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JEE Math Practice Question

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

  1. A.[2, 3)
  2. B.[4, 6]
  3. C.(2 + 23/4, 4)
  4. D.[3, 2 + 23/4]

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