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Sunday, 25 October

JEE Main · Maths · Class 12

Determinants: JEE Main previous year questions

160 questions in 101 of the 108 JEE Main shifts Lumi analysed, asked in 8 of 8 years. Here is what this chapter tests and how.

Study this chapter
Questions
160
in 101 of 108 shifts · 8 of 8 years
Average a shift
1.5
of 25 Maths · 1.3 since 2024 -0.3
Typical range
1.1–1.5
questions a shift; fewest 1.1, most 2.6
Weighted estimate
1.3
model, recent years count more · about 5.3 marks
  • Typical range (fact)
  • Average a shift (fact)
  • Weighted estimate (model)

Questions are counted per shift, out of the 25 each subject has, in the shifts Lumi analysed; papers that offered 30 a subject (2017, 2021–2024) are scaled to 25. Typical range: the middle six of the eight years (2017, 2020–2026), leaving out the single highest and lowest year. The average and the range are historical fact. The weighted estimate is a model: each year's share, with recent years counting more (half-life three years), and chapters NTA dropped from the syllabus set near zero. It is a guide to effort, not a forecast of the paper.

What to do

How to spend time on Determinants

Priority

Must do

One of the 8 Maths chapters that together held the first half of Maths questions in the 108 shifts analysed. How bands are set

Past questions
160in 101 of 108 shifts
Study plan gives it
24 hover 12 months; 18 h over 6
Study this chapter →

Ideas asked most often

  1. Condition for Infinite Solutions25×
  2. Condition for No Solution17×
  3. Inverse Relation to Double Adjoint16×
  4. Evaluating Parameters for Consistency15×
  5. Trap involving |adj(A)| vs |A^-1|10×

66 of the 109 ideas in Lumi’s map of this chapter have not been asked or touched in the shifts analysed. Of its idea-tagged questions from 2024 on, 9% tested an idea not asked in an earlier year, so learn the whole chapter, not just the list above.

Within each subject, chapters in NTA's 2026 syllabus are ranked by their average questions a shift over all 8 years analysed (history, not the model). Going down that list, the chapters that together held the first half of the subject's questions are Must do; the next ones, up to 80%, are Should do; the rest are Lower priority.

Key findings

Determinants at a glance

  1. 01

    91%

    of its 45 questions from 2024 on that Lumi matched to an idea tested one JEE Main had asked in an earlier year; 100% came from a topic asked in an earlier year.

  2. 02

    61%

    of the 109 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    18%

    of its questions asked for a numerical answer, 0.6 times the Maths average.

  4. 04

    16%

    of its questions were rated hard, against 26% across all Maths questions in the same shifts.

Questions a shift, year by year

Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.

0242.6’171.5’201.4’211.1’221.2’231.4’241.1’251.3’26

Raw count: 2017: 3 in 1 shift · 2020: 18 in 12 shifts · 2021: 41 in 24 shifts · 2022: 30 in 24 shifts · 2023: 17 in 12 shifts · 2024: 30 in 18 shifts · 2025: 9 in 8 shifts · 2026: 12 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step41%
  • Calculation28%
  • Numerical answer18%
  • Application13%
  • Conceptual1%

Most common asks: parameters for infinitely many solutions (32); evaluate nested adjoint and inverse of matrix (25); parameters for no solution of linear system (15).

Profile

This chapter in numbers

Where it ranks, how steady it is, and what it costs to study.

Rank, all JEE chapters
#16
of 70 by weighted estimate
Rank in Maths
#6
of 21 chapters
Share of Maths
5.8%
of its questions, all shifts analysed
Busiest year
2017
2.6 questions a shift
Year to year
Some swing
varies by about 0.5 questions a shift
Long-run direction
-0.13
questions a shift, per year
Easy questions
11%
16% rated hard
Numerical answer
18%
0.6× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
24 h
18 h on a 6-month plan
Marks per study hour
0.22
#53 of 70 chapters
Foundation for others
90%
of its ideas are used in other chapters

Difficulty, year by year

Each question rated easy, medium or hard. Each bar is that year’s split, so years compare directly; the number is the questions in that year’s analysed shifts (1 to 24 shifts a year).

  • 20173
  • 202018
  • 202141
  • 202230
  • 202317
  • 202430
  • 20259
  • 202612
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step53%
  • Calculation34%
  • Application13%
  • Conceptual1%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 109 ideas. In the 108 shifts analysed, JEE Main built a question around 33 of them. Most of the chapter has never been the main idea of a question, so past questions alone leave most of it out.

