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Saturday, 31 October

JEE Main · Maths · Determinants

Condition for No Solution

JEE Main asked Condition for No Solution 17 times in 17 of the 108 shifts Lumi analysed, in 2017, 2020, 2021, 2022, 2023 and 2026. It belongs to Cramer's Rule, in Determinants (Maths). The longest wait between two years asking it was 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2020, 2021 and 2022 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
17
in 17 shifts
Years
6 of 8
First asked
2017
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.510.86’170.33’200.17’210.18’220.07’230’240’250.11’26

Raw count: 2017: 1 in 1 shift · 2020: 4 in 12 shifts · 2021: 5 in 24 shifts · 2022: 5 in 24 shifts · 2023: 1 in 12 shifts · 2024: 0 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
  • 20240 of 18
  • 20231 of 12
  • 20225 of 24
  • 20215 of 24
  • 20204 of 12
  • 20171 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: application.

  • Parameters for no solution of linear system
  • Condition for no solution of linear system

Difficulty

Easy 3Medium 13Hard 1

1 of the 17 questions had a numerical answer.

Every question

All 17 questions

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

  1. 2 Apr 2026, Shift 1 · Q3Let α,β∈R\alpha, \beta \in \mathbf{R} be such that the system of linear equations x+2y+z=5x+2y+z=5 2x+y+αz=52x+y+\alpha z=5 8x+4y+βz=188x+4y+\beta z=18 has no…MediumSingle correct
  2. 10 Apr 2023, Shift 2 · Q22Let S be the set of values of λ\lambda, for which the system of equations 6λx−3y+3z=4λ26\lambda x - 3y + 3z = 4\lambda^2,…HardNumerical value
  3. 28 Jun 2022, Shift 1 · Q3If the system of linear equations 2x+3y−z=−22x+3y-z=-2 x+y+z=4x+y+z=4 x−y+∣λ∣z=4λ−4x-y+|\lambda|z=4\lambda-4 where λ∈R\lambda\in\mathbb{R}, has no solution, thenMediumSingle correct
  4. 27 Jun 2022, Shift 1 · Q2Let the system of linear equations x+2y+z=2x+2y+z=2, αx+3y−z=α\alpha x+3y-z=\alpha, −αx+y+2z=−α-\alpha x+y+2z=-\alpha be inconsistent. Then α\alpha is equal to :MediumSingle correct
  5. 26 Jun 2022, Shift 1 · Q4The ordered pair (a, b), for which the system of linear equations 3x−2y+z=b3x - 2y + z = b 5x−8y+9z=35x - 8y + 9z = 3 2x+y+az=−12x + y + az = -1 has no solution,…MediumSingle correct
  6. 24 Jun 2022, Shift 1 · Q6The number of values of α\alpha for which the system of equations : x+y+z=αx+y+z=\alpha αx+2αy+3z=−1\alpha x+2\alpha y+3z=-1 x+3αy+5z=4x+3\alpha y+5z=4 is…MediumSingle correct
  7. 25 Jul 2022, Shift 2 · Q2The number of real values of λ\lambda, such that the system of linear equations 2x−3y+5z=92x-3y+5z=9 x+3y−z=−18x+3y-z=-18…MediumSingle correct
  8. 17 Mar 2021, Shift 1 · Q64The system of equations kx+y+z=1kx+y+z=1, x+ky+z=kx+ky+z=k and x+y+zk=k2x+y+zk=k^{2} has no solution if k is equal to :MediumSingle correct
  9. 25 Jul 2021, Shift 1 · Q79The values of a and b, for which the system of equations 2x+3y+6z=82x+3y+6z=8 x+2y+az=5x+2y+az=5 3x+5y+9z=b3x+5y+9z=b has no solution, are :EasySingle correct
  10. 22 Jul 2021, Shift 2 · Q77The values of λ\lambda and μ\mu such that the system of equations x+y+z=6x+y+z=6, 3x+5y+5z=263x+5y+5z=26, x+2y+λz=μx+2y+\lambda z=\mu has no solution, are :EasySingle correct
  11. 24 Feb 2021, Shift 1 · Q63The system of linear equations 3x−2y−kz=103x - 2y - kz = 10 2x−4y−2z=62x - 4y - 2z = 6 x+2y−z=5mx + 2y - z = 5\mathrm{m} is inconsistent if :MediumSingle correct
  12. 31 Aug 2021, Shift 1 · Q64If the following system of linear equations 2x+y+z=52x+y+z=5 x−y+z=3x-y+z=3 x+y+az=bx+y+\mathrm{a}z=\mathrm{b} has no solution, then :EasySingle correct
  13. 5 Sep 2020, Shift 1 · Q55Let λ∈R\lambda\in\mathbf{R}. The system of linear equations 2x1−4x2+λx3=12x_1-4x_2+\lambda x_3=1 x1−6x2+x3=2x_1-6x_2+x_3=2 λx1−10x2+4x3=3\lambda x_1-10x_2+4x_3=3 is…MediumSingle correct
  14. 2 Sep 2020, Shift 1 · Q55Let SS be the set of all λ∈R\lambda\in\mathbf{R} for which the system of linear equations 2x−y+2z=22x-y+2z=2 x−2y+λz=−4x-2y+\lambda z=-4…MediumSingle correct
  15. 8 Jan 2020, Shift 2 · Q55The system of linear equations λx+2y+2z=5\lambda x + 2y + 2z = 5 2λx+3y+5z=82\lambda x + 3y + 5z = 8 4x+λy+6z=104x + \lambda y + 6z = 10 has :MediumSingle correct
  16. 8 Jan 2020, Shift 1 · Q53For which of the following ordered pairs (μ,δ)(\mu, \delta), the system of linear equations x+2y+3z=1x+2y+3z=1 3x+4y+5z=μ3x+4y+5z=\mu 4x+4y+4z=δ4x+4y+4z=\delta is…MediumSingle correct
  17. 2 Apr 2017 (offline) · Q65If S is the set of distinct values of 'b' for which the following system of linear equations x+y+z=1x+y+z=1 x+ay+z=1x+ay+z=1 ax+by+z=0ax+by+z=0 has no…MediumSingle correct

Shifts: 2 Apr 2017 (offline), 8 Jan 2020, Shift 2, 8 Jan 2020, Shift 1, 2 Sep 2020, Shift 1, 5 Sep 2020, Shift 1, 24 Feb 2021, Shift 1, 17 Mar 2021, Shift 1, 22 Jul 2021, Shift 2, 25 Jul 2021, Shift 1, 31 Aug 2021, Shift 1, 24 Jun 2022, Shift 1, 26 Jun 2022, Shift 1, 27 Jun 2022, Shift 1, 28 Jun 2022, Shift 1, 25 Jul 2022, Shift 2, 10 Apr 2023, Shift 2, 2 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