,\sqrt{27}\] done clear
  C)
  \[-\,\sqrt{29}\] done clear
  D)
  \[\sqrt{27}\] done clear
  View Solution play_arrow

• question_answer6)
  If \[a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}\](where \[a\ne b\ne c\])then abc is equal to [SSC CGL Tier II, 2017]
  A)
  \[+1\] done clear
  B)
  \[-1\] done clear
  C)
  \[+1\]and \[-1\] done clear
  D)
  None of the options, done clear
  View Solution play_arrow

• question_answer7)
  If \[ax+by=1\] and \[bx+ay=\frac{2ab}{{{a}^{2}}+{{b}^{2}}},\]then \[({{x}^{2}}+{{y}^{2}})({{a}^{2}}+{{b}^{2}})\] is equal to  [SSC CGL Tier II, 2017]
  A)
  1 done clear
  B)
  2 done clear
  C)
  0.5 done clear
  D)
  0 done clear
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• question_answer8)
  If x, y, z are the three factors of \[{{a}^{3}}-7a-6,\]then value of x + y + z will be [SSC CGL Tier II, 2017]
  A)
  3 a done clear
  B)
  3 done clear
  C)
  6 done clear
  D)
  a done clear
  View Solution play_arrow

• question_answer9)
  If \[x={{a}^{\frac{1}{2}}}+{{a}^{\frac{1}{2}}},\]\[y={{a}^{\frac{1}{2}}}-{{a}^{\frac{1}{2}}},\]then value of \[({{x}^{4}}-{{x}^{2}}{{y}^{2}}-1)+({{y}^{4}}-{{x}^{2}}{{y}^{2}}+1)\] [SSC CGL Tier II, 2015)
  A)
  12 done clear
  B)
  16 done clear
  C)
  14 done clear
  D)
  13 done clear
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• question_answer10)
  The value of \[\frac{(0.67\times 0.67\times 0.67)-(0.33\times 0.33\times 0.33)}{(0.67\times 0.67)+(0.67\times 0.33)+(0.33\times 0.33)}\]is [SSC CGL Tier II, 2015]
  A)
  3.4 done clear
  B)
  0.34 done clear
  C)
  1.1 done clear
  D)
  11 done clear
  View Solution play_arrow

• question_answer11)
  If \[a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a},\]where \[a\ne b\ne c\ne 0,\]then the value of \[{{a}^{2}}{{b}^{2}}{{c}^{2}}\]is [SSC CGL Tier II, 2015]
  A)
  \[abc\] done clear
  B)
  \[1\] done clear
  C)
  \[-\,1\] done clear
  D)
  \[0\] done clear
  View Solution play_arrow

• question_answer12)
  If \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=xy+yz+zx,\]then the value of \[\frac{3{{x}^{4}}+7{{y}^{4}}+5{{z}^{4}}}{5{{x}^{2}}{{y}^{2}}+7{{y}^{2}}{{z}^{2}}+3{{z}^{2}}{{x}^{2}}}\]is [SSC CGL Tier II, 2015]
  A)
  0 done clear
  B)
  -1 done clear
  C)
  2 done clear
  D)
  1 done clear
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• question_answer13)
  If \[{{\left( \frac{{{p}^{-1}}{{q}^{-\,2}}}{{{p}^{3}}{{q}^{2}}} \right)}^{\frac{1}{3}}}\div {{\left( \frac{{{p}^{6}}{{q}^{-\,3}}}{{{p}^{-\,2}}{{q}^{3}}} \right)}^{\frac{1}{3}}}\]then the value of a+ b, where p and q are different positive primes, is [SSC CGL Tier II, 2015]
  A)
  \[0\] done clear
  B)
  \[2\] done clear
  C)
  \[-1\] done clear
  D)
  \[1\] done clear
  View Solution play_arrow

