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Indices and Surds - Aptitude Questions and Answers

This is aptitude questions and answers section on Indices and Surds with explanation for various interview, competitive examinations and entrance tests. This Indices and Surds section will linearly deal with some fundamental questions of Indices and Surds Quiz which are majorly asked in competitive exams like CAT, XAT, IBPS and government exams.

Indices and Surds Questions - Indices and Surds Quiz Details

Online Test Name Indices and Surds
Exam Type Multiple Choice Questions
Category Aptitude Quiz
Number of Questions 30
26. [(√7 + √5) / ( (√7 - √5)] + [(√7 - √5) / (√7 + √5)] = ?
  • A. 6
  • B. 12
  • C. 14
  • D. 18
  • E. None of these
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Answer & Explanation

Answer: Option B

Explanation:

[(√7 + √5) / ( (√7 - √5)] + [(√7 - √5) / (√7 + √5)] 

= [(√7 + √5)2 + (√7 - √5)2] / (√7 + √5)(√7 - √5)
[(√7 + √5)2 + (√7 - √5)2] / 2 = 12

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27. If x = √11 + √20, y = √15 + √17 and z = √14 + √18, then which of the following holds true?
  • A. x < y < z
  • B. y < z < x
  • C. y < x < z
  • D. x < z < y
  • E. None of these
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Answer & Explanation

Answer: Option D

Explanation:

By squaring and simplifying, 

x2 = 31 + 2√220 
y2 = 32 + 2√255 
z2 = 32 + 2√252 
x2 < z2 < y2 => x < z < y.

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28. If x = √3 - √2, then find (x - 1/x)2
  • A. 2
  • B. 4
  • C. 2√2
  • D. 9
  • E. None of these
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Answer & Explanation

Answer: Option E

Explanation:

x = √3 - √2 

1/x = 1/√3 - √2 = (√3 + √2) / (√3 - √2)(√3 + √2) 
= √3 + √2 
(x - 1/x)2 = [(√3 - √2) - (√3 + √2)]2 
= (-2√2)2 = 8

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29. If x = √8 - √7, y = √6 - √5 and z = √10 - 3, which of the following is true?
  • A. x < z < y
  • B. z < x < y
  • C. x < y < z
  • D. z < y < x
  • E. None of these
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Answer & Explanation

Answer: Option B

Explanation:

x = √8 - √7 = 1/(√8 + √7) and y = √6 - √5 = 1/(√6 + √5) and z = √10 - 3 = 1/(√10 + 3) 

As (√8 + √7) > (√6 + √5), (√8 - √7) < (√6 - √5) 
As (√10 + 3) > (√8 + √7) > (√6 + √5) 
z < x < y.

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30. If x = √196 + √200, then x/2 + 2/x is?
  • A. 14
  • B. 7
  • C. 2√50
  • D. √50
  • E. None of these
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Answer & Explanation

Answer: Option C

Explanation:

x = 14 + 10√2 

x/2 = 7 + 5√2 
2/x = (7 - 5√2) / (7 + 5√2)(7 - 5√2) = 5√2 - 7 
x/2 + 2/x = 10√2 = 2√50

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