If \( x\in N \)(Set of Natural Numbers) and \( \begin{vmatrix}x+3 & -2\\-3x & 2x\end{vmatrix}=8 \), then the value of \( x \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Expanding the 2 × 2 determinant,
\( \displaystyle 2x(x+3)-(-2)(-3x)=8 \)
\( \displaystyle 2x^2+6x-6x=8 \)
\( \displaystyle x^2=4 \)
\( \displaystyle x=\pm 2 \)
Since x must be a natural number, x = 2.
Why the other options are incorrect
Option (1) \( -2 \) — Incorrect. −2 satisfies the equation, but it is not a natural number.
Option (3) \( \pm 2 \) — Incorrect. Both roots satisfy the equation, but −2 is not a natural number.
Option (4) 1 — Incorrect. x = 1 gives \( x^2=1 \), not 4.