• question_answer14)
  Let \[x=\frac{\sqrt{13}+\sqrt{11}}{\sqrt{13}-\sqrt{11}}\]and \[y=\frac{1}{x},\]then the value of\[3{{x}^{2}}-5xy+5{{y}^{2}}\]is [SSC CGL Tier II, 2015]
  A)
  1771 done clear
  B)
  1177 done clear
  C)
  1717 done clear
  D)
  1171 done clear
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• question_answer15)
  If \[x-\sqrt{3}-\sqrt{2}=0\]and \[y-\sqrt{3}+\sqrt{2}=0,\]then the value of \[({{x}^{3}}-20\sqrt{2})-({{y}^{3}}+2\sqrt{2})\]is [SSC CGL Tier II, 2015]
  A)
  1 done clear
  B)
  0 done clear
  C)
  3 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer16)
  If \[a-\frac{1}{a-3}=5,\]then the value of  \[{{(a-3)}^{3}}-\frac{1}{{{(a-3)}^{3}}}\]is [SSC CGL Tier II, 2015]
  A)
  7 done clear
  B)
  5 done clear
  C)
  2 done clear
  D)
  14 done clear
  View Solution play_arrow

• question_answer17)
  If \[3\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})={{(a+b+c)}^{2}},\]then the relation between a, b and c is  [SSC CGL Tier II, 2015]
  A)
  \[a=b\ne c\] done clear
  B)
  \[a\ne b=c\] done clear
  C)
  \[a=b=c\] done clear
  D)
  \[a\ne b\ne c\] done clear
  View Solution play_arrow

• question_answer18)
  If \[x+\frac{1}{x}=5,\]then the value of \[\frac{{{x}^{4}}+\frac{1}{{{x}^{2}}}}{{{x}^{2}}-3x+1}\]is
  A)
  70 done clear
  B)
  50 done clear
  C)
  110 done clear
  D)
  55 done clear
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• question_answer19)
  If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=2\,(a-b-c)-3,\]then the value of \[2a-3b+4c\]is
  A)
  3 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  4 done clear
  View Solution play_arrow

• question_answer20)
  If \[a=\frac{2+\sqrt{3}}{2-\sqrt{3}}\]and \[b=\frac{2-\sqrt{3}}{2+\sqrt{3}},\]then the value of \[({{a}^{2}}+{{b}^{2}}+ab)\]is
  A)
  195 done clear
  B)
  200 done clear
  C)
  175 done clear
  D)
  185 done clear
  View Solution play_arrow

• question_answer21)
  Out of the given responses, one of the factors of \[{{({{a}^{2}}-{{b}^{2}})}^{3}}+{{({{b}^{2}}-{{c}^{2}})}^{3}}+{{({{c}^{2}}-{{a}^{2}})}^{3}}\] is
  A)
  \[(a+b)(a-b)\] done clear
  B)
  \[(a+b)(a+b)\] done clear
  C)
  \[(a-b)(a-b)\] done clear
  D)
  \[(a-b)(a-b)\] done clear
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• question_answer22)
  If \[\frac{x-{{a}^{2}}}{b+c}+\frac{x-{{b}^{2}}}{c+a}+\frac{x-{{c}^{2}}}{a+b}\]then x is equal to
  A)
  \[{{(a+b+c)}^{2}}\] done clear
  B)
  \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] done clear
  C)
  \[ab+bc+ca\] done clear
  D)
  \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-bc-ca\] done clear
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• question_answer23)
  If \[x=3+2\sqrt{2},\]then the value of \[\left( \sqrt{x}-\frac{1}{\sqrt{x}} \right)\]is
  A)
  \[1\] done clear
  B)
  \[2\] done clear
  C)
  \[2\sqrt{2}\] done clear
  D)
  \[3\sqrt{3}\] done clear
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• question_answer24)
  If \[x=\sqrt[3]{5}+2,\]then the value of \[{{x}^{3}}-6{{x}^{2}}+12x-13\]is
  A)
  -1 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  0 done clear
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• question_answer25)
  If \[{{x}^{2}}=y+z,\]\[{{y}^{2}}=z+x\]and\[{{z}^{2}}=x+y\]then the value of \[\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}\]is
  A)
  \[-\,1\] done clear
  B)
  \[1\] done clear
  C)
  \[2\] done clear
  D)
  \[4\] done clear
  View Solution play_arrow