Asked as the main idea
33
Touched on in a question
10
Never asked
66

Topics

What repeats, topic by topic

This chapter's questions per topic in each year's analysed shifts. The number is the count; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. 23 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
021+questions in that year’s analysed shifts, shaded per shift
  • Cramer's Rule

    As a topic: 87 questions in 8 of 8 years, most often single correct, 14% numerical answer. Recent asks: parameters for infinitely many solutions; non-trivial solution then sum trig roots; parameters for no solution of linear system.

  • Matrix Inverse

    As a topic: 51 questions in 8 of 8 years, most often single correct, 25% numerical answer. Recent asks: determinant involving adjoint matrix; numerical: matrix identity with adjoints; singular matrix parameter then extrema of integral.

  • Matrix Multiplication

    As a topic: 60 questions in 7 of 8 years, most often single correct, 40% numerical answer.

  • Chain Rule

    As a topic: 31 questions in 6 of 8 years, most often single correct, 26% numerical answer.

Drill down

Topic, idea, question

Open a topic to see every idea JEE Main tested inside it, then open an idea to read the questions. Each row shows its 8 years.

  • Open83 · 52%11211891445

    16 ideas inside

    • OpenRepeated24 · 29%253382
    • OpenRepeated17 · 20%455
    • OpenRepeated15 · 18%24323
    • OpenRepeated9 · 11%42
    • OpenRepeated4 · 5%2
    • OpenRepeated4 · 5%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open37 · 23%2576745
  • Open9 · 6%233
  • Open3 · 2%2
  • Open2 · 1%
  • Open1 · 1%
  • Open1 · 1%
  • Open1 · 1%

Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.

Ideas

The exact ideas JEE Main has asked

Inside the topics, 28 different ideas were tested; 14 came more than once. These are the repeats, then the ideas new since 2024.

Dots are the 8 years with analysed shifts, 2017 to 2026.

Every question

All 160 Determinants questions

Newest first, shift by shift. The newest 40 show their opening words; older ones name the idea they tested. Each opens with its options and the official answer.

JEE Main 202612 questions

  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. 4 Apr 2026, Shift 1 · Q6Let A=[112−201135]A=\begin{bmatrix}1&1&2\\-2&0&1\\1&3&5\end{bmatrix}. Then the sum of all elements of the matrix…MediumSingle correct
  3. 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
  4. 4 Apr 2026, Shift 2 · Q6Let A=[1274−2838−7]A=\begin{bmatrix}1&2&7\\4&-2&8\\3&8&-7\end{bmatrix} and det⁡(A−αI)=0\det(A-\alpha I)=0, where α\alpha is a real number. If the largest…HardSingle correct
  5. 5 Apr 2026, Shift 1 · Q3Let A be a 3×33 \times 3 matrix such that AT[101]=[522]A^T\begin{bmatrix}1\\0\\1\end{bmatrix}=\begin{bmatrix}5\\2\\2\end{bmatrix},…HardSingle correct
  6. 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
  7. 5 Apr 2026, Shift 2 · Q3If f:N→Zf: \mathbf{N} \to \mathbf{Z} is defined by…HardSingle correct
  8. 6 Apr 2026, Shift 1 · Q21Let A=[−11−1101001]A=\begin{bmatrix}-1&1&-1\\1&0&1\\0&0&1\end{bmatrix} satisfy…MediumNumerical value
  9. 6 Apr 2026, Shift 2 · Q4The sum of all possible values of θ∈[0,2π]\theta\in[0,2\pi], for which the system of equations : xcos⁡3θ−8y−12z=0x\cos 3\theta-8y-12z=0…MediumSingle correct
  10. 6 Apr 2026, Shift 2 · Q17Let A=[13−121α01−1]A=\begin{bmatrix}1&3&-1\\2&1&\alpha\\0&1&-1\end{bmatrix} be a singular matrix. Let f(x)=∫0x(t2+2t+3)dtf(x)=\int_0^x\left(t^2+2t+3\right)dt,…MediumSingle correct
  11. 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
  12. 8 Apr 2026, Shift 2 · Q4Let A=[α12230045]A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix} and…HardSingle correct

