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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Choose the correct answer from given four options in each of the Exercise : If $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix},$ then value of $x$ is:
  • A
    $3$
  • B
    $\pm3$
  • ✓
    $ \pm6$
  • D
    $6$
✓

Answer

Correct option: C.
$ \pm6$
We have, $\begin{vmatrix}2\text{x}&5\\8&\text{x}\end{vmatrix}=\begin{vmatrix}6&-2\\7&3\end{vmatrix}$
$\Rightarrow\ 2\text{x}^2-40=18+17$
$\Rightarrow\ 2\text{x}^2=32+40$
$\Rightarrow\ \text{x}^2=\frac{72}{2}=36$
$\Rightarrow\ \text{x}^2=36$
$\Rightarrow\ \text{x}=\pm6$

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