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Questions  >>  CBSE XII  >>  Math  >>  Determinants
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Q)

Evaluate : $ \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$

$\begin{array}{1 1} 1 \\ -1 \\ \pm 1 \\ 0 \end{array}$

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A)
Toolbox:
  • If $A= \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$
  • Then $|A|=a_{11} \times a_{22}- a_{12} \times a_{21}$
  • $log _b a \times log_ab=1$
Step 1:
Let $\Delta= \begin{vmatrix} 1 & log_ba \\ log_ab & 1 \end{vmatrix}$
on expanding we get
$\Delta= 1\times 1 -log _b ^a \times log_a^b$
But $log _b a \times log_ab=1$
Therefore $\Delta=1-1=0$
Solution:option D is correct

 

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