If $a_1, a_2, a_3, \ldots, a_n, \ldots$ are in G.P., then the determinant…

If $a_1, a_2, a_3, \ldots, a_n, \ldots$ are in G.P., then the determinant $\Delta=\left|\begin{array}{lll}\log a_n & \log a_{n+1} & \log a_{n+2} \\ \log a_{n+3} & \log a_{n+4} & \log a_{n+5} \\ \log a_{n+6} & \log a_{n+7} & \log a_{n+8}\end{array}\right|$ is equal to
  1. 1
  2. 0
  3. 4
  4. 2

Solution

$\mathrm{C}_1-\mathrm{C}_2, \mathrm{C}_2-\mathrm{C}_3$ two rows becomes identical Answer: 0.

Asked in: JEE Main 2005

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