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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Sequences and Series

NDA 2013 · Mathematics · Sequences and Series

The harmonic mean H of two numbers is 4 and the arithmetic mean A...

The harmonic mean H of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the equation 2A+G2=272 \mathrm{ A}+\mathrm{G}^2=27. The two numbers are

Options

  1. A6,36,3
  2. B9,59,5
  3. C12,712,7
  4. D3,13,1

Correct answer

A. 6,36,3

Step-by-step solution

2A+AH=27A(2+4)=27\begin{aligned} & 2 \mathrm{ A}+\mathrm{AH}=27 \\ & \mathrm{ A}(2+4)=27\end{aligned}A=92a+b=9a×b=AH=18\begin{aligned} & \mathrm{A}=\frac{9}{2} \\ & a+b=9 \\ & a \times b=\mathrm{AH}=18\end{aligned}a=3$ and b=6 or a=6 and b=3
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