• question_answer26)
  If \[x+\frac{1}{x}=\sqrt{3},\]then the value of \[{{x}^{18}}+{{x}^{12}}+{{x}^{6}}+1\]is
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  3 done clear
  View Solution play_arrow

• question_answer27)
  If\[(x-a)(x-b)=1\]and \[a-b+5=0,\] then the value of \[{{(x-a)}^{3}}-\frac{1}{{{(x-a)}^{3}}}\]is
  A)
  \[-125\] done clear
  B)
  \[1\] done clear
  C)
  \[125\] done clear
  D)
  \[140\] done clear
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• question_answer28)
  If \[\sqrt{x}=\sqrt{3}-\sqrt{5},\]then the value of \[{{x}^{2}}-16x+6\]is
  A)
  0 done clear
  B)
  \[-\,2\] done clear
  C)
  2 done clear
  D)
  4 done clear
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• question_answer29)
  If \[x=y=333\] and \[z=334,\] the values of \[{{x}^{3}}+{{y}^{3}}+{{z}^{3}}-3xyz\]is
  A)
  0 done clear
  B)
  667 done clear
  C)
  1000 done clear
  D)
  2334 done clear
  View Solution play_arrow

• question_answer30)
  \[\left( x+\frac{1}{x} \right)\left( x-\frac{1}{x} \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}-1 \right)\left( {{x}^{2}}+\frac{1}{{{x}^{2}}}+1 \right)\]is equal to
  A)
  \[{{x}^{6}}+\frac{1}{{{x}^{6}}}\] done clear
  B)
  \[{{x}^{8}}+\frac{1}{{{x}^{8}}}\] done clear
  C)
  \[{{x}^{8}}-\frac{1}{{{x}^{8}}}\] done clear
  D)
  \[{{x}^{6}}-\frac{1}{{{x}^{6}}}\] done clear
  View Solution play_arrow

