jee-main 2023 Q74

jee-main · India · session1_25jan_shift1 Matrices Determinant and Rank Computation

Let $x , y , z > 1$ and $A = \left[ \begin{array} { l l l } 1 & \log _ { x } y & \log _ { x } z \\ \log _ { y } x & 2 & \log _ { y } z \\ \log _ { z } x & \log _ { z } y & 3 \end{array} \right]$. Then $\left| \operatorname { adj } \left( \operatorname { adj } \mathrm { A } ^ { 2 } \right) \right|$ is equal to
(1) $6 ^ { 4 }$
(2) $2 ^ { 8 }$
(3) $4 ^ { 8 }$
(4) $2 ^ { 4 }$

Let $x , y , z > 1$ and $A = \left[ \begin{array} { l l l } 1 & \log _ { x } y & \log _ { x } z \\ \log _ { y } x & 2 & \log _ { y } z \\ \log _ { z } x & \log _ { z } y & 3 \end{array} \right]$. Then $\left| \operatorname { adj } \left( \operatorname { adj } \mathrm { A } ^ { 2 } \right) \right|$ is equal to\\
(1) $6 ^ { 4 }$\\
(2) $2 ^ { 8 }$\\
(3) $4 ^ { 8 }$\\
(4) $2 ^ { 4 }$

Paper Questions

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