JEE Main Maths · Determinants

Condition for Infinite Solutions

Condition for Infinite Solutions (Determinants) was asked 10 times in 10 JEE Main shifts, 2023–2026, out of the 42 shifts Lumi analysed. 1 of the 10 had a numerical answer.

Times asked: 10; in 10 shifts
Years: 2023–2026
Usual format: Single correct; Calculation
Pattern: Comes in cycles; repeats across shifts

How it is asked

Parameters for infinitely many solutions
Identify incorrect statement on consistency of system

Difficulty

Easy 2Medium 8Hard 0

Where it sits

Chapter: Determinants. Topic: Cramer's Rule, 31 questions over 9 ideas.

All 10 questions

Newest first, each with its options and official answer.

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
31 Jan 2024, Shift 1 · Q4If the system of linear equations $x-2y+z=-4$ $2x+\alpha y+3z=5$ $3x-y+\beta z=3$ has infinitely many solutions, then $12\alpha+13\beta$ …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
13 Apr 2023, Shift 2 · Q4If the system of equations $2x+y-z=5$ $2x-5y+\lambda z=\mu$ $x+2y-5z=7$ has infinitely many solutions, then…MediumSingle correct