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Sunday, 25 October

JEE Main · Maths · Class 11

Complex Numbers and Quadratic Equations: JEE Main previous year questions

205 questions in 108 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
205
in 108 of 108 shifts · 8 of 8 years
Average a shift
1.6
of 25 Maths · 1.8 since 2024 +0.3
Typical range
1.4–1.9
questions a shift; fewest 0.9, most 2.1
Weighted estimate
1.7
model, recent years count more · about 6.9 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 Complex Numbers and Quadratic Equations

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
205in 108 of 108 shifts
Study plan gives it
30 hover 12 months; 22 h over 6
Study this chapter →

Ideas asked most often

  1. Newton's Sums16×
  2. Root-Coefficient Relation15×
  3. Modulus and Argument13×
  4. Symmetric Functions12×
  5. Roots of Modulus Quadratics12×

169 of the 249 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, 13% 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

Complex Numbers and Quadratic Equations at a glance

  1. 01

    87%

    of its 60 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

    68%

    of the 249 ideas in Lumi's map of the chapter have not been asked or touched on in the shifts analysed.

  3. 03

    29%

    of its questions asked for a numerical answer, 1.0 times the Maths average.

  4. 04

    27%

    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.

0240.9’172.1’201.5’211.7’221.4’231.8’241.9’251.8’26

Raw count: 2017: 1 in 1 shift · 2020: 25 in 12 shifts · 2021: 43 in 24 shifts · 2022: 47 in 24 shifts · 2023: 20 in 12 shifts · 2024: 38 in 18 shifts · 2025: 15 in 8 shifts · 2026: 16 in 9 shifts.

Kind of question

SHARE OF QUESTIONS
  • Multi-step46%
  • Numerical answer29%
  • Calculation10%
  • Application9%
  • Conceptual3%
  • Two statements2%

Most common asks: value from roots of linked quadratics (23); count real roots of modulus equation (9); modulus from locus and argument conditions (2).

Profile

This chapter in numbers

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

Rank, all JEE chapters
#5
of 70 by weighted estimate
Rank in Maths
#3
of 21 chapters
Share of Maths
6.5%
of its questions, all shifts analysed
Busiest year
2020
2.1 questions a shift
Year to year
Steady
varies by about 0.3 questions a shift
Long-run direction
+0.07
questions a shift, per year
Easy questions
11%
27% rated hard
Numerical answer
29%
1.0× the Maths rate
With a figure
0%
graph, diagram or structure
Study time
30 h
22 h on a 6-month plan
Marks per study hour
0.23
#35 of 70 chapters
Foundation for others
74%
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).

  • 20171
  • 202025
  • 202143
  • 202247
  • 202320
  • 202438
  • 202515
  • 202616
  • Easy
  • Medium
  • Hard

What it asks you to do

SHARE OF QUESTIONS
  • Multi-step69%
  • Calculation16%
  • Application11%
  • Conceptual4%

Coverage

How much of the chapter JEE Main has used

We split the chapter into 249 ideas. In the 108 shifts analysed, JEE Main built a question around 58 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
58
Touched on in a question
22
Never asked
169

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. 30 questions had no close topic in Lumi's map and count for the chapter only.

’17’20’21’22’23’24’25’26
020+questions in that year’s analysed shifts, shaded per shift
  • Quadratic Roots

    As a topic: 104 questions in 8 of 8 years, most often single correct, 33% numerical answer. Recent asks: quadratic root ratio then conic latus rectum; value from roots of linked quadratics; numerical: sum of powers of quadratic roots.

  • Complex Numbers - Polar Form

    As a topic: 57 questions in 7 of 8 years, most often single correct, 23% numerical answer.

  • Roots of Unity

    As a topic: 18 questions in 6 of 8 years, most often single correct, 44% numerical answer.

  • Location of Roots

    As a topic: 6 questions in 3 of 8 years, most often single correct, 17% 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.

