Thank you for reporting, we will resolve it shortly
Q.
Let the number 2,b,c be in an A.P. and $A = \begin{bmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{bmatrix} $ .If det $\left(A\right)\in\left[2,16\right] $ , then c lies in the interval :
put $b = \frac{2+c}{2} $ in determinant of A
$ \left|A\right| =\frac{c^{3}-6c^{2}+12c-8}{4} \in\left[2,16\right] $
$ \Rightarrow \left(c-2\right)^{3} \in\left[8,64\right] $
$ \Rightarrow c \in \left[4,6\right]$