JEE Main 20259 questions

  1. 2 Apr 2025, Shift 1 · Q15Let a∈Ra\in\mathbf{R} and A be a matrix of order 3×33\times3 such that det⁡(A)=−4\det(A)=-4 and…MediumSingle correct
  2. 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
  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. 3 Apr 2025, Shift 1 · Q5Let AA be a matrix of order 3×33 \times 3 and ∣A∣=5|A| = 5. If ∣2 adj(3A adj(2A))∣=2α⋅3β⋅5γ|2\,adj(3A\,adj(2A))| = 2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma},…MediumSingle correct
  5. 3 Apr 2025, Shift 1 · Q16If y(x)=∣sin⁡xcos⁡xsin⁡x+cos⁡x+1272827111∣y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{vmatrix}, x∈Rx \in \mathbb{R}, then…MediumSingle correct
  6. 3 Apr 2025, Shift 2 · Q22Let I be the identity matrix of order 3×33 \times 3 and for the matrix…HardNumerical value
  7. 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
  8. 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
  9. 8 Apr 2025, Shift 2 · Q4Let A=[22+p2+p+q46+2p8+3p+2q612+3p20+6p+3q]A = \begin{bmatrix} 2 & 2+p & 2+p+q \\ 4 & 6+2p & 8+3p+2q \\ 6 & 12+3p & 20+6p+3q \end{bmatrix}. If…MediumSingle correct

JEE Main 202430 questions

  1. 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
  2. 4 Apr 2024, Shift 1 · Q5Let α∈(0,∞)\alpha \in (0, \infty) and A=[12α101012]A=\begin{bmatrix}1&2&\alpha\\1&0&1\\0&1&2\end{bmatrix}. If…HardSingle correct
  3. 4 Apr 2024, Shift 1 · Q22Let A be a 3×33\times3 matrix of non-negative real elements such that…HardNumerical value
  4. 4 Apr 2024, Shift 2 · Q23Let AA be a 2×22\times2 symmetric matrix such that A[11]=[37]A\begin{bmatrix}1\\1\end{bmatrix}=\begin{bmatrix}3\\7\end{bmatrix} and the…MediumNumerical value
  5. 5 Apr 2024, Shift 1 · Q3Let A and B be two square matrices of order 3 such that ∣A∣=3|A|=3 and ∣B∣=2|B|=2. Then…MediumSingle correct
  6. 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
  7. 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
  8. 5 Apr 2024, Shift 2 · Q5Let αβ≠0\alpha\beta \neq 0 and…MediumSingle correct
  9. 6 Apr 2024, Shift 1 · Q5For α,β∈R\alpha, \beta \in \mathbb{R} and a natural number nn, let…MediumSingle correct
  10. 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
  11. 6 Apr 2024, Shift 2 · Q4If AA is a square matrix of order 3 such that det⁡(A)=3\det(A)=3 and…MediumSingle correct
  12. 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
  13. 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
  14. 8 Apr 2024, Shift 2 · Q4If α≠a\alpha \neq a, β≠b\beta \neq b, γ≠c\gamma \neq c and…HardSingle correct
  15. 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
  16. 9 Apr 2024, Shift 1 · Q23Let A be a non-singular matrix of order 3. If det⁡(3 adj(2 adj((det⁡A)A)))=3−13⋅2−10\det(3\,\mathrm{adj}(2\,\mathrm{adj}((\det A)A)))=3^{-13}\cdot2^{-10} and…HardNumerical value
  17. 9 Apr 2024, Shift 2 · Q22Consider the matrices : A=[2−53m], B=[20m]A=\begin{bmatrix}2&-5\\3&m\end{bmatrix},\ B=\begin{bmatrix}20\\m\end{bmatrix} and…MediumNumerical value
  18. 1 Feb 2024, Shift 1 · Q3If A=[21−12]A=\begin{bmatrix}\sqrt{2}&1\\-1&\sqrt{2}\end{bmatrix}, B=[1011]B=\begin{bmatrix}1&0\\1&1\end{bmatrix}, C=ABATC=ABA^T and X=ATC2AX=A^TC^2A, then…EasySingle correct
  19. 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
  20. 1 Feb 2024, Shift 2 · Q5Evaluating Parameters for Consistency · Medium · Single correct
  21. 27 Jan 2024, Shift 1 · Q22Determinant of Product · Medium · Numerical value
  22. 29 Jan 2024, Shift 1 · Q5Open the question · Easy · Single correct
  23. 30 Jan 2024, Shift 1 · Q3Evaluating Parameters for Consistency · Medium · Single correct
  24. 30 Jan 2024, Shift 1 · Q4Differentiating Determinants via Chain Rule · Medium · Single correct
  25. 30 Jan 2024, Shift 2 · Q3Inverse Relation to Double Adjoint · Hard · Other
  26. 30 Jan 2024, Shift 2 · Q4Condition for Infinite Solutions · Medium · Single correct
  27. 31 Jan 2024, Shift 1 · Q3Chain Rule in Determinants · Medium · Single correct
  28. 31 Jan 2024, Shift 1 · Q4Condition for Infinite Solutions · Medium · Single correct
  29. 31 Jan 2024, Shift 2 · Q4Condition for Unique Solution · Medium · Single correct
  30. 31 Jan 2024, Shift 2 · Q22Inverse Relation to Double Adjoint · Medium · Numerical value