  • Open92 · 45%13201971958

    19 ideas inside

    • OpenRepeated16 · 17%42332
    • OpenRepeated15 · 16%4225
    • OpenRepeated11 · 12%7
    • OpenRepeated10 · 11%432
    • OpenRepeated10 · 11%2222
    • OpenRepeated7 · 8%232
    • OpenRepeated5 · 5%22
    • OpenRepeated4 · 4%
    • OpenRepeated2 · 2%
    • OpenRepeated2 · 2%
    • OpenRepeated2 · 2%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
    • Open1 · 1%
  • Open57 · 28%8131551222
  • Open15 · 7%25422
  • Open5 · 2%22
  • Open1 · 0%
  • Open1 · 0%
  • Open1 · 0%
  • Open1 · 0%
  • Open1 · 0%
  • Open1 · 0%

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, 54 different ideas were tested; 27 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 205 Complex Numbers and Quadratic Equations 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 202616 questions

  1. 2 Apr 2026, Shift 1 · Q1Let α,α+2,α∈Z\alpha, \alpha+2, \alpha \in \mathbb{Z}, be the roots of the quadratic equation…HardSingle correct
  2. 2 Apr 2026, Shift 1 · Q2Let xx and yy be real numbers such that 50(2x1+3i−y1−2i)=31+17i50\left(\frac{2x}{1+3i}-\frac{y}{1-2i}\right)=31+17i, i=−1i=\sqrt{-1}. Then the value of…EasySingle correct
  3. 2 Apr 2026, Shift 2 · Q1Let α,β\alpha, \beta be the roots of the equation x2−3x+r=0x^2 - 3x + r = 0, and α2,2β\frac{\alpha}{2}, 2\beta be the roots of the equation…MediumSingle correct
  4. 2 Apr 2026, Shift 2 · Q2Let the circles C1:∣z∣=rC_1: |z| = r and C2:∣z−3−4i∣=5,z∈CeC_2: |z - 3 - 4i| = 5, z \in \mathbb{C}_e be such that C2C_2 lies within C1C_1. If z1z_1 moves on…MediumSingle correct
  5. 4 Apr 2026, Shift 1 · Q2If the set of all solutions of ∣x2+x−9∣=∣x∣+∣x2−9∣|x^2+x-9|=|x|+|x^2-9| is [α,β]∪[γ,∞)[\alpha,\beta]\cup[\gamma,\infty), then (α2+β2+γ2)(\alpha^2+\beta^2+\gamma^2) is equal…HardSingle correct
  6. 4 Apr 2026, Shift 1 · Q3Let zz be a complex number such that ∣z+2∣=∣z−2∣|z+2|=|z-2| and arg⁡(z+3z−i)=π4\arg\left(\frac{z+3}{z-i}\right)=\frac{\pi}{4}. Then ∣z∣2|z|^2 is equal to:MediumSingle correct
  7. 4 Apr 2026, Shift 2 · Q2Let S={z∈C:z2+4z+16=0}S=\{z\in\mathbb{C}:z^2+4z+16=0\}. Then ∑z∈S∣z+3 i∣2\sum_{z\in S}|z+\sqrt{3}\,i|^2 is equal to:EasySingle correct
  8. 4 Apr 2026, Shift 2 · Q5If the quadratic equation (λ+2)x2−3λx+4λ=0(\lambda+2)x^2-3\lambda x+4\lambda=0, λ≠−2\lambda\neq-2, has two positive roots, then the number of possible…MediumSingle correct
  9. 5 Apr 2026, Shift 1 · Q1Let a,b∈Ca, b \in \mathbb{C}. Let α,β\alpha, \beta be the roots of the equation x2+ax+b=0x^2 + ax + b = 0. If β−α=11\beta - \alpha = \sqrt{11} and…MediumSingle correct
  10. 5 Apr 2026, Shift 2 · Q1Let α,β\alpha, \beta be the roots of the equation x2−x+p=0x^2-x+p=0 and γ,δ\gamma, \delta be the roots the equation x2−4x+q=0x^2-4x+q=0;…MediumSingle correct
  11. 5 Apr 2026, Shift 2 · Q2Let z1,z2∈Cz_1, z_2 \in \mathbb{C} be the distinct solutions of the equation z2+4z−(1+12i)=0z^2+4z-(1+12i)=0. Then ∣z1∣2+∣z2∣2|z_1|^2+|z_2|^2 is equal to :MediumSingle correct
  12. 6 Apr 2026, Shift 1 · Q4Let the set of all values of k∈Rk\in\mathbb{R} such that the equation z(z‾+2+i)+k(2+3i)=0z(\overline{z}+2+i)+k(2+3i)=0, z∈Cz\in\mathbb{C}, has at least one…HardSingle correct
  13. 6 Apr 2026, Shift 2 · Q2Consider the quadratic equation (n2−2n+2)x2−3x+(n2−2n+2)2=0(n^2-2n+2)x^2-3x+(n^2-2n+2)^2=0, n∈Rn\in\mathbf{R}. Let α\alpha be the minimum value of the product of…MediumSingle correct
  14. 6 Apr 2026, Shift 2 · Q3Let S={z∈C:z2+6 iz−3=0}S=\{z\in\mathbb{C}: z^2+\sqrt{6}\,iz-3=0\}. Then ∑z∈Sz8\sum_{z\in S} z^8 is equal to :MediumSingle correct
  15. 6 Apr 2026, Shift 2 · Q16Let lim⁡x→2(tan⁡(x−2))(rx2+(p−2)x−2p)(x−2)2=5\lim_{x\to2}\frac{(\tan(x-2))\left(rx^2+(p-2)x-2p\right)}{(x-2)^2}=5 for some r,p∈Rr, p\in\mathbf{R}. If the set of all possible values…HardSingle correct
  16. 8 Apr 2026, Shift 2 · Q2The number of values of z∈Cz \in \mathbb{C}, satisfying the equations ∣z−(4+8i)∣=10|z - (4 + 8i)| = \sqrt{10} and…HardSingle correct

