JEE Main Maths · Determinants

Parameter Evaluation in Homogeneous Systems

Parameter Evaluation in Homogeneous Systems (Determinants) was asked 5 times in 5 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 1 of the 5 had a numerical answer.

Times asked: 5; in 5 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Parameter values for non-trivial homogeneous solution
Parameters for infinitely many solutions

Difficulty

Easy 0Medium 4Hard 1

Where it sits

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

All 5 questions

Newest first, each with its options and official answer.

5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in $x, y, z$ : $x + 2y + tz = 0$ , $6x + y + 5tz = 0$ , $3x + t^2y + f(t)\,z = 0$ , where…MediumSingle correct
8 Apr 2023, Shift 2 · Q3Let S be the set of all values of $\theta \in [-\pi, \pi]$ for which the system of linear equations $x + y + \sqrt{3}z = 0$ …MediumSingle correct
3 Aug 2021, Shift 2 · Q65For the system of linear equations $(k-3)x + y + z = 0$ $x + (k-3)y + z = 0$ $x + y + (k-3)z = 0$ the number of distinct values of $k$ ,…MediumSingle correct
18 Mar 2021, Shift 1 · Q64Let $\alpha,\beta,\gamma$ be the real roots of the equation, $x^3+ax^2+bx+c=0$ , ( $a,b,c\in\mathbf{R}$ and $a,b\ne0$ ). If the system of…HardSingle correct
6 Sep 2020, Shift 2 · Q71The sum of distinct values of $\lambda$ for which the system of equations $(\lambda-1)x+(3\lambda+1)y+2\lambda z=0$ …MediumNumerical value