Search any question & find its solution
Question:
Answered & Verified by Expert
Let $\mathrm{a}, \mathrm{x}, \mathrm{y}, \mathrm{z}, \mathrm{b}$ be in $\mathrm{AP}$, where $\mathrm{x}+\mathrm{y}+\mathrm{z}=15$. Let $\mathrm{a}, \mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{b}$ be
in HP, where $\mathrm{p}^{-1}+\mathrm{q}^{-1}+\mathrm{r}^{-1}=\frac{5}{3}$
What is the value of pqr?
Options:
in HP, where $\mathrm{p}^{-1}+\mathrm{q}^{-1}+\mathrm{r}^{-1}=\frac{5}{3}$
What is the value of pqr?
Solution:
1744 Upvotes
Verified Answer
The correct answer is:
$243 / 35$
since a, $\mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{b}$ or $1, \mathrm{p}, \mathrm{q}, \mathrm{r}, 9$ are in H.P.
$\begin{aligned} \Rightarrow & \frac{1}{1+4 \mathrm{~d}}=9 \Rightarrow d=-\frac{2}{9} . \\ & \frac{1}{\mathrm{p}}=1-\frac{2}{9}=\frac{7}{9} \Rightarrow p=\frac{9}{7} \\ & \frac{1}{\mathrm{q}}=\frac{7}{9}-\frac{2}{9}=\frac{5}{9} \Rightarrow q=\frac{9}{5} \\ & \& \frac{1}{\mathrm{r}}=\frac{5}{9}-\frac{2}{9}=\frac{3}{9} \Rightarrow r=\frac{9}{3} \\ \Rightarrow & \mathrm{p} \times \mathrm{q} \times \mathrm{r}=\frac{243}{35} \end{aligned}$
$\begin{aligned} \Rightarrow & \frac{1}{1+4 \mathrm{~d}}=9 \Rightarrow d=-\frac{2}{9} . \\ & \frac{1}{\mathrm{p}}=1-\frac{2}{9}=\frac{7}{9} \Rightarrow p=\frac{9}{7} \\ & \frac{1}{\mathrm{q}}=\frac{7}{9}-\frac{2}{9}=\frac{5}{9} \Rightarrow q=\frac{9}{5} \\ & \& \frac{1}{\mathrm{r}}=\frac{5}{9}-\frac{2}{9}=\frac{3}{9} \Rightarrow r=\frac{9}{3} \\ \Rightarrow & \mathrm{p} \times \mathrm{q} \times \mathrm{r}=\frac{243}{35} \end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.