Q57 / 125 · BITSAT 2016 · Mathematics

If [ ] denotes the greatest integer less than or equal to the real number under consideration and $-1 \leq x<0 ; 0 \leq y<1 ; 1 \leq z<2,$ then the value of the determinant Figure
is

  • Correct answer
    A
    $[z]$
  • B
    $[y]$
  • C
    $[\mathrm{x}]$
  • D
    None of these

Solution

Since, $-1 \leq x<0$ $\begin{array}{ll}\therefore \quad & {[\mathrm{x}]=-1} \\ & 0 \leq \mathrm{y}<1 \quad \therefore[\mathrm{y}]=0 \\ & 1 \leq \mathrm{z}<2 \quad \therefore[\mathrm{z}]=1 \\ \therefore \quad & \text { Given determinant }=\left|\begin{array}{ccc}0 & 0 & 1 \\ -1 & 1 & 1 \\ -1 & 0 & 2\end{array}\right|=1=[\mathrm{z}]\end{array}$

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

Relevant Questions