Surds and Indices Questions Answers

Surds and Indices Questions Answers (MCQ) listings with explanations are important for BANK PO, Clerk, IBPS, SBI-PO, RBI, MBA, MAT, CAT, IIFT, IGNOU, SSC CGL, CBI, CPO, CLAT, CTET, NDA, CDS, Specialist Officers and other competitive exams.

11) Find the value of, \begin{aligned} \frac{1}{216^{-\frac{2}{3}}}+\frac{1}{256^{-\frac{3}{4}}}+\frac{1}{32^{-\frac{1}{5}}} \end{aligned}

  • 1) 100
  • 2) 101
  • 3) 102
  • 4) 103
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Ans.   C
Explanation :

12) Find the value of \begin{aligned} (10)^{150} \div (10)^{146} \end{aligned}

  • 1) 10
  • 2) 100
  • 3) 1000
  • 4) 10000
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Ans.   D
Explanation :
\begin{aligned} = \frac{(10)^{150}}{(10)^{146}} = 10^4 = 10000 \end{aligned}

13) \begin{aligned} (1000)^7 \div (10)^{18} = ? \end{aligned}

  • 1) 10
  • 2) 100
  • 3) 1000
  • 4) 10000
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Ans.   C
Explanation :
\begin{aligned} = \frac{(10^3)^7}{(10)^{18}} \end{aligned} \begin{aligned} = \frac{(10)^{21}}{(10)^{18}} = 10^3 = 1000 \end{aligned}

14) If m and n are whole numbers such that \begin{aligned} m^n=121 \end{aligned} , the value of \begin{aligned} (m-1)^{n + 1} \end{aligned}

  • 1) 1
  • 2) 10
  • 3) 100
  • 4) 1000
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Ans.   D
Explanation :
We know that \begin{aligned} (11)^2 = 121 \end{aligned} So, putting values in said equation we get, \begin{aligned} (11-1)^{2 + 1} = (10)^3 = 1000 \end{aligned}

15) Evaluate \begin{aligned} 256^{0.16} \times (256)^{0.09} \end{aligned}

  • 1) 2
  • 2) 4
  • 3) 8
  • 4) 16
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Ans.   B
Explanation :
\begin{aligned} = 256^{0.16+0.09} = 256^{0.25} = 256^{\frac{25}{100}} \end{aligned} \begin{aligned} = 256^{\frac{1}{4}}= (4^4)^{\frac{1}{4}} \end{aligned} \begin{aligned} =(4)^{4 \times \frac{1}{4}} = 4 \end{aligned}
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