JEE Main 202515 questions

  1. 2 Apr 2025, Shift 1 · Q2Let zz be a complex number such that ∣z∣=1|z|=1. If 2+k2zk+zˉ=kz\frac{2+k^2z}{k+\bar{z}}=kz, k∈Rk\in\mathbf{R}, then the maximum distance of k+ik2k+ik^2…HardSingle correct
  2. 2 Apr 2025, Shift 1 · Q17Let Pn=αn+βnP_n=\alpha^n+\beta^n, n∈Nn\in\mathbf{N}. If P10=123P_{10}=123, P9=76P_9=76, P8=47P_8=47 and P1=1P_1=1, then the quadratic equation having roots…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q21If the set of all a∈R−{1}a \in \mathbf{R} - \{1\}, for which the roots of the equation (1−a)x2+2(a−3)x+9=0(1-a)x^2 + 2(a-3)x + 9 = 0 are positive is…MediumNumerical value
  4. 3 Apr 2025, Shift 1 · Q3Let α\alpha and β\beta be the roots of x2+3x−16=0x^2 + \sqrt{3}x - 16 = 0, and γ\gamma and δ\delta be the roots of x2+3x−1=0x^2 + 3x - 1 = 0. If…MediumSingle correct
  5. 3 Apr 2025, Shift 1 · Q4Let z∈Cz \in \mathbb{C} be such that z2+3iz−2+i=2+3i\frac{z^2 + 3i}{z - 2 + i} = 2 + 3i. Then the sum of all possible values of z2z^2 isMediumSingle correct
  6. 3 Apr 2025, Shift 2 · Q4Let the equation x(x+2)(12−k)=2x(x + 2)(12 - k) = 2 have equal roots. Then the distance of the point (k,k2)\left(k, \frac{k}{2}\right) from the line…EasySingle correct
  7. 3 Apr 2025, Shift 2 · Q5If z1,z2,z3∈Cz_1, z_2, z_3 \in \mathbb{C} are the vertices of an equilateral triangle, whose centroid is z0z_0, then…MediumSingle correct
  8. 4 Apr 2025, Shift 2 · Q3Let the product of ω1=(8+i)sin⁡θ+(7+4i)cos⁡θ\omega_1=(8+i)\sin\theta+(7+4i)\cos\theta and ω2=(1+8i)sin⁡θ+(4+7i)cos⁡θ\omega_2=(1+8i)\sin\theta+(4+7i)\cos\theta be α+iβ\alpha+i\beta,…HardSingle correct
  9. 4 Apr 2025, Shift 2 · Q21If α\alpha is a root of the equation x2+x+1=0x^2+x+1=0 and ∑k=1n(αk+1αk)2=20\sum_{k=1}^{n}\left(\alpha^k+\frac{1}{\alpha^k}\right)^2=20, then n is equal to…MediumNumerical value
  10. 7 Apr 2025, Shift 1 · Q2Among the statements (S1) : The set {z∈C−{−i}:∣z∣=1\{z \in \mathbb{C} - \{-i\} : |z| = 1 and z−iz+i\frac{z-i}{z+i} is purely real}\} contains exactly two…MediumTwo statements
  11. 7 Apr 2025, Shift 1 · Q3Let the set of all values of p∈Rp \in \mathbb{R}, for which both the roots of the equation x2−(p+2)x+(2p+9)=0x^2 - (p+2)x + (2p+9) = 0 are negative real…EasySingle correct
  12. 7 Apr 2025, Shift 2 · Q3The number of real roots of the equation x∣x−2∣+3∣x−3∣+1=0x|x-2|+3|x-3|+1=0 is :MediumSingle correct
  13. 7 Apr 2025, Shift 2 · Q4If the locus of z∈Cz\in\mathbf{C}, such that…HardSingle correct
  14. 8 Apr 2025, Shift 2 · Q2The sum of the squares of the roots of ∣x−2∣2+∣x−2∣−2=0|x-2|^2 + |x-2| - 2 = 0 and the squares of the roots of x2−2∣x−3∣−5=0x^2 - 2|x-3| - 5 = 0, isMediumSingle correct
  15. 8 Apr 2025, Shift 2 · Q3Let…HardSingle correct

