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4-2.Quadratic Equations and Inequations
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Below are four equations in $x$. Assume that $0 < r < 4$. Which of the following equations has the largest solution for $x$ ?
A
$5\left(1+\frac{r}{\pi}\right)^x=9$
B
$5\left(1+\frac{r}{17}\right)^x=9$
C
$5(1+2 r)^x=9$
D
$5\left(1+\frac{1}{r}\right)^x=9$
(KVPY-2011)
Solution
(b)
Given,$0 < r < 4$
$A=5\left(1+\frac{r}{\pi}\right)^x=9$
$\left(1+\frac{r}{\pi}\right)^x=\frac{9}{5}$
$B=\left(1+\frac{r}{17}\right)^x=\frac{9}{5}$
$C=(1+2 r)^x=\frac{9}{5}$
$D=\left(1+\frac{1}{r}\right)^x=\frac{9}{5}$
All $A, B, C, D$ are in the form of $(a)^x=b$ $x$ is largest when $a$ is smallest.
$\therefore \operatorname{In} A, B, C, D$
$ 0 < r < 4$
$1+\frac{r}{17}$ is smallest
Option $(b)$ is correct.
Standard 11
Mathematics