JEE Main 202317 questions

  1. 6 Apr 2023, Shift 1 · Q4Condition for Infinite Solutions · Medium · Single correct
  2. 6 Apr 2023, Shift 2 · Q5Evaluating Parameters for Consistency · Medium · Single correct
  3. 8 Apr 2023, Shift 1 · Q4Inverse Relation to Double Adjoint · Medium · Single correct
  4. 8 Apr 2023, Shift 2 · Q3Parameter Evaluation in Homogeneous Systems · Medium · Single correct
  5. 10 Apr 2023, Shift 1 · Q3Condition for Infinite Solutions · Medium · Single correct
  6. 10 Apr 2023, Shift 1 · Q4Trap involving |adj(A)| vs |A^-1| · Medium · Single correct
  7. 10 Apr 2023, Shift 2 · Q4Inverse Relation to Double Adjoint · Medium · Single correct
  8. 10 Apr 2023, Shift 2 · Q22Condition for No Solution · Hard · Numerical value
  9. 11 Apr 2023, Shift 2 · Q4Evaluating Parameters for Consistency · Medium · Single correct
  10. 11 Apr 2023, Shift 2 · Q5Open the question · Medium · Single correct
  11. 12 Apr 2023, Shift 1 · Q22Open the question · Hard · Numerical value
  12. 13 Apr 2023, Shift 1 · Q3Inverse Relation to Double Adjoint · Hard · Single correct
  13. 13 Apr 2023, Shift 1 · Q4Evaluating Parameters for Consistency · Medium · Single correct
  14. 13 Apr 2023, Shift 2 · Q4Condition for Infinite Solutions · Medium · Single correct
  15. 13 Apr 2023, Shift 2 · Q5Trap involving |adj(A)| vs |A^-1| · Medium · Single correct
  16. 15 Apr 2023, Shift 1 · Q4Inverse Relation to Double Adjoint · Medium · Single correct
  17. 15 Apr 2023, Shift 1 · Q5Consistency of Overdetermined Systems (3 eq, 2 var) · Medium · Single correct

