Q165 / 270 · NDA 2023 (Phase 2) · Mathematics

If $\left|\begin{array}{ccc}x^2-3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}\right|=a x^4+b x^3+c x^2+d x+e$, then what is the value of $e$ ?

  • A
    -1
  • Correct answer
    B
    0
  • C
    1
  • D
    2

Solution

If we put $x=0$ $\left|\begin{array}{ccr} 0 & -1 & 3 \\ 1 & 0 & -4 \\ -3 & 4 & 0 \end{array}\right|=0+0+0+0+\mathrm{e}$ it is skew-symmetric of order $3 \times 3$ $\Rightarrow \text { So, } \quad \mathrm{e}=0$

Hence, the correct answer is option: 'B'.

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