JEE Main 202438 questions

  1. 4 Apr 2024, Shift 1 · Q2Let α\alpha and β\beta be the sum and the product of all the non-zero solutions of the equation (zˉ)2+∣z∣=0(\bar{z})^2+|z|=0, z∈Cz \in C. Then…MediumSingle correct
  2. 4 Apr 2024, Shift 1 · Q3If 2 and 6 are the roots of the equation ax2+bx+1=0ax^2+bx+1=0, then the quadratic equation, whose roots are 12a+b\frac{1}{2a+b} and…EasySingle correct
  3. 4 Apr 2024, Shift 2 · Q2The area (in sq. units) of the region S={z∈C:∣z−1∣≤2; (z+zˉ)+i(z−zˉ)≤2, Im(z)≥0}S=\{z\in\mathbb{C}:|z-1|\le 2;\ (z+\bar z)+i(z-\bar z)\le 2,\ \mathrm{Im}(z)\ge 0\} isHardSingle correct
  4. 4 Apr 2024, Shift 2 · Q22Let S={sin⁡22θ:(sin⁡4θ+cos⁡4θ)x2+(sin⁡2θ)x+(sin⁡6θ+cos⁡6θ)=0 has real roots}S=\{\sin^2 2\theta:(\sin^4\theta+\cos^4\theta)x^2+(\sin2\theta)x+(\sin^6\theta+\cos^6\theta)=0\ \text{has real roots}\}. If α\alpha…HardNumerical value
  5. 5 Apr 2024, Shift 1 · Q2Consider the following two statements : Statement I : For any two non-zero complex numbers z1,z2z_1, z_2,…HardTwo statements
  6. 5 Apr 2024, Shift 1 · Q22The number of distinct real roots of the equation ∣x∣∣x+2∣−5∣x+1∣−1=0|x||x+2|-5|x+1|-1=0 is ________.MediumNumerical value
  7. 5 Apr 2024, Shift 2 · Q3Let S1={z∈C:∣z∣≤5}S_1 = \{z \in C : |z| \leq 5\}, S2={z∈C:Im(z+1−3i1−3i)≥0}S_2 = \left\{z \in C : \mathrm{Im}\left(\frac{z+1-\sqrt{3}i}{1-\sqrt{3}i}\right) \geq 0\right\}…HardSingle correct
  8. 5 Apr 2024, Shift 2 · Q30The number of real solutions of the equation x∣x+5∣+2∣x+7∣−2=0x|x+5| + 2|x+7| - 2 = 0 is ________.MediumNumerical value
  9. 6 Apr 2024, Shift 1 · Q4Let α,β\alpha, \beta be the distinct roots of the equation x2−(t2−5t+6)x+1=0x^2-(t^2-5t+6)x+1=0, t∈Rt \in \mathbb{R} and an=αn+βna_n=\alpha^n+\beta^n. Then the…HardSingle correct
  10. 6 Apr 2024, Shift 1 · Q21Root-Coefficient Relation · Hard · Numerical value
  11. 6 Apr 2024, Shift 2 · Q3Modulus and Argument · Hard · Single correct
  12. 6 Apr 2024, Shift 2 · Q21Newton's Sums · Easy · Numerical value
  13. 8 Apr 2024, Shift 1 · Q2Polar Conjugate and Inverse · Medium · Single correct
  14. 8 Apr 2024, Shift 1 · Q3Exponential Reducible to Quadratic · Easy · Single correct
  15. 8 Apr 2024, Shift 1 · Q6Open the question · Medium · Single correct
  16. 8 Apr 2024, Shift 2 · Q7Purely Real and Imaginary Euler Conditions · Medium · Single correct
  17. 8 Apr 2024, Shift 2 · Q21Roots of Modulus Quadratics · Medium · Numerical value
  18. 9 Apr 2024, Shift 1 · Q2Equation Formation · Medium · Single correct
  19. 9 Apr 2024, Shift 1 · Q22Open the question · Medium · Numerical value
  20. 9 Apr 2024, Shift 2 · Q2Polar Triangle Inequality Extrema · Medium · Single correct
  21. 9 Apr 2024, Shift 2 · Q3Newton's Sums · Medium · Single correct
  22. 1 Feb 2024, Shift 1 · Q1Modulus and Argument · Hard · Single correct
  23. 1 Feb 2024, Shift 1 · Q2Exponential Reducible to Quadratic · Medium · Single correct
  24. 1 Feb 2024, Shift 1 · Q22Polar Triangle Inequality Extrema · Hard · Numerical value
  25. 1 Feb 2024, Shift 2 · Q4Root-Coefficient Relation · Medium · Single correct
  26. 27 Jan 2024, Shift 1 · Q3Open the question · Medium · Single correct
  27. 27 Jan 2024, Shift 1 · Q21Periodicity of Omega Powers · Medium · Numerical value
  28. 29 Jan 2024, Shift 1 · Q3Modulus and Argument · Easy · Single correct
  29. 29 Jan 2024, Shift 1 · Q21Higher Degree Evaluation via Root Substitution · Medium · Numerical value
  30. 30 Jan 2024, Shift 1 · Q2Modulus and Argument · Medium · Single correct
  31. 30 Jan 2024, Shift 1 · Q22Integer Roots Condition · Medium · Numerical value
  32. 30 Jan 2024, Shift 2 · Q2Roots of z^2 + z + 1 = 0 · Medium · Single correct
  33. 31 Jan 2024, Shift 1 · Q2Always Negative Condition · Easy · Single correct
  34. 31 Jan 2024, Shift 1 · Q7Complex Conjugate Roots · Hard · Single correct
  35. 31 Jan 2024, Shift 1 · Q8Zero Sum of Coefficients Shortcut · Medium · Two statements
  36. 31 Jan 2024, Shift 1 · Q22Modulus and Argument · Medium · Numerical value
  37. 31 Jan 2024, Shift 2 · Q3Symmetric Functions · Hard · Single correct
  38. 31 Jan 2024, Shift 2 · Q24Nature of Roots · Hard · Numerical value

