JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left(\begin{array}{ccc}{[x+1]} & {[x+2]} & {[x+3]} \\ {[x]} & {[x+3]} & {[x+3]} \\ {[x]} & {[x+2]} & {[x+4]}\end{array}\right),\) where \([t]\) denotes the greatest integer less than or equal to \(\mathrm{t}\). If \(\operatorname{det}(\mathrm{A})=192\), then the set of values of \(\mathrm{x}\) is the interval
- A \([68,69)\)
- B \([62,63)\)
- C \([65,66)\)
- D \([60,61)\)
Answer & Solution
Correct Answer
(B) \([62,63)\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}{[x+1]} & {[x+2]} & {[x+3]} \\ {[x]} & {[x+3]} & {[x+3]} \\ {[x]} & {[x+2]} & {[x+4]}\end{array}\right|=192\) \(\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}-\mathrm{R}_{3} \;and\; \mathrm{R}_{2} \rightarrow \mathrm{R}_{2}-\mathrm{R}_{3}\)…
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