JEE Main 2024 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 30 January 2024, Shift 2, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Consider the system of linear equations

x + y + z = 5

x + 2y + \lambda^2 z = 9

x + 3y + \lambda z = \mu

, where

\lambda, \mu \in \mathbb{R}

. Then, which of the following statement is NOT correct?

(1)System is consistent if $\lambda \neq 1$ and $\mu = 13$
(2)System is inconsistent if $\lambda = 1$ and $\mu \neq 13$
(3)System has unique solution if $\lambda \neq 1$ and $\mu \neq 13$ Official answer
(4)System has infinite number of solutions if $\lambda = 1$ and $\mu = 13$

Official answer

Option 3

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Condition for Infinite Solutions

Same idea in other shifts

Asked 10× in all

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.