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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2005

  • question_answer
        \[l,m,n\]are the\[{{p}^{th}},{{q}^{th}}\]and\[{{r}^{th}}\]term of an G.P. and all positive, then \[\left| \begin{matrix}    \log l & p & 1  \\    \log m & q & 1  \\    \log n & r & 1  \\ \end{matrix} \right|\]equals:

    A)  3                                            

    B)  2

    C)  1                                            

    D)  zero

    Correct Answer: D

    Solution :

                    \[l=A{{R}^{n-1}}\Rightarrow \log l=\log A+(p-1)\log R\] \[m=A{{R}^{n-1}}\Rightarrow \log m=\log A+(q-1)\log R\] \[n=A{{r}^{r-1}}\Rightarrow \log n=\log A+(r-1)\log R\] Now, \[\left| \begin{matrix}    \log l & p & 1  \\    \log m & q & 1  \\    \log  & r & 1  \\ \end{matrix} \right|=\left| \begin{matrix}    \log A+(p-1)\log R & p & 1  \\    \log A+(q-1)\log R & q & 1  \\    \log A+(r-1)\log R & r & 1  \\ \end{matrix} \right|=0\]


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