Q205 / 270 · NDA 2021 (Phase 1) · Mathematics
With the numbers $2,4,6,8$, all the possible determinants with these four different elements are constructed. What is the sum of the values of all such determinants?
- A$128$
- B$64$
- C$32$
- Correct answerD$0$
Solution
All possible determinants from $2,4,6$ and 8
$\left|\begin{array}{ll}8 & 6 \\ 4 & 2\end{array}\right|+\left|\begin{array}{ll}8 & 4 \\ 2 & 6\end{array}\right|+\left|\begin{array}{ll}2 & 4 \\ 8 & 6\end{array}\right|+\left|\begin{array}{ll}4 & 2 \\ 6 & 8\end{array}\right|+\left|\begin{array}{ll}4 & 8 \\ 6 & 2\end{array}\right|+\left|\begin{array}{ll}6 & 8 \\ 2 & 4\end{array}\right|$
$\begin{aligned} &=(16-24)+(48-8)+(12-32)+(32-12) \\ &+(8-48)+(24-16) \\ &=0\end{aligned}$
Hence, the correct answer is option: 'D'.