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CBSE Class 12 Math 2013 Solved Paper

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Question : 4 of 29
Marks: +1, -0
If ∣x+1x−1x−3x+2∣\begin{vmatrix} x+1 & x-1 \\ x-3 & x+2 \end{vmatrix} = ∣4−113∣\begin{vmatrix} 4 & -1 \\ 1 & 3 \end{vmatrix}, then write the value of x.
Solution:  
∣x+1x−1x−3x+2∣\begin{vmatrix} x+1 & x-1 \\ x-3 & x+2 \end{vmatrix} = ∣4−113∣\begin{vmatrix} 4 & -1 \\ 1 & 3 \end{vmatrix}
⇒ (x + 1) (x + 2) - (x - 1) (x - 3) = 12 + 1
⇒ x2x^2 + 3x + 2 - x2x^2 + 4x - 3 = 13
⇒ 7x - 1 = 13
⇒ 7x = 14
⇒ x = 2
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