Q62 / 125 · BITSAT 2012 · Mathematics

The value of the determinant $\left|\begin{array}{lll}265 & 240 & 219 \\ 240 & 225 & 198 \\ 219 & 198 & 181\end{array}\right|$ is

  • A
    1000
  • B
    779
  • C
    679
  • Correct answer
    D
    0

Solution

Applying $\mathrm{C}_{1}-\mathrm{C}_{2}$ and $\mathrm{C}_{2}-\mathrm{C}_{3},$ we get $\begin{aligned} \text { Det. } &=\left|\begin{array}{ccc} 25 & 21 & 219 \\ 15 & 27 & 198 \\ 21 & 17 & 181 \end{array}\right|=\left|\begin{array}{ccc} 4 & 21 & 9 \\ -12 & 27 & -72 \\ 4 & 17 & 11 \end{array}\right| \\ =&\left[\begin{array}{llc} 4 & 21 & 9 \\ 0 & 90 & -45 \\ 0 & -4 & 2 \end{array} \mid\left[\mathrm{By} \mathrm{R}_{2}+3 \mathrm{R}_{1}, \mathrm{R}_{3}-\mathrm{R}_{1}\right]\right.\\ =4(180-180)=0 \end{aligned}$

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

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