JEE Main 2022 · 25 Jul · Shift 2 · Mathematics Q2

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MathematicsSingle correct+4 / -1Question 2 of 90

The number of real values of $\lambda$ , such that the system of linear equations
$2x-3y+5z=9$
$x+3y-z=-18$
$3x-y+\left(\lambda^2-|\lambda|\right)z=16$
has no solutions, is

Answer and worked solution

Official answer: C

Determinant. With $k=\lambda^2-|\lambda|$ : $\Delta=9k-43$ , zero when $\lambda^2-|\lambda|=\frac{43}9$ , which gives $|\lambda|=\frac{1+\sqrt{181/9}}2$ , two real values of $\lambda$ . At these the equations are inconsistent.

(C)

Topics:Systems of linear equations Inequalities and modulus

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JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 2