jee-main 2024 Q71

jee-main · India · session2_06apr_shift1 3x3 Matrices Direct Determinant Computation

For $\alpha , \beta \in \mathbb { R }$ and a natural number $n$, let $A _ { r } = \left| \begin{array} { c c c } r & 1 & \frac { n ^ { 2 } } { 2 } + \alpha \\ 2 r & 2 & n ^ { 2 } - \beta \\ 3 r - 2 & 3 & \frac { n ( 3 n - 1 ) } { 2 } \end{array} \right|$. Then $\sum_{r=1}^{n} A_r$ is
(1) 0
(2) $4 \alpha + 2 \beta$
(3) $2 \alpha + 4 \beta$
(4) $2 n$

For $\alpha , \beta \in \mathbb { R }$ and a natural number $n$, let $A _ { r } = \left| \begin{array} { c c c } r & 1 & \frac { n ^ { 2 } } { 2 } + \alpha \\ 2 r & 2 & n ^ { 2 } - \beta \\ 3 r - 2 & 3 & \frac { n ( 3 n - 1 ) } { 2 } \end{array} \right|$. Then $\sum_{r=1}^{n} A_r$ is\\
(1) 0\\
(2) $4 \alpha + 2 \beta$\\
(3) $2 \alpha + 4 \beta$\\
(4) $2 n$

Paper Questions

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