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JCECE Engineering JCECE Engineering Solved Paper-2006

  • question_answer
    \[l,\,\,\,m,\,\,\,n\] are the \[p\text{th}\], \[q\text{th}\] and \[r\text{th}\] terms of a \[GP\] 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 :

    Let the first term and common ratio of a \[GP\] be \[A\] and R\[R\] respectively.   \[l=A{{R}^{p-1}}\Rightarrow \log l=A+(p-1)\log R\] \[m=A{{R}^{q-1}}\Rightarrow \log m=\log A+(q-1)\log R\]  \[n=A{{R}^{r-1}}\Rightarrow \log n=A+(r-1)\log R\] Now, \[\left| \begin{matrix}    \log l & p & 1  \\    \log m & q & 1  \\    \log n & r & 1  \\ \end{matrix} \right|\]                 \[=\left| \begin{matrix}    \log A+(p-1) & \log R & p\,\,\,1  \\    \log A+(q-1) & \log R & q\,\,\,1  \\    \log A+(r=1) & \log R & r\,\,\,1  \\ \end{matrix} \right|=0\]


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