JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q63

MathematicsSingle correct+4 / -1Question 63 of 90

If the system of linear equations

$\lambda x+y-z=-1$
$x-y-3z=2$
$-x+y+z=\mu$

has infinitely many solutions, then the equation of the line passing through the points $(\lambda+2\mu,\ 2\lambda+\mu)$ and $(1,\ \lambda\mu)$ is

4x − 6y = −5

2x − 2y = 5

2x − 2y = −1

4x + 6y = 5

Answer and worked solution

Official answer: C

Singular. $\det=2\lambda+2=0$ gives $\lambda=-1$ . Then row 3 $=\frac12$ (row 1) $-\frac12$ (row 2) needs $\mu=-\frac12-1=-\frac32$ .

Points $\left(-4,-\frac72\right)$ and $\left(1,\frac32\right)$ : slope 1, line $2x-2y=-1$ .

(C)

Topics:Systems of linear equations Equations of a line

JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 63