JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 29 June 2022, Shift 1, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

If the system of linear equations

2x + y - z = 7

x - 3y + 2z = 1

x + 4y + \delta z = k

, where

\delta, k \in \mathbf{R}

has infinitely many solutions, then

\delta + k

is equal to :

(1) $-3$
(2)3Official answer
(3)6
(4)9

Official answer

Option 2

NTA final key (2022 Session 1).

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Evaluating Parameters for Consistency

Same idea in other shifts

Asked 4× in all

2 Apr 2025, Shift 2 · Q4If the system of equations $2x + \lambda y + 3z = 5$ $3x + 2y - z = 7$ $4x + 5y + \mu z = 9$ has infinitely many solutions, then…MediumSingle correct
7 Apr 2025, Shift 1 · Q4Let the system of equations : $2x + 3y + 5z = 9$ , $7x + 3y - 2z = 8$ , $12x + 3y - (4+\lambda)z = 16 - \mu$ , have infinitely many…MediumSingle correct
7 Apr 2025, Shift 2 · Q5Let the system of equations $x+5y-z=1$ $4x+3y-3z=7$ $24x+y+\lambda z=\mu$ $\lambda,\mu\in\mathbf{R}$ , have infinitely many solutions. Then…HardSingle 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 42 of the 174 JEE Main shifts held from 2017 to 2026.