• question_answer31)
  If \[2x+\frac{2}{x}=3,\]then the Value of \[{{x}^{3}}+\frac{1}{{{x}^{3}}+}2\]is
  A)
  \[-\frac{9}{8}\] done clear
  B)
  \[-\frac{25}{8}\] done clear
  C)
  \[\frac{7}{8}\] done clear
  D)
  \[11\] done clear
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• question_answer32)
  If \[x+\frac{1}{x}=5,\]then the value of \[\frac{2x}{3{{x}^{2}}-5x+3}\]is
  A)
  \[2\] done clear
  B)
  \[1\frac{1}{5}\] done clear
  C)
  \[\frac{1}{5}\] done clear
  D)
  \[\frac{3}{5}\] done clear
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• question_answer33)
  If \[x=\sqrt{3}+\sqrt{2},\]then the value of\[\left( x+\frac{1}{x} \right)\]is
  A)
  \[2\] done clear
  B)
  \[3\] done clear
  C)
  \[2\sqrt{2}\] done clear
  D)
  \[2\sqrt{3}\] done clear
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• question_answer34)
     If \[{{a}^{2}}+\frac{1}{{{a}^{2}}}=98\,(a>0),\]then the value of \[{{a}^{3}}+\frac{1}{{{a}^{3}}}\]
  A)
  535 done clear
  B)
  1030 done clear
  C)
  790 done clear
  D)
  970 done clear
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• question_answer35)
  If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=2\,(a-b-c)-3,\]then the value of \[4a-3b+5c\]is
  A)
  2 done clear
  B)
  3 done clear
  C)
  5 done clear
  D)
  6 done clear
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• question_answer36)
  If \[x+\frac{a}{x}=1,\]then the value of  \[\frac{{{x}^{2}}+x+a}{{{x}^{3}}-{{x}^{2}}}\]is
  A)
  \[-\,2\] done clear
  B)
  \[-\frac{a}{2}\] done clear
  C)
  \[\frac{2}{a}\] done clear
  D)
  \[-\frac{2}{a}\] done clear
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• question_answer37)
  If \[5a+\frac{1}{3a}=5,\]then the value of \[9{{a}^{2}}+\frac{1}{25{{a}^{2}}}\]is
  A)
  \[\frac{34}{5}\] done clear
  B)
  \[\frac{39}{5}\] done clear
  C)
  \[\frac{42}{5}\] done clear
  D)
  \[\frac{52}{5}\] done clear
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• question_answer38)
  If \[x\left( 3-\frac{2}{x} \right)=\frac{3}{x},x\ne 0,\]then the value of \[{{x}^{2}}+\frac{1}{{{x}^{2}}}\]is
  A)
  \[2\frac{1}{3}\] done clear
  B)
  \[2\frac{2}{3}\] done clear
  C)
  \[2\frac{4}{9}\] done clear
  D)
  \[2\frac{5}{9}\] done clear
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• question_answer39)
  Is \[{{2}^{32}}-(2+1)({{2}^{2}}+1)({{2}^{4}}+1)({{2}^{8}}+1)({{2}^{16}}+1)\]equal to
  A)
  \[0\] done clear
  B)
  \[1\] done clear
  C)
  \[2\] done clear
  D)
  \[{{2}^{16}}\] done clear
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• question_answer40)
  If \[x=\frac{\sqrt{3}}{2},\] then the value of \[\frac{1+x}{1+\sqrt{1+x}}+\frac{1-x}{1-\sqrt{1-x}}\] is equal to
  A)
  \[0\] done clear
  B)
  \[1\] done clear
  C)
  \[\frac{\sqrt{3}}{2}\] done clear
  D)
  \[\sqrt{3}\] done clear
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• question_answer41)
  Find the value of \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc\]when \[a=225,\]\[b=226,\]\[c=227.\]
  A)
  2304 done clear
  B)
  2430 done clear
  C)
  2034 done clear
  D)
  2340 done clear
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• question_answer42)
  If\[a=23\]and \[b=-\,29,\]then the value of \[25{{a}^{2}}+40ab+16{{b}^{2}}\]is
  A)
  \[1\] done clear
  B)
  \[-1\] done clear
  C)
  \[0\] done clear
  D)
  \[2\] done clear
  View Solution play_arrow

• question_answer43)
  If \[{{a}^{4}}+{{b}^{4}}={{a}^{2}}{{b}^{2}},\]then \[({{a}^{6}}+{{b}^{6}})\]equals to
  A)
  \[0\] done clear
  B)
  \[-1\] done clear
  C)
  \[{{a}^{2}}+{{b}^{2}}\] done clear
  D)
  \[{{a}^{2}}{{b}^{4}}+{{a}^{4}}{{b}^{2}}\] done clear
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• question_answer44)
  If \[3x+\frac{1}{2x}=5,\]then the value of \[8{{x}^{3}}+\frac{1}{27{{x}^{3}}}\] is
  A)
  (a)\[118\frac{1}{2}\] done clear
  B)
  \[30\frac{10}{27}\] done clear
  C)
  \[0\] done clear
  D)
  \[1\] done clear
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• question_answer45)
  If \[a+\frac{1}{a}+2=0,\]then the value of \[{{a}^{37}}-\frac{1}{{{a}^{100}}}\]is
  A)
  \[0\] done clear
  B)
  \[-\,2\] done clear
  C)
  \[1\] done clear
  D)
  \[2\] done clear
  View Solution play_arrow

