question_answer

If\[{{a}_{1}},{{a}_{2}},{{a}_{3}},....,{{a}_{n}},....\]are in GP, then the determinant \[\Delta =\left| \begin{matrix}    \log {{a}_{n}} & \log {{a}_{n+1}} & \log {{a}_{n+2}}  \\    \log {{a}_{n+3}} & \log {{a}_{n+4}} & \log {{a}_{n+5}}  \\    \log {{a}_{n+6}} & \log {{a}_{n+7}} & {{\log }_{n+8}}  \\ \end{matrix} \right|\]is equal to     AIEEE  Solved  Paper-2005

A) 2             

B)        4             

C)        0             

D)        1

Correct Answer: C

Solution :

Since,are  in  GP.  Then, in AP.   (common difference and a = first term) Applying (since, two columns are similar)