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Home AptitudeIndices and Surds

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.


1. Simplify the following: 
(169/121)-3/2 * 27/2 * (13/22)-1
  • A. 13-1 114 33
  • B. 13-2 114 34
  • C. 13-3 114 34
  • D. 13-4 114 33
  • E. None of these
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Answer & Explanation

Answer: Option D

Explanation:

(169/121)-3/2 * 27/2 * (13/22)-1 

(132/112)-3/2 * 27/2 * 22/13 = 13-3/11-3 * 27/2 * 22/13
= 13-4 114 33 

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2. (272/4-3)-5/6 = ?
  • A. 1/1296
  • B. 1/46656
  • C. 1/7256
  • D. 1/7776
  • E. None of theses
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Answer & Explanation

Answer: Option D

Explanation:

(272/4-3)-5/6 = [(33)2/(22)-3]-5/6 

= (36 * 26)-5/6 
= (66)-5/6 = 1/65 = 1/ 7776.

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3. (5 - 7)2 * (6 - 9)2 / (23)-2 = ?
  • A. -2304
  • B. 2304
  • C. -2382
  • D. 2382
  • E. None of these
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Answer & Explanation

Answer: Option B

Explanation:

(5 - 7)2 * (6 - 9)2 / (23)-2 = (-2)2 * (-3)2 * 1/(23)-2 

= 4 * 9 * 64 = 2304.

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4. (a-3 b-2 / a2 b2)-3 * (a3 b-4 / a-3 b3) / (a-2 b3/a-4 b-3) = ?
  • A. a-19 b-1
  • B. a-19 b
  • C. a19 b-1
  • D. a19 b
  • E. None of these
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Answer & Explanation

Answer: Option C

Explanation:

(a-3 b-2 / a2 b2)-3 * (a3 b-4 / a-3 b3) / (a-2 b3/a-4 b-3) 

= (a-5 b-4)-3 * a6b-7 / a2b6 
= a15b12 * a6b-7 * a-2b-6 
= a19 b-1

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5. (8x9 / 27y-6)-2/3 = ?
  • A. 9/4 x-6 y-4
  • B. 9/4 x-4 y-6
  • C. 9/4 x-6 y4
  • D. 9/4 x-4 y6
  • E. None of these
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Answer & Explanation

Answer: Option A

Explanation:

(8x9 / 27y-6)-2/3 = (8x9y6 / 27)-2/3 = [(2/3 x3 y2)3]-2/3 

= 9/4 x-6 y-4.

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