• question_answer46)
  \[{{(y-z)}^{3}}+{{(z-x)}^{3}}+{{(x-y)}^{3}}\]is equal to
  A)
  \[3\,\,(y-z)(z+x)(y-x)\] done clear
  B)
  \[(x-y)(y+z)(x-z)\] done clear
  C)
  \[3\,(y-z)(z-x)(x-y)\] done clear
  D)
  \[(y-z)(z-x)(x-y)\] done clear
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• question_answer47)
  \[x+y=z,\]then the expression \[{{x}^{3}}+{{y}^{3}}-{{z}^{3}}+3xyz\] will be equal to
  A)
  \[0\] done clear
  B)
  \[3xyz\] done clear
  C)
  \[-\,3xyz\] done clear
  D)
  \[{{z}^{3}}\] done clear
  View Solution play_arrow

• question_answer48)
  If \[2p+\frac{1}{p}=4,\]then the value of \[{{p}^{3}}+\frac{1}{8{{p}^{3}}}\]is
  A)
  4 done clear
  B)
  5 done clear
  C)
  8 done clear
  D)
  15 done clear
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• question_answer49)
  If \[a=11\]and \[b=9,\]then the value of \[\left( \frac{{{a}^{2}}+{{b}^{2}}+ab}{{{a}^{3}}-{{b}^{3}}} \right)\]is
  A)
  \[\frac{1}{2}\] done clear
  B)
  \[2\] done clear
  C)
  \[\frac{1}{20}\] done clear
  D)
  \[20\] done clear
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• question_answer50)
  If \[{{a}^{4}}+{{a}^{2}}{{b}^{2}}+{{b}^{4}}=8\]and \[{{a}^{2}}+ab+{{b}^{2}}=4,\] then the value of ab is
  A)
  \[-1~\] done clear
  B)
  \[0\] done clear
  C)
  \[2\] done clear
  D)
  \[1\] done clear
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• question_answer51)
  If \[a=25,\]\[b=15,\]\[c=-10,\]then the value of \[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{{{(a-b)}^{2}}+{{(b-c)}^{2}}+{{(c-a)}^{2}}}\]
  A)
  \[30\] done clear
  B)
  \[-15\] done clear
  C)
  \[-\,30\] done clear
  D)
  \[15\] done clear
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• question_answer52)
  If \[a=0.25,\] \[b=0.05\]and \[c=0.5,\]then the value of \[\frac{{{a}^{2}}-{{b}^{2}}-{{c}^{2}}-2bc}{{{a}^{2}}+{{b}^{2}}-2ab-{{c}^{2}}}\]is
  A)
  \[\frac{8}{7}\] done clear
  B)
  \[\frac{14}{17}\] done clear
  C)
  \[1\] done clear
  D)
  \[\frac{25}{16}\] done clear
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• question_answer53)
  If \[{{a}^{3}}-{{b}^{3}}=56\]and \[a-b=2,\]then value of \[{{a}^{2}}+{{b}^{2}}\]will be
  A)
  5 done clear
  B)
  48 done clear
  C)
  20 done clear
  D)
  22 done clear
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• question_answer54)
  The value of\[{{(x+y+z)}^{3}}-{{(y-z-x)}^{3}}\]\[-\,\,{{(z+x-y)}^{3}}-(x+y-z)\]
  A)
  0 done clear
  B)
  12 xyz done clear
  C)
  24 xyz done clear
  D)
  36 xyz done clear
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• question_answer55)
  If \[a=1,\]\[b=2\]and \[c=-\,3,\]then the value of\[\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{ab+bc+ca-({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}\]is
  A)
  3 done clear
  B)
  2 done clear
  C)
  0 done clear
  D)
  1 done clear
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• question_answer56)
  If  \[a+\frac{1}{a}=\sqrt{3},\]then the value of \[{{a}^{6}}-\frac{1}{{{a}^{6}}}+2\]is
  A)
  4 done clear
  B)
  \[-6\] done clear
  C)
  \[\sqrt{3}\] done clear
  D)
   2 done clear
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