It is given that the mean, median and mode of a data set is 1, 3^x and 9^x re...

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Question Id : 11670 | Context :NIMCET 2024

It is given that the mean, median and mode of a data set is

$1, 3^x$ and

$9^x$ respectively. The possible values of the mode is

🎥 Video solution / Text Solution of this question is given below:

Given:

Use empirical formula:

$\text{Mode} = 3 \cdot \text{Median} - 2 \cdot \text{Mean}$

$9^x = 3 \cdot 3^x - 2 \Rightarrow (3^x)^2 = 3 \cdot 3^x - 2$

Let $y = 3^x$ , then:

$y^2 = 3y - 2 \Rightarrow y^2 - 3y + 2 = 0 \Rightarrow (y - 1)(y - 2) = 0$

So, $y = 1 \text{ or } 2 \Rightarrow 9^x = y^2 = 1 \text{ or } 4$

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