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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Sequences and Series

NDA 2016 · Mathematics · Sequences and Series

Paragraph: Let a, x, y, z, b be in AP , where x+y+z=15 . Let a, p,...

Paragraph: Let a,x,y,z,b\mathrm{a}, \mathrm{x}, \mathrm{y}, \mathrm{z}, \mathrm{b} be in AP , where x+y+z=15\mathrm{x}+\mathrm{y}+\mathrm{z}=15. Let a,p,q,r,b\mathrm{a}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{b} be in HP , where \mathrmp−1+\mathrmq−1+\mathrmr−1=53\mathrmp^{-1}+\mathrmq^{-1}+\mathrmr^{-1}=\frac{5}{3}
Question: What is the value of pqr?

Options

  1. A35/24335/243
  2. B81/3581 / 35
  3. C243/35243/35
  4. DCannot be determined

Correct answer

C. 243/35243/35

Step-by-step solution

Since a, p, q, r, b or 1,p,q,r,91, \mathrm{p}, \mathrm{q}, \mathrm{r}, 9 are in H.P. ⇒11+4d=9⇒d=−291p=1−29=79⇒p=971q=79−29=59⇒q=951r=59−29=39⇒r=93⇒p×q×r=24335\begin{aligned} \Rightarrow & \frac{1}{1+4 \mathrm{ d}}=9 \Rightarrow d=-\frac{2}{9} \\ & \frac{1}{\mathrm{p}}=1-\frac{2}{9}=\frac{7}{9} \Rightarrow p=\frac{9}{7} \\ & \frac{1}{\mathrm{q}}=\frac{7}{9}-\frac{2}{9}=\frac{5}{9} \Rightarrow q=\frac{9}{5} \\ & \quad & \frac{1}{\mathrm{r}}=\frac{5}{9}-\frac{2}{9}=\frac{3}{9} \Rightarrow r=\frac{9}{3} \\ \Rightarrow & \mathrm{p} \times \mathrm{q} \times \mathrm{r}=\frac{243}{35}\end{aligned}
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