If l,m,n\; are\; the\; p^{th},q^{th}and\; r^{th}\; term\; of\; a\; GP,all

positive, then   equals

  • Option 1)

    –1

  • Option 2)

         2

  • Option 3)

    1

  • Option 4)

    0

 

Answers (2)

As we learnt in 

Property of determinant -

If each element in a row ( or column ) of a determinant is written as the sum of two or more terms then the determinant can be written as the sum of two or more determinants

- wherein

 

 Given that 

l= a\times R^{p-1}

m= a\times R^{q-1}

n= a\times R^{r-1}

\therefore \log l= \log a +(p-1) \log R

\log m= \log a +(q-1) \log R

\log n= \log a +(r-1) \log R

so that \begin{vmatrix} \log a & p &1 \\ \log a& q & 1\\ \log a & r & 1 \end{vmatrix} + \log R \begin{vmatrix} p-1 &p &1 \\ q-1&q &1 \\ r-1&r &1 \end{vmatrix}

\log a\begin{vmatrix} \1 & p &1 \\ \1& q & 1\\ \1 & r & 1 \end{vmatrix} + \log a \begin{vmatrix} p-1 &p-1 &1 \\ q-1&q-1 &1 \\ r-1&r-1 &1 \end{vmatrix}

0+0 = 0


Option 1)

–1

Incorrect option

Option 2)

     2

Incorrect option

Option 3)

1

Incorrect option

Option 4)

0

Correct option

N neha

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