JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q3

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MathematicsSingle correct+4 / -1Question 3 of 90

If the system of linear equations.
$8x+y+4z=-2$
$x+y+z=0$
$\lambda x-3y=\mu$
has infinitely many solutions, then the distance of the point $\left(\lambda,\mu,-\dfrac12\right)$ from the plane $8x+y+4z+2=0$ is :

3\sqrt5

\dfrac{26}9

\dfrac{10}3

Answer and worked solution

Official answer: D

Infinitely many solutions. Row 3 must be a combination of the first two with no $z$ : $\frac{1}{3}(\text{row 1})-\frac43(\text{row 2})$ gives $\frac43x-y=-\frac23$ , so $\lambda=4$ , $\mu=-2$ .

Distance of $\left(4,-2,-\frac12\right)$ : $\dfrac{|32-2-2+2|}9=\dfrac{10}3$ .

(D)

Topics:Systems of linear equations Angles and distances

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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 3