Question

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 $\left| \begin{matrix} 5 & 4 & 3 \\ x51 & y41 & z31 \\ x & y & z \end{matrix} \right|$ is

• A. x + y + z
• B. 0
• C. x – y + z
• D. x – y – z

Answer 1

Answer: (B)

0

Answer 2

$\left| \begin{matrix} 5 & 4 & 3 \\ 100x + 51 & 100y + 41 & 100z + 31 \\ x & y & z \end{matrix} \right|$R₂ → R₂ – 100 × R₃

= $\left| \begin{matrix} 5 & 4 & 3 \\ 51 & 41 & 31 \\ x & y & z \end{matrix} \right|$= 0