Question

If \( [x] \) denotes the greatest integer less than or equal to \( x \), and \( -1 < x < 0 < y < 1 < z < 2 \), then the value of the determinant

\( \begin{vmatrix} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{vmatrix} \)
is

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

Hint:

Always evaluate floor values before determinant expansion.

Answer 1

The Correct Option is A

Step 1: Given ranges: [x]=-1, [y]=0, [z]=1
Step 2: Substituting: beginvmatrix 0 & 0 & 1
-1 & 1 & 1
-1 & 0 & 2 endvmatrix=1