JEE Main 202320 questions

  1. 6 Apr 2023, Shift 1 · Q2Quadratics with Absolute Values · Medium · Single correct
  2. 6 Apr 2023, Shift 2 · Q21Distance Formula in Polar Coordinates · Medium · Numerical value
  3. 8 Apr 2023, Shift 1 · Q2Modulus and Argument · Medium · Single correct
  4. 8 Apr 2023, Shift 1 · Q3Root-Coefficient Relation · Medium · Single correct
  5. 8 Apr 2023, Shift 2 · Q2Purely Real and Imaginary Euler Conditions · Medium · Single correct
  6. 8 Apr 2023, Shift 2 · Q22Roots of Modulus Quadratics · Hard · Numerical value
  7. 10 Apr 2023, Shift 1 · Q2Open the question · Medium · Single correct
  8. 10 Apr 2023, Shift 1 · Q22Open the question · Easy · Numerical value
  9. 10 Apr 2023, Shift 2 · Q3Open the question · Medium · Single correct
  10. 11 Apr 2023, Shift 1 · Q1490-Degree Rotation via 'i' · Medium · Single correct
  11. 11 Apr 2023, Shift 1 · Q24Newton's Sums · Medium · Numerical value
  12. 11 Apr 2023, Shift 2 · Q3Open the question · Medium · Two statements
  13. 11 Apr 2023, Shift 2 · Q21Purely Real and Imaginary Euler Conditions · Hard · Numerical value
  14. 12 Apr 2023, Shift 1 · Q2Newton's Sums · Hard · Single correct
  15. 12 Apr 2023, Shift 1 · Q7Open the question · Hard · Single correct
  16. 13 Apr 2023, Shift 1 · Q21Radical axis of two circles · Hard · Numerical value
  17. 13 Apr 2023, Shift 2 · Q2Open the question · Hard · Single correct
  18. 13 Apr 2023, Shift 2 · Q3Newton's Sums · Medium · Single correct
  19. 15 Apr 2023, Shift 1 · Q2Roots of Modulus Quadratics · Medium · Single correct
  20. 15 Apr 2023, Shift 1 · Q3Open the question · Hard · Single correct