JEE Main 202230 questions

  1. 25 Jul 2022, Shift 1 · Q4Trigonometric Coefficients and Solution Counting · Medium · Single correct
  2. 25 Jul 2022, Shift 2 · Q2Condition for No Solution · Medium · Single correct
  3. 26 Jul 2022, Shift 1 · Q3Condition for Infinite Solutions · Medium · Single correct
  4. 27 Jul 2022, Shift 2 · Q21Inverse Relation to Double Adjoint · Hard · Numerical value
  5. 28 Jul 2022, Shift 1 · Q14Trap involving |adj(A)| vs |A^-1| · Hard · Single correct
  6. 29 Jul 2022, Shift 1 · Q3Homogeneous System Solutions · Medium · Single correct
  7. 29 Jul 2022, Shift 1 · Q27Quick Identification via Proportionality · Hard · Numerical value
  8. 29 Jul 2022, Shift 2 · Q3Condition for Infinite Solutions · Easy · Single correct
  9. 30 Jul 2022, Shift 2 · Q63Evaluating Parameters for Consistency · Medium · Single correct
  10. 24 Jun 2022, Shift 1 · Q6Condition for No Solution · Medium · Single correct
  11. 24 Jun 2022, Shift 1 · Q9Trap involving |adj(A)| vs |A^-1| · Medium · Single correct
  12. 24 Jun 2022, Shift 2 · Q3Condition for Unique Solution · Medium · Single correct
  13. 25 Jun 2022, Shift 1 · Q5Parametrizing Infinite Solutions · Hard · Single correct
  14. 25 Jun 2022, Shift 2 · Q4Evaluating Parameters for Consistency · Medium · Single correct
  15. 26 Jun 2022, Shift 1 · Q3Trap involving |adj(A)| vs |A^-1| · Medium · Single correct
  16. 26 Jun 2022, Shift 1 · Q4Condition for No Solution · Medium · Single correct
  17. 26 Jun 2022, Shift 2 · Q2Evaluating Parameters for Consistency · Medium · Single correct
  18. 27 Jun 2022, Shift 1 · Q2Condition for No Solution · Medium · Single correct
  19. 27 Jun 2022, Shift 1 · Q23Inverse Relation to Double Adjoint · Medium · Numerical value
  20. 27 Jun 2022, Shift 2 · Q2Open the question · Medium · Single correct
  21. 27 Jun 2022, Shift 2 · Q3Complex Coefficients in Cramer's Rule · Medium · Single correct
  22. 27 Jun 2022, Shift 2 · Q4Determinant of Adjoint of Inverse · Medium · Single correct
  23. 28 Jun 2022, Shift 1 · Q3Condition for No Solution · Medium · Single correct
  24. 28 Jun 2022, Shift 1 · Q4Determinant of Adjoint of Inverse · Medium · Single correct
  25. 28 Jun 2022, Shift 2 · Q26Condition for Infinite Solutions · Easy · Numerical value
  26. 29 Jun 2022, Shift 1 · Q7Evaluating Parameters for Consistency · Easy · Single correct
  27. 29 Jun 2022, Shift 2 · Q3Binomial Expansion for Commuting Matrices · Medium · Single correct
  28. 30 Jun 2022, Shift 1 · Q4Determinant of Product · Medium · Single correct
  29. 30 Jun 2022, Shift 1 · Q5Determinant of Product · Medium · Single correct
  30. 30 Jun 2022, Shift 1 · Q23L'Hopital on Determinant Functions · Hard · Numerical value

JEE Main 202141 questions

  1. 3 Aug 2021, Shift 1 · Q63Determinant of Adjoint of Inverse · Medium · Single correct
  2. 3 Aug 2021, Shift 1 · Q64Evaluating Parameters for Consistency · Medium · Single correct
  3. 3 Aug 2021, Shift 2 · Q63Open the question · Medium · Single correct
  4. 3 Aug 2021, Shift 2 · Q64Open the question · Easy · Single correct
  5. 3 Aug 2021, Shift 2 · Q65Parameter Evaluation in Homogeneous Systems · Medium · Single correct
  6. 4 Aug 2021, Shift 1 · Q63Cofactor Matrix and Adjoint · Medium · Single correct
  7. 4 Aug 2021, Shift 1 · Q64Condition for Infinite Solutions · Medium · Single correct
  8. 4 Aug 2021, Shift 2 · Q62Determinant of Adjoint of Inverse · Medium · Single correct
  9. 4 Aug 2021, Shift 2 · Q63Condition for Infinite Solutions · Medium · Single correct
  10. 4 Aug 2021, Shift 2 · Q90Open the question · Hard · Numerical value
  11. 26 Aug 2021, Shift 1 · Q64Parameter Evaluation in Homogeneous Systems · Medium · Single correct
  12. 26 Aug 2021, Shift 2 · Q63Probability in Linear Systems · Medium · Single correct
  13. 26 Aug 2021, Shift 2 · Q82Trap involving |adj(A)| vs |A^-1| · Medium · Numerical value
  14. 27 Aug 2021, Shift 1 · Q82Condition for Infinite Solutions · Medium · Numerical value
  15. 27 Aug 2021, Shift 2 · Q63Evaluating Parameters for Consistency · Medium · Single correct
  16. 27 Aug 2021, Shift 2 · Q64Open the question · Medium · Single correct
  17. 31 Aug 2021, Shift 1 · Q63Evaluating Determinants with Cube Roots · Hard · Single correct
  18. 31 Aug 2021, Shift 1 · Q64Condition for No Solution · Easy · Single correct
  19. 31 Aug 2021, Shift 2 · Q64Homogeneous System Solutions · Medium · Single correct
  20. 24 Feb 2021, Shift 1 · Q63Condition for No Solution · Medium · Single correct
  21. 24 Feb 2021, Shift 2 · Q69Determinant Form Differential Equations · Medium · Single correct
  22. 24 Feb 2021, Shift 2 · Q72Condition for Unique Solution · Medium · Other
  23. 25 Feb 2021, Shift 1 · Q82Powers of Square Matrices · Hard · Numerical value
  24. 25 Feb 2021, Shift 1 · Q83Condition for Infinite Solutions · Medium · Numerical value
  25. 25 Feb 2021, Shift 2 · Q62Open the question · Easy · Single correct
  26. 25 Feb 2021, Shift 2 · Q63Condition for Unique Solution · Easy · Single correct
  27. 26 Feb 2021, Shift 1 · Q64Open the question · Easy · Single correct
  28. 26 Feb 2021, Shift 2 · Q74Condition for Infinite Solutions · Medium · Single correct
  29. 22 Jul 2021, Shift 2 · Q77Condition for No Solution · Easy · Single correct
  30. 25 Jul 2021, Shift 1 · Q79Condition for No Solution · Easy · Single correct
  31. 25 Jul 2021, Shift 1 · Q88Open the question · Medium · Numerical value
  32. 25 Jul 2021, Shift 2 · Q61Open the question · Medium · Single correct
  33. 16 Mar 2021, Shift 2 · Q77Extrema of Linear Trigonometric Forms · Medium · Single correct
  34. 17 Mar 2021, Shift 1 · Q63Determinant of Product · Easy · Single correct
  35. 17 Mar 2021, Shift 1 · Q64Condition for No Solution · Medium · Single correct
  36. 17 Mar 2021, Shift 1 · Q82Cofactor Matrix and Adjoint · Medium · Numerical value
  37. 17 Mar 2021, Shift 2 · Q64Arithmetic Progression Coefficients Trick · Medium · Single correct
  38. 17 Mar 2021, Shift 2 · Q83Open the question · Medium · Numerical value
  39. 18 Mar 2021, Shift 1 · Q64Parameter Evaluation in Homogeneous Systems · Hard · Single correct
  40. 18 Mar 2021, Shift 1 · Q79Open the question · Medium · Single correct
  41. 18 Mar 2021, Shift 2 · Q75Parameter Evaluation in Homogeneous Systems · Easy · Single correct

