JEE Main 2023 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 6 April 2023, Shift 2, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

For the system of equations

x+y+z=6

x+2y+\alpha z=10

x+3y+5z=\beta

, which one of the following is NOT true?

(1)System has a unique solution for $\alpha=-3,\beta=14$ .
(2)System has no solution for $\alpha=3,\beta=24$ .
(3)System has infinitely many solutions for $\alpha=3,\beta=14$ .
(4)System has a unique solution for $\alpha=3,\beta\neq14$ .Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 15× 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
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
1 Feb 2024, Shift 2 · Q5Let the system of equations $x+2y+3z=5$ , $2x+3y+z=9$ , $4x+3y+\lambda z=\mu$ have infinite number of solutions. Then $\lambda+2\mu$ is…MediumSingle correct
30 Jan 2024, Shift 1 · Q3Consider 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…MediumSingle correct
11 Apr 2023, Shift 2 · Q4If the system of linear equations $7x + 11y + \alpha z = 13$ $5x + 4y + 7z = \beta$ $175x + 194y + 57z = 361$ has infinitely many…MediumSingle correct
13 Apr 2023, Shift 1 · Q4For the system of linear equations $2x+4y+2az=b$ $x+2y+3z=4$ $2x-5y+2z=8$ which of the following is NOT correct?MediumSingle correct
30 Jul 2022, Shift 2 · Q63If the system of linear equations $\lambda x + y - z = -1$ $x - y - 3z = 2$ $-x + y + z = \mu$ has infinitely many solutions, then the…MediumSingle 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 108 of the 174 JEE Main shifts held from 2017 to 2026.