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Q.

If x, y, z are integers in A.P lying between 1 and 9 and x51, y41 and z31 are three-digit numbers, then the value of $|\begin{matrix} 5 & 4 & 3 \\ x 51 & y 41 & z 31 \\ x & y & z \end{matrix}|$

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a

$x + y + z$

b

$x - y + z$

c

0

d

$x + 2 y + z$

answer is C.

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Detailed Solution

$R_{2} \to R_{2} - 100 R_{3} - 10 R_{1}$

Question Image

$|\begin{matrix} 5 & 4 & 3 \\ 1 & 1 & 1 \\ x & y & z \end{matrix}|$

and $C_{1} \to C_{1} + C_{3} - 2 C_{2}$
$|\begin{matrix} 0 & 4 & 3 \\ 0 & 1 & 1 \\ 0 & y & z \end{matrix}|$ =0

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If x, y, z are integers in A.P lying between 1 and 9 and x51, y41 and z31 are three-digit numbers, then the value of 543x51y41z31xyz