Learn

Saturday, 31 October

JEE Main · Maths · Determinants

Condition for Infinite Solutions

JEE Main asked Condition for Infinite Solutions 25 times in 25 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to Cramer's Rule, in Determinants (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2022, 2023, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
25
in 25 shifts
Years
7 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, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.20.40’170.17’200.17’210.11’220.21’230.38’240.13’250.33’26

Raw count: 2017: 0 in 1 shift · 2020: 2 in 12 shifts · 2021: 5 in 24 shifts · 2022: 3 in 24 shifts · 2023: 3 in 12 shifts · 2024: 8 in 18 shifts · 2025: 1 in 8 shifts · 2026: 3 in 9 shifts.

Shift by shift

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

  • 20263 of 9
  • 20251 of 8
  • 20248 of 18
  • 20233 of 12
  • 20223 of 24
  • 20215 of 24
  • 20202 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: calculation.

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

Difficulty

Easy 5Medium 20Hard 0

5 of the 25 questions had a numerical answer.

Every question

All 25 questions

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

  1. 8 Apr 2026, Shift 2 · Q3If the system of linear equations : x+y+z=6x + y + z = 6, x+2y+5z=10x + 2y + 5z = 10, 2x+3y+λz=μ2x + 3y + \lambda z = \mu has infinitely many solutions, then…EasySingle correct
  2. 4 Apr 2026, Shift 2 · Q3If the system of equations: x+y+z=5x+y+z=5 x+2y+3z=9x+2y+3z=9 x+3y+λz=μx+3y+\lambda z=\mu has infinitely many solutions, then the value of λ+μ\lambda+\mu is:EasySingle correct
  3. 2 Apr 2026, Shift 2 · Q3If the system of equations x+5y+6z=4,x + 5y + 6z = 4, 2x+3y+4z=7,2x + 3y + 4z = 7, x+6y+az=bx + 6y + az = b has infinitely many solutions, then the point (a,b)(a, b)…MediumSingle correct
  4. 2 Apr 2025, Shift 1 · Q20If the system of linear equations 3x+y+βz=33x+y+\beta z=3 2x+αy−z=−32x+\alpha y-z=-3 x+2y+z=4x+2y+z=4 has infinitely many solutions, then the value of…MediumSingle correct
  5. 31 Jan 2024, Shift 1 · Q4If the system of linear equations x−2y+z=−4x-2y+z=-4 2x+αy+3z=52x+\alpha y+3z=5 3x−y+βz=33x-y+\beta z=3 has infinitely many solutions, then 12α+13β12\alpha+13\beta…MediumSingle correct
  6. 30 Jan 2024, Shift 2 · Q4Consider the system of linear equations x+y+z=5x + y + z = 5, x+2y+λ2z=9x + 2y + \lambda^2 z = 9, x+3y+λz=μx + 3y + \lambda z = \mu, where…MediumSingle correct
  7. 1 Feb 2024, Shift 1 · Q5If the system of equations 2x+3y−z=52x+3y-z=5 x+αy+3z=−4x+\alpha y+3z=-4 3x−y+βz=73x-y+\beta z=7 has infinitely many solutions, then 13αβ13\alpha\beta is equal to…MediumSingle correct
  8. 9 Apr 2024, Shift 1 · Q3Let λ,μ∈R\lambda,\mu\in\mathbf{R}. If the system of equations 3x+5y+λz=33x+5y+\lambda z=3 7x+11y−9z=27x+11y-9z=2 97x+155y−189z=μ97x+155y-189z=\mu has infinitely many…MediumSingle correct
  9. 8 Apr 2024, Shift 2 · Q3If the system of equations x+4y−z=λx + 4y - z = \lambda, 7x+9y+μz=−37x + 9y + \mu z = -3, 5x+y+2z=−15x + y + 2z = -1 has infinitely many solutions, then…MediumSingle correct
  10. 6 Apr 2024, Shift 2 · Q22If the system of equations 2x+7y+λz=32x+7y+\lambda z=3 3x+2y+5z=43x+2y+5z=4 x+μy+32z=−1x+\mu y+32z=-1 has infinitely many solutions, then (λ−μ)(\lambda-\mu) is equal…MediumNumerical value
  11. 5 Apr 2024, Shift 2 · Q4The values of m,nm, n, for which the system of equations x+y+z=4x+y+z=4, 2x+5y+5z=172x+5y+5z=17, x+2y+mz=nx+2y+mz=n has infinitely many solutions, satisfy the…MediumSingle correct
