JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 31 January 2024, Shift 1, Maths Q4

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

If the system of linear equations

x-2y+z=-4

2x+\alpha y+3z=5

3x-y+\beta z=3

has infinitely many solutions, then

12\alpha+13\beta

is equal to

(1) $54$
(2) $58$ Official answer
(3) $60$
(4) $64$

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 10× in all

2 Apr 2026, Shift 2 · Q3If the system of equations $x + 5y + 6z = 4,$ $2x + 3y + 4z = 7,$ $x + 6y + az = b$ has infinitely many solutions, then the point $(a, b)$ …MediumSingle correct
4 Apr 2026, Shift 2 · Q3If the system of equations: $x+y+z=5$ $x+2y+3z=9$ $x+3y+\lambda z=\mu$ has infinitely many solutions, then the value of $\lambda+\mu$ is:EasySingle correct
8 Apr 2026, Shift 2 · Q3If the system of linear equations : $x + y + z = 6$ , $x + 2y + 5z = 10$ , $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then…EasySingle correct
2 Apr 2025, Shift 1 · Q20If the system of linear equations $3x+y+\beta z=3$ $2x+\alpha y-z=-3$ $x+2y+z=4$ has infinitely many solutions, then the value of…MediumSingle correct
6 Apr 2024, Shift 2 · Q22If the system of equations $2x+7y+\lambda z=3$ $3x+2y+5z=4$ $x+\mu y+32z=-1$ has infinitely many solutions, then $(\lambda-\mu)$ is equal…MediumNumerical value
9 Apr 2024, Shift 1 · Q3Let $\lambda,\mu\in\mathbf{R}$ . If the system of equations $3x+5y+\lambda z=3$ $7x+11y-9z=2$ $97x+155y-189z=\mu$ has infinitely many…MediumSingle correct
30 Jan 2024, Shift 2 · Q4Consider the system of linear equations $x + y + z = 5$ , $x + 2y + \lambda^2 z = 9$ , $x + 3y + \lambda z = \mu$ , where…MediumSingle correct
6 Apr 2023, Shift 1 · Q4If the system of equations $x+y+az=b$ $2x+5y+2z=6$ $x+2y+3z=3$ has infinitely many solutions, then $2a+3b$ is equal toMediumSingle 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.