JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the numbers \(2, b, c\) be in an \(A.P\) and \(A = \left[ {\begin{array}{*{20}{c}}
1&1&1 \\
2&b&c \\
4&{{b^2}}&{{c^2}}
\end{array}} \right]\). If \(det(A) \in [2,16]\) then \(c\) lies in the interval
- A \([3,2 + 2^{2/4} ]\)
- B \((2 + 2^{3/4},4)\)
- C \((2,3)\)
- D \([4, 6]\)
Answer & Solution
Correct Answer
(D) \([4, 6]\)
Step-by-step Solution
Detailed explanation
\(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 2&b&c\\ 4&{{b^2}}&{{c^2}} \end{array}} \right|\) \({C_2} \to {C_2} - {C_1},{C_3} \to {C_3} - {C_1}\) \( \Rightarrow \left| {\begin{array}{*{20}{c}} 1&0&0\\ 2&{b - 2}&{c - 2}\\ 4&{{b^2} - 4}&{{c^2} - 4} \end{array}} \right|\)…
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