Question

If [.] denotes the greatest integer less than or equal to the real number under consideration, and –1 ≤ x < 0; 0 ≤ y < 1; 1 ≤ z < 2, then the value of determinant $\left| \begin{matrix} \lbrack x\rbrack + 1 & \lbrack y\rbrack & \lbrack z\rbrack \\ \lbrack x\rbrack & \lbrack y\rbrack + 1 & \lbrack z\rbrack \\ \lbrack x\rbrack & \lbrack y\rbrack & \lbrack z\rbrack + 1 \end{matrix} \right|$ is

• A. [x]
• B. [y]
• C. [z]
• D. None of these

Answer 1

Answer: (C)

$z$

Answer 2

[x] = –1, [y] = 0, [z] = 1 ∴$\left| \begin{matrix} 0 & 0 & 1 \

• 1 & 1 & 1 \
• 1 & 0 & 2 \end{matrix} \right|$ = 1 = [z]