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Quantitative Aptitude

ALGEBRA MCQs

Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 29 of 101 pages
Question 281. If $${\text{2}}x - \frac{1}{{2x}} = 5{\text{,}}$$    $${\text{x}} \ne {\text{0,}}$$   then find the value of $${x^2} + \frac{1}{{16{x^2}}} - 2$$    = ?
  1.    $$\frac{{19}}{4}$$
  2.    $$\frac{{23}}{4}$$
  3.    $$\frac{{27}}{4}$$
  4.    $$\frac{{31}}{4}$$
 Discuss Question
Answer: Option A. -> $$\frac{{19}}{4}$$
Question 282. If a(x + y) = b(x - y) = 2ab, then the value of 2(x2 + y2) is?
  1.    2(a2 - b2)
  2.    2(a2 + b2)
  3.    4(a2 - b2)
  4.    4(a2 + b2)
 Discuss Question
Answer: Option D. -> 4(a2 + b2)
Question 283. If $$2x + \frac{1}{{4x}} = 1{\text{,}}$$   then the value of $${x^2} + \frac{1}{{64{x^2}}}$$   is?
  1.    0
  2.    1
  3.    $$\frac{1}{4}$$
  4.    2
 Discuss Question
Answer: Option A. -> 0
Question 284. If $$\sqrt x $$  - $$\sqrt y $$  = 1, $$\sqrt x $$  + $$\sqrt y $$  = 17, then $$\sqrt {xy} $$  = ?
  1.    $$\sqrt {72} $$
  2.    72
  3.    32
  4.    24
 Discuss Question
Answer: Option B. -> 72
Question 285. If $$\sqrt 3 + \frac{1}{{\sqrt 3 }}{\text{,}}$$   then the value of $$\left( {x - \frac{{\sqrt {126} }}{{\sqrt {42} }}} \right)$$ $$\left( {x - \frac{1}{{x - \frac{{2\sqrt 3 }}{3}}}} \right)$$   is?
  1.    $${\text{5}}\frac{{\sqrt 3 }}{6}$$
  2.    $$\frac{{2\sqrt 3 }}{3}$$
  3.    $$\frac{5}{6}$$
  4.    $$\frac{2}{3}$$
 Discuss Question
Answer: Option C. -> $$\frac{5}{6}$$
Question 286. If $$\frac{{2 + a}}{a}$$  + $$\frac{{2 + b}}{b}$$  + $$\frac{{2 + c}}{c}$$  = 4, then the value of $$\frac{{ab + bc + ca}}{{abc}}$$   is?
  1.    2
  2.    1
  3.    0
  4.    $$\frac{1}{2}$$
 Discuss Question
Answer: Option D. -> $$\frac{1}{2}$$
Question 287. If $$x + \frac{1}{x} = 5{\text{,}}$$   then the value of $$\frac{{5x}}{{{x^2} + 5x + 1}}$$   is?
  1.    $$\frac{1}{3}$$
  2.    $$\frac{1}{4}$$
  3.    $$\frac{1}{2}$$
  4.    $$\frac{1}{5}$$
 Discuss Question
Answer: Option C. -> $$\frac{1}{2}$$
Question 288. If $$\frac{1}{a}\left( {{a^2} + 1} \right) = 3{\text{,}}$$    then the value of $$\frac{{{a^6} + 1}}{{{a^3}}}$$   = ?
  1.    9
  2.    18
  3.    27
  4.    1
 Discuss Question
Answer: Option B. -> 18
Question 289. If (x - 5)2 + (y - 2)2 + (z - 9)2 = 0, then the value of (x + y - z) is?
  1.    16
  2.    -1
  3.    -2
  4.    12
 Discuss Question
Answer: Option C. -> -2
Question 290. If x = 999, y = 1000, z = 1001 then the value of $$\frac{{{x^3} + {y^3} + {z^3} - 3xyz}}{{x - y + z}}$$     is?
  1.    1000
  2.    9000
  3.    1
  4.    9
 Discuss Question
Answer: Option D. -> 9

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