JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 15 April 2023, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

Let the system of linear equations

-x+2y-9z=7

-x+3y+7z=9

-2x+y+5z=8

-3x+y+13z=\lambda

has a unique solution

x=\alpha, y=\beta, z=\gamma

. Then the distance of the point

(\alpha,\beta,\gamma)

from the plane

2x-2y+z=\lambda

(1) $7$ Official answer
(2) $9$
(3) $11$
(4) $13$

Official answer

Option 1

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Consistency of Overdetermined Systems (3 eq, 2 var)

Same topic in other shifts

All Cramer's Rule questions

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2 Apr 2026, Shift 2 · Q3If the system of equations $x + 5y + 6z = 4,$ $2x + 3y + 4z = 7,$ $x + 6y + az = b$ has infinitely many solutions, then the point $(a, b)$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q3If the system of equations: $x+y+z=5$ $x+2y+3z=9$ $x+3y+\lambda z=\mu$ has infinitely many solutions, then the value of $\lambda+\mu$ is:EasySingle correct
5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in $x, y, z$ : $x + 2y + tz = 0$ , $6x + y + 5tz = 0$ , $3x + t^2y + f(t)\,z = 0$ , where…MediumSingle correct
6 Apr 2026, Shift 2 · Q4The sum of all possible values of $\theta\in[0,2\pi]$ , for which the system of equations : $x\cos 3\theta-8y-12z=0$ …MediumSingle correct
8 Apr 2026, Shift 2 · Q3If the system of linear equations : $x + y + z = 6$ , $x + 2y + 5z = 10$ , $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then…EasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.