Learn

Saturday, 31 October

JEE Main · Maths · Determinants

Evaluating Parameters for Consistency

JEE Main asked Evaluating Parameters for Consistency 15 times in 15 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2025. It belongs to Cramer's Rule, in Determinants (Maths). The longest wait between two years asking it was 1 year. In 2021, 2022, 2023, 2024 and 2025 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 15 shifts
Years
6 of 8
First asked
2020
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.20.40’170.08’200.07’210.14’220.21’230.09’240.38’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 2 in 24 shifts · 2022: 4 in 24 shifts · 2023: 3 in 12 shifts · 2024: 2 in 18 shifts · 2025: 3 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

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

  • 20260 of 9
  • 20253 of 8
  • 20242 of 18
  • 20233 of 12
  • 20224 of 24
  • 20212 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.

  • Parameters for infinitely many solutions
  • Parameter for consistent linear system

Difficulty

Easy 1Medium 13Hard 1

Every question was multiple choice.

Every question

All 15 questions

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

  1. 7 Apr 2025, Shift 2 · Q5Let the system of equations x+5y−z=1x+5y-z=1 4x+3y−3z=74x+3y-3z=7 24x+y+λz=μ24x+y+\lambda z=\mu λ,μ∈R\lambda,\mu\in\mathbf{R}, have infinitely many solutions. Then…HardSingle correct
  2. 7 Apr 2025, Shift 1 · Q4Let the system of equations : 2x+3y+5z=92x + 3y + 5z = 9, 7x+3y−2z=87x + 3y - 2z = 8, 12x+3y−(4+λ)z=16−μ12x + 3y - (4+\lambda)z = 16 - \mu, have infinitely many…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q4If the system of equations 2x+λy+3z=52x + \lambda y + 3z = 5 3x+2y−z=73x + 2y - z = 7 4x+5y+μz=94x + 5y + \mu z = 9 has infinitely many solutions, then…MediumSingle correct
  4. 30 Jan 2024, Shift 1 · Q3Consider the system of linear equations x+y+z=4μx+y+z=4\mu, x+2y+2λz=10μx+2y+2\lambda z=10\mu, x+3y+4λ2z=μ2+15x+3y+4\lambda^2z=\mu^2+15, where…MediumSingle correct
  5. 1 Feb 2024, Shift 2 · Q5Let the system of equations x+2y+3z=5x+2y+3z=5, 2x+3y+z=92x+3y+z=9, 4x+3y+λz=μ4x+3y+\lambda z=\mu have infinite number of solutions. Then λ+2μ\lambda+2\mu is…MediumSingle correct
  6. 13 Apr 2023, Shift 1 · Q4For the system of linear equations 2x+4y+2az=b2x+4y+2az=b x+2y+3z=4x+2y+3z=4 2x−5y+2z=82x-5y+2z=8 which of the following is NOT correct?MediumSingle correct
  7. 11 Apr 2023, Shift 2 · Q4If the system of linear equations 7x+11y+αz=137x + 11y + \alpha z = 13 5x+4y+7z=β5x + 4y + 7z = \beta 175x+194y+57z=361175x + 194y + 57z = 361 has infinitely many…MediumSingle correct
  8. 6 Apr 2023, Shift 2 · Q5For the system of equations x+y+z=6x+y+z=6 x+2y+αz=10x+2y+\alpha z=10 x+3y+5z=βx+3y+5z=\beta, which one of the following is NOT true?MediumSingle correct
  9. 29 Jun 2022, Shift 1 · Q7If the system of linear equations 2x+y−z=72x + y - z = 7 x−3y+2z=1x - 3y + 2z = 1 x+4y+δz=kx + 4y + \delta z = k, where δ,k∈R\delta, k \in \mathbf{R} has…EasySingle correct
  10. 26 Jun 2022, Shift 2 · Q2If the system of equations αx+y+z=5,x+2y+3z=4,x+3y+5z=β\alpha x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = \beta has infinitely many solutions, then the ordered…MediumSingle correct
  11. 25 Jun 2022, Shift 2 · Q4The system of equations −kx+3y−14z=25-kx + 3y - 14z = 25 −15x+4y−kz=3-15x + 4y - kz = 3 −4x+y+3z=4-4x + y + 3z = 4 is consistent for all kk in the setMediumSingle correct
  12. 30 Jul 2022, Shift 2 · Q63If the system of linear equations λx+y−z=−1\lambda x + y - z = -1 x−y−3z=2x - y - 3z = 2 −x+y+z=μ-x + y + z = \mu has infinitely many solutions, then the…MediumSingle correct
  13. 27 Aug 2021, Shift 2 · Q63Let [λ][\lambda] be the greatest integer less than or equal to λ\lambda. The set of all values of λ\lambda for which the system of linear…MediumSingle correct
  14. 3 Aug 2021, Shift 1 · Q64For the system of linear equations x+3y+2z=7x + 3y + 2z = 7 x+λy+3z=8x + \lambda y + 3z = 8 x−2y+7z=μx - 2y + 7z = \mu, which of the following statements is…MediumSingle correct
  15. 9 Jan 2020, Shift 1 · Q55If for some α\alpha and β\beta in R\mathbf{R}, the intersection of the following three planes x+4y−2z=1x+4y-2z=1 x+7y−5z=βx+7y-5z=\beta…MediumSingle correct

Shifts: 9 Jan 2020, Shift 1, 3 Aug 2021, Shift 1, 27 Aug 2021, Shift 2, 25 Jun 2022, Shift 2, 26 Jun 2022, Shift 2, 29 Jun 2022, Shift 1, 30 Jul 2022, Shift 2, 6 Apr 2023, Shift 2, 11 Apr 2023, Shift 2, 13 Apr 2023, Shift 1, 30 Jan 2024, Shift 1, 1 Feb 2024, Shift 2, 2 Apr 2025, Shift 2, 7 Apr 2025, Shift 2, 7 Apr 2025, 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