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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

If H is the Harmonic Mean of three numbers ^ 10 C_4, ^ 10 C_5 , and...

If H is the Harmonic Mean of three numbers 10C4,10C5{ }^{10} \mathrm{C}_4,{ }^{10} \mathrm{C}_5, and 10C6{ }^{10} \mathrm{C}_6, then what is the value of 270H\frac{270}{H} ?

Options

  1. A1
  2. B1417\frac{14}{17}
  3. C1714\frac{17}{14}
  4. D131\frac{1}{31}

Correct answer

C. 1714\frac{17}{14}

Step-by-step solution

Since, Harmonic Mean (H) H=3110C4+110C5+110C6H=31210+1252+1210=3×105×252357\mathrm{H}=\frac{3}{\frac{1}{{ }^{10} \mathrm{C}_4}+\frac{1}{{ }^{10} \mathrm{C}_5}+\frac{1}{{ }^{10} \mathrm{C}_6}}H=\frac{3}{\frac{1}{210}+\frac{1}{252}+\frac{1}{210}}=\frac{3 \times 105 \times 252}{357} Hence, 270H=1714\frac{270}{\mathrm{H}}=\frac{17}{14}
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