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Quantitative Aptitude

ALGEBRA MCQs

Basic Algebraic Identities Of School Algebra & Elementary Surds

Total Questions : 1010 | Page 37 of 101 pages
Question 361. If $${x^2} - 3x + 1 = 0,$$    then the value of $${x^3}{\text{ + }}\frac{1}{{{x^3}}}\,{\text{is?}}$$
  1.    9
  2.    18
  3.    27
  4.    1
 Discuss Question
Answer: Option B. -> 18
Question 362. If $$x + \frac{1}{{4x}} = \frac{3}{2}{\text{,}}$$   find the value of $${\text{8}}{x^3}{\text{ + }}\frac{1}{{8{x^3}}} = ?$$
  1.    18
  2.    36
  3.    24
  4.    16
 Discuss Question
Answer: Option A. -> 18
Question 363. If x + y = z, then the expression x3 + y3 - z3 + 3xyz will be equal to?
  1.    0
  2.    3xyz
  3.    -3xyz
  4.    3z
 Discuss Question
Answer: Option A. -> 0
Question 364. If $$3x + \frac{1}{{2x}} = 5{\text{,}}$$   then the value of $${\text{8}}{x^3}{\text{ + }}\frac{1}{{27{x^3}}}\,{\text{is?}}$$
  1.    $${\text{118}}\frac{1}{2}$$
  2.    $${\text{30}}\frac{{10}}{{27}}$$
  3.    0
  4.    1
 Discuss Question
Answer: Option B. -> $${\text{30}}\frac{{10}}{{27}}$$
Question 365. If a = 2.361, b = 3.263, and c = 5.624, then the value of a3 + b3 - c3 + 3abc is?
  1.    (p- q)(q - r)3 + (r - p)3
  2.    3(p - q)(q - r)(r - p)
  3.    0
  4.    1
 Discuss Question
Answer: Option C. -> 0
Question 366. If a3 - b3 - c3 - 3abc = 0, then -
  1.    a = b = c
  2.    a + b + c = 0
  3.    a + c = b
  4.    a = b + c
 Discuss Question
Answer: Option D. -> a = b + c
Question 367. If p = 124, then the value of $$\root 3 \of {p\left( {{p^2} + 3p + 3} \right) + 1} = ?$$
  1.    5
  2.    7
  3.    123
  4.    125
 Discuss Question
Answer: Option D. -> 125
Question 368. If $$x + \frac{1}{x} = 2$$   and x is real, then the value of $${x^{17}}{\text{ + }}\frac{1}{{{x^{19}}}}\,{\text{is?}}$$
  1.    1
  2.    0
  3.    2
  4.    -2
 Discuss Question
Answer: Option C. -> 2
Question 369. If a3b = abc = 180, a, b, c are positive integers, then the value of c is?
  1.    110
  2.    1
  3.    4
  4.    25
 Discuss Question
Answer: Option B. -> 1
Question 370. If $$\frac{{2p}}{{{p^2} - 2p + 1}} = \frac{1}{4}{\text{,}}$$    p ≠ 0 then the value of $$p + \frac{1}{p}\,{\text{is?}}$$
  1.    4
  2.    5
  3.    10
  4.    12
 Discuss Question
Answer: Option C. -> 10

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