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Saturday, 31 October

JEE Main · Maths · Determinants

Parameter Evaluation in Homogeneous Systems

JEE Main asked Parameter Evaluation in Homogeneous Systems 9 times in 9 of the 108 shifts Lumi analysed, in 2020, 2021, 2023, 2024 and 2026. It belongs to Cramer's Rule, in Determinants (Maths). The longest wait between two years asking it was 2 years. In 2021 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
9
in 9 shifts
Years
5 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2023, 2024 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170.08’200.14’210’220.07’230.09’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 4 in 24 shifts · 2022: 0 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20261 of 9
  • 20250 of 8
  • 20242 of 18
  • 20231 of 12
  • 20220 of 24
  • 20214 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

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

Difficulty

Easy 1Medium 7Hard 1

2 of the 9 questions had a numerical answer.

Every question

All 9 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in x,y,zx, y, z: x+2y+tz=0x + 2y + tz = 0, 6x+y+5tz=06x + y + 5tz = 0, 3x+t2y+f(t) z=03x + t^2y + f(t)\,z = 0, where…MediumSingle correct
  2. 6 Apr 2024, Shift 1 · Q22Let αβγ=45\alpha\beta\gamma=45; α,β,γ∈R\alpha, \beta, \gamma \in \mathbb{R}. If x(α,1,2)+y(1,β,2)+z(2,3,γ)=(0,0,0)x(\alpha,1,2)+y(1,\beta,2)+z(2,3,\gamma)=(0,0,0) for some…MediumNumerical value
  3. 4 Apr 2024, Shift 1 · Q4If the system of equations x+(2sin⁡α)y+(2cos⁡α)z=0x+(\sqrt{2}\sin\alpha)y+(\sqrt{2}\cos\alpha)z=0 x+(cos⁡α)y+(sin⁡α)z=0x+(\cos\alpha)y+(\sin\alpha)z=0…MediumSingle correct
  4. 8 Apr 2023, Shift 2 · Q3Let S be the set of all values of θ∈[−π,π]\theta \in [-\pi, \pi] for which the system of linear equations x+y+3z=0x + y + \sqrt{3}z = 0…MediumSingle correct
  5. 18 Mar 2021, Shift 2 · Q75Let the system of linear equations 4x+λy+2z=04x+\lambda y+2z=0 2x−y+z=02x-y+z=0 μx+2y+3z=0\mu x+2y+3z=0, λ,μ∈R\lambda, \mu\in\mathbb{R}. has a non-trivial…EasySingle correct
  6. 18 Mar 2021, Shift 1 · Q64Let α,β,γ\alpha,\beta,\gamma be the real roots of the equation, x3+ax2+bx+c=0x^3+ax^2+bx+c=0, (a,b,c∈Ra,b,c\in\mathbf{R} and a,b≠0a,b\ne0). If the system of…HardSingle correct
  7. 26 Aug 2021, Shift 1 · Q64Let θ∈(0,π2)\theta \in \left(0, \frac{\pi}{2}\right). If the system of linear equations.…MediumSingle correct
  8. 3 Aug 2021, Shift 2 · Q65For the system of linear equations (k−3)x+y+z=0(k-3)x + y + z = 0 x+(k−3)y+z=0x + (k-3)y + z = 0 x+y+(k−3)z=0x + y + (k-3)z = 0 the number of distinct values of kk,…MediumSingle correct
  9. 6 Sep 2020, Shift 2 · Q71The sum of distinct values of λ\lambda for which the system of equations (λ−1)x+(3λ+1)y+2λz=0(\lambda-1)x+(3\lambda+1)y+2\lambda z=0…MediumNumerical value

Shifts: 6 Sep 2020, Shift 2, 18 Mar 2021, Shift 2, 18 Mar 2021, Shift 1, 3 Aug 2021, Shift 2, 26 Aug 2021, Shift 1, 8 Apr 2023, Shift 2, 4 Apr 2024, Shift 1, 6 Apr 2024, Shift 1, 5 Apr 2026, Shift 1.

Same topic

Other ideas in Cramer's Rule

Cramer's Rule has 19 ideas JEE Main has asked; 6 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas