JEE Main 2021 (Online) 25th February Evening ShiftQuestion 1
The following system of linear equations
$2x+3y+2z=9$
$3x+2y+2z=9$
$x-y+4z=8$
Determinant
Solution
$\Delta=\begin{vmatrix}2&3&2\\3&2&2\\1&-1&4\end{vmatrix}=-20\neq0$, so a unique solution exists: $(x,y,z)=(1,1,2)$. Then $\alpha+\beta^2+\gamma^3=1+1+8=10\ne12$, so (D) is false. Option (B).