JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q7

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MathematicsSingle correct+4 / -1Question 7 of 90

If the system of linear equations
$2x+y-z=7$
$x-3y+2z=1$
$x+4y+\delta z=k,\ \text{where }\delta,k\in\mathbf R$
has infinitely many solutions, then $\delta+k$ is equal to :

-3

Answer and worked solution

Official answer: B

Determinant. $-7\delta-21=0$ , $\delta=-3$ .

Consistency. Row 3 $=$ row 1 $-$ row 2 (check: $2-1=1$ , $1+3=4$ , $-1-2=-3$ ), so $k=7-1=6$ .

$\delta+k=3$ .

(B)

Topics:Systems of linear equations

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JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 7