jee-advanced 2015 Q50

jee-advanced · India · paper1 Matrices Determinant and Rank Computation

Which of the following values of $\alpha$ satisfy the equation $$\left| \begin{array} { c c c } ( 1 + \alpha ) ^ { 2 } & ( 1 + 2 \alpha ) ^ { 2 } & ( 1 + 3 \alpha ) ^ { 2 } \\ ( 2 + \alpha ) ^ { 2 } & ( 2 + 2 \alpha ) ^ { 2 } & ( 2 + 3 \alpha ) ^ { 2 } \\ ( 3 + \alpha ) ^ { 2 } & ( 3 + 2 \alpha ) ^ { 2 } & ( 3 + 3 \alpha ) ^ { 2 } \end{array} \right| = - 648 \alpha$$?
(A) $-4$
(B) $9$
(C) $-9$
(D) $4$

Which of the following values of $\alpha$ satisfy the equation
$$\left| \begin{array} { c c c } ( 1 + \alpha ) ^ { 2 } & ( 1 + 2 \alpha ) ^ { 2 } & ( 1 + 3 \alpha ) ^ { 2 } \\ ( 2 + \alpha ) ^ { 2 } & ( 2 + 2 \alpha ) ^ { 2 } & ( 2 + 3 \alpha ) ^ { 2 } \\ ( 3 + \alpha ) ^ { 2 } & ( 3 + 2 \alpha ) ^ { 2 } & ( 3 + 3 \alpha ) ^ { 2 } \end{array} \right| = - 648 \alpha$$?\\
(A) $-4$\\
(B) $9$\\
(C) $-9$\\
(D) $4$

Paper Questions

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