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Why Aptitude Indices and Surds is Required?

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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
21. 242 + 420 + 1611 + 647 equals
  • A. (240) (5)
  • B. (241)(1)
  • C. (242)(52)
  • D. 240 * 52
  • E. None of these
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Answer & Explanation

Answer: Option D

Explanation:

242 + 240 + 244 + 242 

= 240(22 + 1 + 24 + 22) 
= 240 * 25 = 240 * 52

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22. If a + b + c = 0 and abc ≠ 0, then [Xa3 / abc][Xb3 / abc][Xc3 / abc] equals
  • A. X2
  • B. X
  • C. X3
  • D. X0
  • E. None of these
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Answer & Explanation

Answer: Option C

Explanation:

Xa3 / abc * Xb3 / abc * Xc3 / abc 

= X(a3 + b3 + c3) / abc 
As a + b + c = 0, (a3 + b3 + c3) / abc = 3 
The given expression equals X3

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23. Simplify: yp(q - r) . yq(r - p) . yr(p - q)
  • A. 0
  • B. 1
  • C. y
  • D. y2
  • E. None of these
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Answer & Explanation

Answer: Option B

Explanation:

yp(q - r) . yq(r - p) . yr(p - q) 

= ypq - pr + qr - qp + rp - rq 
= yp0 = 1.

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24. Which of the following is the greatest?
  • A. 323
  • B. 332
  • C. 232
  • D. (23)2
  • E. 222
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Answer & Explanation

Answer: Option B

Explanation:

323 = 38 

332 = 39 
232 = 29 
(23)2 = 26 
222 = 24 
As 39 > 38 , 29 > 26 > 24 and 39 > 29 , 39 is the greatest among the five.

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25. Which of the following is the greatest?
  • A. 3333
  • B. 3333
  • C. 3333
  • D. 3333
  • E. 3333
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Answer & Explanation

Answer: Option E

Explanation:

3333 = 339 

In choice (b), the base 333 lies between 243 = (35) and 729 = (36) 3333 lies between 37 and 38 
Hence 3333 lies between (35)3 and (36)3, i.e., between 315 and 318 
In choice (c), the base 33 lies between 27 = (33) and 81 = (34).
Hence 3333 lies between (33)33 and (34)33 i.e., between 399 and 3132. Hence 3333 is greatest.

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