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JEE Advanced 2010Paper 2
Exam
JEE Advanced
Year
2010
Paper
Paper 2
Subject
Mathematics
Chapter
Determinants

JEE Advanced 2010 · Paper 2 · Mathematics · Determinants

Let k be a positive real number and let aligned A & =[ array ccc 2...

Let kbeapositiverealnumberandletk be a positive real number and letA=[2k−12k2k2k1−2k−2k2k−1] and B=[02k−1k1−2k02k−k−2k0]\begin{aligned} A & =\left[\begin{array}{ccc}2 k-1 & 2 \sqrt{k} & 2 \sqrt{k} \\ 2 \sqrt{k} & 1 & -2 k \\ -2 \sqrt{k} & 2 k & -1\end{array}\right] \text{ and } \\ B & =\left[\begin{array}{ccc}0 & 2 k-1 & \sqrt{k} \\ 1-2 k & 0 & 2 \sqrt{k} \\ -\sqrt{k} & -2 \sqrt{k} & 0\end{array}\right]\end{aligned}IfIf\operatorname{det}(\operatorname{adj} A)+\operatorname{det}(\operatorname{adj} B)=10^6,then, then[k]isequalto[Note:adjis equal to [Note : adjMdenotestheadjointofasquarematrixdenotes the adjoint of a square matrixM and [k]denotesthelargestintegerlessthanorequaltodenotes the largest integer less than or equal tok ].

Correct answer

0

Step-by-step solution

|A|=(2 k+1)^3,|B|=0ButBut\operatorname{det}(\operatorname{adj} A)=\operatorname{det}(\operatorname{adj} B)=10^6 ⇒(2k+1)6=106⇒k=92⇒[k]=4\begin{aligned}& \Rightarrow(2 k+1)^6=10^6 \\ & \Rightarrow k=\frac{9}{2} \Rightarrow[k]=4 \end{aligned}
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