Q60 / 160 · TS EAMCET 2004 · Mathematics

The value of $\left|\begin{array}{lll}1990 & 1991 & 1992 \\ 1991 & 1992 & 1993 \\ 1992 & 1993 & 1994\end{array}\right|$ is

  • A
    $1992$
  • B
    $1993$
  • C
    $1994$
  • Correct answer
    D
    $0$

Solution

Let $A=\left|\begin{array}{lll}1990 & 1991 & 1992 \\ 1991 & 1992 & 1993 \\ 1992 & 1993 & 1994\end{array}\right|$ Applying $\begin{aligned} C_2 & \rightarrow C_2-C_1, C_3 \rightarrow C_3-C_2 \\ & =\left|\begin{array}{ccc}1990 & 1 & 1 \\ 1991 & 1 & 1 \\ 1992 & 1 & 1\end{array}\right| \\ & =0[\because \text { two columns are identical }]\end{aligned}$

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

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