JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q4

Question 4 of 75 in this shift, Maths question 4 of 25, Section A.

Let the system of equations :

2x + 3y + 5z = 9

7x + 3y - 2z = 8

12x + 3y - (4+\lambda)z = 16 - \mu

, have infinitely many solutions. Then the radius of the circle centred at

(\lambda, \mu)

and touching the line

4x = 3y

(1) $7$
(2) $\frac{21}{5}$
(3) $\frac{7}{5}$ Official answer
(4) $\frac{17}{5}$

Official answer

Option 3

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 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
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.