  12. 5 Apr 2024, Shift 1 · Q4If the system of equations 11x+y+λz=−511x+y+\lambda z=-5 2x+3y+5z=32x+3y+5z=3 8x−19y−39z=μ8x-19y-39z=\mu has infinitely many solutions, then λ4−μ\lambda^4-\mu is equal…MediumSingle correct
  13. 13 Apr 2023, Shift 2 · Q4If the system of equations 2x+y−z=52x+y-z=5 2x−5y+λz=μ2x-5y+\lambda z=\mu x+2y−5z=7x+2y-5z=7 has infinitely many solutions, then…MediumSingle correct
  14. 10 Apr 2023, Shift 1 · Q3For the system of linear equations 2x−y+3z=52x-y+3z=5 3x+2y−z=73x+2y-z=7 4x+5y+αz=β4x+5y+\alpha z=\beta, which of the following is NOT correct?MediumSingle correct
  15. 6 Apr 2023, Shift 1 · Q4If the system of equations x+y+az=bx+y+az=b 2x+5y+2z=62x+5y+2z=6 x+2y+3z=3x+2y+3z=3 has infinitely many solutions, then 2a+3b2a+3b is equal toMediumSingle correct
  16. 28 Jun 2022, Shift 2 · Q26If the system of linear equations 2x−3y=γ+52x-3y=\gamma+5, αx+5y=β+1\alpha x+5y=\beta+1, where α,β,γ∈R\alpha, \beta, \gamma \in \mathbf{R} has infinitely…EasyNumerical value
  17. 29 Jul 2022, Shift 2 · Q3If the system of equations x+y+z=6x+y+z=6 2x+5y+αz=β2x+5y+\alpha z=\beta x+2y+3z=14x+2y+3z=14 has infinitely many solutions, then α+β\alpha+\beta is equal toEasySingle correct
  18. 26 Jul 2022, Shift 1 · Q3If the system of linear equations. 8x+y+4z=−28x + y + 4z = -2 x+y+z=0x + y + z = 0 λx−3y=μ\lambda x - 3y = \mu has infinitely many solutions, then the…MediumSingle correct
  19. 26 Feb 2021, Shift 2 · Q74Consider the following system of equations : x+2y−3z=ax+2y-3z=a 2x+6y−11z=b2x+6y-11z=b x−2y+7z=cx-2y+7z=c, where a, b and c are real constants. Then the system…MediumSingle correct
  20. 25 Feb 2021, Shift 1 · Q83If the system of equations kx+y+2z=1kx + y + 2z = 1 3x−y−2z=23x - y - 2z = 2 −2x−2y−4z=3-2x - 2y - 4z = 3 has infinitely many solutions, then k is equal to…MediumNumerical value
  21. 27 Aug 2021, Shift 1 · Q82If the system of linear equations 2x+y−z=32x+y-z=3 x−y−z=αx-y-z=\alpha 3x+3y+βz=33x+3y+\beta z=3 has infinitely many solution, then…MediumNumerical value
  22. 4 Aug 2021, Shift 2 · Q63The system of equations x+2y+pz=4x+2y+pz=4 x+qy+z=5x+qy+z=5 2x+4y+z=82x+4y+z=8 hasMediumSingle correct
  23. 4 Aug 2021, Shift 1 · Q64If the system of linear equations x+y+z=3x+y+z=3 x+by+b2z=7x+by+b^2z=7 and ax+a2y+a3z=1ax+a^2y+a^3z=1 has infinitely many solutions, then the ordered pair…MediumSingle correct
  24. 4 Sep 2020, Shift 2 · Q54If the system of equations x+y+z=2x+y+z=2 2x+4y−z=62x+4y-z=6 3x+2y+λz=μ3x+2y+\lambda z=\mu has infinitely many solutions, then :EasySingle correct
  25. 4 Sep 2020, Shift 1 · Q71If the system of equations x−2y+3z=9x - 2y + 3z = 9 2x+y+z=b2x + y + z = b x−7y+az=24x - 7y + az = 24, has infinitely many solutions, then a−ba - b is equal to…MediumNumerical value

Shifts: 4 Sep 2020, Shift 2, 4 Sep 2020, Shift 1, 25 Feb 2021, Shift 1, 26 Feb 2021, Shift 2, 4 Aug 2021, Shift 2, 4 Aug 2021, Shift 1, 27 Aug 2021, Shift 1, 28 Jun 2022, Shift 2, 26 Jul 2022, Shift 1, 29 Jul 2022, Shift 2, 6 Apr 2023, Shift 1, 10 Apr 2023, Shift 1, 13 Apr 2023, Shift 2, 30 Jan 2024, Shift 2, 31 Jan 2024, Shift 1, 1 Feb 2024, Shift 1, 5 Apr 2024, Shift 2, 5 Apr 2024, Shift 1, 6 Apr 2024, Shift 2, 8 Apr 2024, Shift 2, 9 Apr 2024, Shift 1, 2 Apr 2025, Shift 1, 2 Apr 2026, Shift 2, 4 Apr 2026, Shift 2, 8 Apr 2026, Shift 2.

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