JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q63

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MathematicsSingle correct+4 / -1Question 63 of 90

The system of linear equations

$3x-2y-kz=10$
$2x-4y-2z=6$
$x+2y-z=5m$

is inconsistent if :

(no option printed)

k=3,\ m=\dfrac45

k=3,\ m\ne\dfrac45

k\ne3,\ m\in\mathbf R

Answer and worked solution

Official answer: C

Singular. $\det=24-8k=0$ at $k=3$ .

Consistency. With $k=3$ , row 1 = row 2 + row 3 on the left, so the system is consistent only if $10=6+5m$ , i.e. $m=\frac45$ . Inconsistent for $k=3$ , $m\ne\frac45$ .

(C)

Topics:Systems of linear equations

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 63