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. 2^{42} + 4^{20} + 16^{11} + 64^{7} equals
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Answer: Option D

Explanation:

2^{42} + 2^{40} + 2^{44} + 2^{42}

= 2^{40}(2^{2} + 1 + 2^{4} + 2^{2})

= 2^{40} * 25 = 2^{40} * 5^{2}

22. If a + b + c = 0 and abc â‰ 0, then [X^{a3 / abc}][X^{b3 / abc}][X^{c3 / abc}] equals
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Answer: Option C

Explanation:

X^{a3 / abc} * X^{b3 / abc} * X^{c3 / abc}

= X^{(a3 + b3 + c3) / abc}

As a + b + c = 0, (a^{3} + b^{3} + c^{3}) / abc = 3

The given expression equals X^{3}

23. Simplify: y^{p(q - r)} . y^{q(r - p)} . y^{r(p - q)}
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Answer: Option B

Explanation:

y^{p(q - r)} . y^{q(r - p)} . y^{r(p - q)}

= y^{pq - pr + qr - qp + rp - rq}

= y^{p0} = 1.

24. Which of the following is the greatest?
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Answer: Option B

Explanation:

3^{23} = 3^{8}

3^{32} = 3^{9}

2^{32} = 2^{9}

(2^{3})^{2} = 2^{6}

2^{22} = 2^{4}

As 3^{9} > 3^{8} , 2^{9} > 2^{6} > 2^{4} and 3^{9} > 2^{9} , 3^{9} is the greatest among the five.

25. Which of the following is the greatest?
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Answer: Option E

Explanation:

3^{333} = 3^{39}

In choice (b), the base 333 lies between 243 = (3^{5}) and 729 = (3^{6}) 3333 lies between 3^{7} and 3^{8}

Hence 333^{3} lies between (3^{5})^{3} and (3^{6})^{3}, i.e., between 3^{15} and 3^{18}

In choice (c), the base 33 lies between 27 = (3^{3}) and 81 = (3^{4}).

Hence 33^{33} lies between (3^{3})^{33} and (3^{4})^{33} i.e., between 3^{99} and 3^{132}. Hence 3^{333} is greatest.