Q113 / 155 · WBJEE 2021 · Mathematics

$\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 7 x-2 & 17 x+6 & 12 x-1\end{array}\right|=0$ is true for

  • A
    only one value of $x$
  • B
    only two values of $x$
  • C
    only three values of $x$
  • Correct answer
    D
    infinitely many values of $x$

Solution

$\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 7 x-2 & 17 x+6 & 12 x-1\end{array}\right|=0$ $\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-3 \mathrm{R}_{1}-2 \mathrm{R}_{2}$ $\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 0 & 0 & 0\end{array}\right|=0$ Infinite values of $x$ is possible.

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

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