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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Determinants

BITSAT 2016 · Mathematics · Determinants

If [ ] denotes the greatest integer less than or equal to the real...

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

Options

  1. A[z][z]
  2. B[y][y]
  3. C[x][\mathrm{x}]
  4. DNone of these

Correct answer

A. [z][z]

Step-by-step solution

Since, −1≤x<0-1 \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}
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