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 |

11. Simplify : 1 - {1 + (a^{2} - 1)^{-1}}^{-1}
### Answer & Explanation

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Answer: Option A

Explanation:

1 - {1 + (a^{2} - 1)^{-1}}^{-1} = 1 - {1 + 1/a^{2} - 1}^{-1}
= 1 - {a^{2} / a^{2} - 1}^{-1} = 1 - (a^{2} - 1)/a^{2} = 1/a^{2}.

12. Simplify : (y^{4b-a} . y^{4c-b} . y^{4a-c}) / (y^{a} . y^{b} . y^{c})^{3}
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Answer: Option B

Explanation:

(y^{4b-a} . y^{4c-b} . y^{4a-c}) / (y^{a} . y^{b} . y^{c})^{3}

= (y^{4b-a} . y^{4c-b} . y^{4a-c}) / (y^{a+b+c})^{3}

= y^{4b-a+4c-b+4a-c} / y^{3(a+b+c)}

= y^{3(a+b+c)} / y^{3(a+b+c)} = 1.

13. If 3^{4m+1} = 3^{7m-5}, solve for m.
### Answer & Explanation

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Answer: Option A

Explanation:

3^{4m+1} = 3^{7m-5} equating powers of 3 on both sides, 4m+1
= 7m - 5 => 3m = 6 => m = 2.

14. If 2^{4m+2} = 4^{6m-4}, solve for m.
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Answer: Option C

Explanation:

2^{4m+2} = 4^{6m-4} = 2^{4m+2} = (2^{2})^{6m-4} => 2^{4m+2} = 22^{12m-8}
Equating powers of 2 both sides.

4m + 2 = 12m - 8 => 10 = 8m => m = 5/4.

15. Solve for m if 36 (6^{m}) = (216)^{3m+4}
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Answer: Option C

Explanation:

36 (6^{m}) = (216)^{3m+4} => 6^{2} 6^{m} = (6^{3})^{3m+4} => 6^{2+m} = 6^{9m+12}
Equating powers of 6 on both sides.

m + 2 = 9m + 12 => -10 = 8m => m = -5/4