JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 7 April 2025, Shift 2, Maths Q5

Question 5 of 75 in this shift, Maths question 5 of 25, Section A.

Let 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 the number of the solutions of this system, if

x,y,z

are integers and satisfy

7\le x+y+z\le 77

, is :

(1)3Official answer
(2)4
(3)5
(4)6

Official answer

Option 1

NTA final key.

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
29 Jun 2022, Shift 1 · Q7If 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…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 42 of the 174 JEE Main shifts held from 2017 to 2026.