Let the numbers 2 be in an . and then |MatricesJEEMain2019

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JEE MAIN 2019

08-04-2019 S2

Question

Let the numbers 2, $\mathrm{b}, \mathrm{c}$ be in an A.P. and $\mathrm{A}=\left|\begin{array}{ccc}1 & 1 & 1 \\ 2 & \mathrm{~b} & \mathrm{c} \\ 4 & \mathrm{~b}^2 & \mathrm{c}^2\end{array}\right|$. If $\operatorname{det}(\mathrm{A}) \in[2,16]$, then c lies in the interval :

Select the correct option:

A

$[2,3)$

B

$\left(2+2^{3 / 4}, 4\right)$

C

$\left[3,2+2^{3 / 4}\right]$

D

$[4,6]$

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