jee-main 2021 Q70

jee-main · India · session1_25feb_shift2 Simultaneous equations
The following system of linear equations $2 x + 3 y + 2 z = 9$ $3 x + 2 y + 2 z = 9$ $x - y + 4 z = 8$
(1) has infinitely many solutions
(2) has a unique solution
(3) has a solution ( $\alpha , \beta , \gamma$ ) satisfying $\alpha + \beta ^ { 2 } + \gamma ^ { 3 } = 12$
(4) does not have any solution
The following system of linear equations\\
$2 x + 3 y + 2 z = 9$\\
$3 x + 2 y + 2 z = 9$\\
$x - y + 4 z = 8$\\
(1) has infinitely many solutions\\
(2) has a unique solution\\
(3) has a solution ( $\alpha , \beta , \gamma$ ) satisfying $\alpha + \beta ^ { 2 } + \gamma ^ { 3 } = 12$\\
(4) does not have any solution