jee-main 2019 Q75

jee-main · India · session2_09apr_shift1 3x3 Matrices Determinant of Parametric or Structured Matrix

Let $\alpha$ and $\beta$ be the roots of the equation $x ^ { 2 } + x + 1 = 0$. Then for $y \neq 0$ in $R , \left| \begin{array} { c c c } y + 1 & \alpha & \beta \\ \alpha & y + \beta & 1 \\ \beta & 1 & y + \alpha \end{array} \right|$ is equal to
(1) $y ^ { 3 }$
(2) $y \left( y ^ { 2 } - 1 \right)$
(3) $y ^ { 3 } - 1$
(4) $y \left( y ^ { 2 } - 3 \right)$

Let $\alpha$ and $\beta$ be the roots of the equation $x ^ { 2 } + x + 1 = 0$. Then for $y \neq 0$ in $R , \left| \begin{array} { c c c } y + 1 & \alpha & \beta \\ \alpha & y + \beta & 1 \\ \beta & 1 & y + \alpha \end{array} \right|$ is equal to\\
(1) $y ^ { 3 }$\\
(2) $y \left( y ^ { 2 } - 1 \right)$\\
(3) $y ^ { 3 } - 1$\\
(4) $y \left( y ^ { 2 } - 3 \right)$

Paper Questions

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