JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q2

MathematicsSingle correct+4 / -1Question 2 of 90

Let the system of linear equations $x+2y+z=2$ , $\alpha x+3y-z=\alpha$ , $-\alpha x+y+2z=-\alpha$ be inconsistent. Then $\alpha$ is equal to :

\dfrac52

-\dfrac52

\dfrac72

-\dfrac72

Answer and worked solution

Official answer: D

Determinant. $\begin{vmatrix}1&2&1\\\alpha&3&-1\\-\alpha&1&2\end{vmatrix}=7-2\alpha+4\alpha=7+2\alpha$ .

Inconsistent needs it to vanish: $\alpha=-\dfrac72$ (and the system then has no solution).

(D)

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 2