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JEE Main 29-Jan-2024 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 29-Jan-2024 Paper - Shift 14 Marks
MCQ
Let $A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]$ and $|2 A|^3=2^{21}$ where $\alpha, \beta \in Z,$ Then a value of $\alpha$ is
  • A
    3
  • B
    5
  • C
    17
  • D
    9
✓

Answer

$|A|=\alpha^2-\beta^2$
$|2 A|^3=2^{21}$
$ \Rightarrow|A|=2^4$
$\alpha^2-\beta^2=16$
$(\alpha+\beta)(\alpha-\beta)=16 $
$\Rightarrow \alpha=4 $ or  $5$

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