JEE Main 202018 questions

  1. 8 Jan 2020, Shift 1 · Q53Condition for No Solution · Medium · Single correct
  2. 8 Jan 2020, Shift 2 · Q55Condition for No Solution · Medium · Single correct
  3. 9 Jan 2020, Shift 1 · Q54Inverse Relation to Double Adjoint · Medium · Single correct
  4. 9 Jan 2020, Shift 1 · Q55Evaluating Parameters for Consistency · Medium · Single correct
  5. 9 Jan 2020, Shift 2 · Q54Open the question · Medium · Single correct
  6. 9 Jan 2020, Shift 2 · Q55Homogeneous System Solutions · Easy · Single correct
  7. 2 Sep 2020, Shift 1 · Q55Condition for No Solution · Medium · Single correct
  8. 2 Sep 2020, Shift 2 · Q55Geometric Meaning of Non-Trivial Homogeneous Solutions · Medium · Single correct
  9. 3 Sep 2020, Shift 1 · Q54Open the question · Medium · Single correct
  10. 3 Sep 2020, Shift 2 · Q54Inverse Relation to Double Adjoint · Medium · Single correct
  11. 3 Sep 2020, Shift 2 · Q71Variable Ratios in Homogeneous Systems · Hard · Numerical value
  12. 4 Sep 2020, Shift 1 · Q71Condition for Infinite Solutions · Medium · Numerical value
  13. 4 Sep 2020, Shift 2 · Q54Condition for Infinite Solutions · Easy · Single correct
  14. 4 Sep 2020, Shift 2 · Q55Determinant of Product · Medium · Single correct
  15. 5 Sep 2020, Shift 1 · Q54Open the question · Medium · Single correct
  16. 5 Sep 2020, Shift 1 · Q55Condition for No Solution · Medium · Single correct
  17. 6 Sep 2020, Shift 2 · Q54Open the question · Hard · Single correct
  18. 6 Sep 2020, Shift 2 · Q71Parameter Evaluation in Homogeneous Systems · Medium · Numerical value

JEE Main 20173 questions

  1. 2 Apr 2017 (offline) · Q63Evaluating Determinants with Cube Roots · Medium · Single correct
  2. 2 Apr 2017 (offline) · Q64Cofactor Matrix and Adjoint · Medium · Single correct
  3. 2 Apr 2017 (offline) · Q65Condition for No Solution · Medium · Single correct

Questions from the official JEE Main papers published by NTA. Chapter, topic and idea tags, counts and notes are Lumi’s. Pattern: Asked most years.

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