JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 30 January 2024, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Consider the system of linear equations

x+y+z=4\mu

x+2y+2\lambda z=10\mu

x+3y+4\lambda^2z=\mu^2+15

, where

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

. Which one of the following statements is NOT correct ?

(1)The system is consistent if $\lambda\neq\frac{1}{2}$
(2)The system is inconsistent if $\lambda=\frac{1}{2}$ and $\mu\neq1$ Official answer
(3)The system has unique solution if $\lambda\neq\frac{1}{2}$ and $\mu\neq1,15$
(4)The system has infinite number of solutions if $\lambda=\frac{1}{2}$ and $\mu=15$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 15× 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 108 of the 174 JEE Main shifts held from 2017 to 2026.