JEE Main 202247 questions

  1. 25 Jul 2022, Shift 1 · Q2Sum of p-th Powers of Roots · Medium · Single correct
  2. 25 Jul 2022, Shift 2 · Q1Polar Triangle Inequality Extrema · Medium · Single correct
  3. 25 Jul 2022, Shift 2 · Q22Common Root Condition · Hard · Numerical value
  4. 26 Jul 2022, Shift 1 · Q2Coni Method (Rotation Theorem) · Medium · Single correct
  5. 26 Jul 2022, Shift 1 · Q21Common Root Condition · Hard · Numerical value
  6. 26 Jul 2022, Shift 2 · Q1Symmetric Functions · Easy · Single correct
  7. 26 Jul 2022, Shift 2 · Q2Open the question · Medium · Single correct
  8. 27 Jul 2022, Shift 1 · Q3Open the question · Hard · Single correct
  9. 27 Jul 2022, Shift 1 · Q30Polar Conjugate and Inverse · Medium · Numerical value
  10. 27 Jul 2022, Shift 2 · Q2Open the question · Hard · Single correct
  11. 28 Jul 2022, Shift 1 · Q15Polar Triangle Inequality Extrema · Hard · Single correct
  12. 28 Jul 2022, Shift 1 · Q26Difference of Roots · Medium · Numerical value
  13. 28 Jul 2022, Shift 1 · Q30Root-Coefficient Relation · Medium · Numerical value
  14. 28 Jul 2022, Shift 2 · Q62Transformation of Roots · Medium · Single correct
  15. 28 Jul 2022, Shift 2 · Q64Open the question · Medium · Single correct
  16. 28 Jul 2022, Shift 2 · Q88Modulus and Argument · Hard · Numerical value
  17. 29 Jul 2022, Shift 1 · Q2Simplifying Conjugate Binomial Sums · Easy · Single correct
  18. 29 Jul 2022, Shift 2 · Q1Polar Triangle Inequality Extrema · Medium · Single correct
  19. 29 Jul 2022, Shift 2 · Q17Locus of Full Line via Argument · Hard · Single correct
  20. 29 Jul 2022, Shift 2 · Q22Newton's Sums · Medium · Numerical value
  21. 30 Jul 2022, Shift 2 · Q62Modulus and Argument · Medium · Two statements
  22. 30 Jul 2022, Shift 2 · Q81Roots of Modulus Quadratics · Medium · Numerical value
  23. 24 Jun 2022, Shift 1 · Q1Open the question · Medium · Single correct
  24. 24 Jun 2022, Shift 1 · Q7Symmetric Functions · Medium · Single correct
  25. 24 Jun 2022, Shift 2 · Q2Exponential Reducible to Quadratic · Easy · Single correct
  26. 24 Jun 2022, Shift 2 · Q21Open the question · Hard · Numerical value
  27. 25 Jun 2022, Shift 1 · Q20Geometric Rotation · Hard · Single correct
  28. 25 Jun 2022, Shift 2 · Q2Symmetric Functions · Medium · Single correct
  29. 25 Jun 2022, Shift 2 · Q3Principal Argument Arithmetic · Medium · Single correct
  30. 26 Jun 2022, Shift 1 · Q2Locus of Argument Ratio (Circular Arc) · Hard · Single correct
  31. 26 Jun 2022, Shift 1 · Q21Newton's Sums · Medium · Numerical value
  32. 26 Jun 2022, Shift 2 · Q22Symmetric Functions · Medium · Numerical value
  33. 26 Jun 2022, Shift 2 · Q23Roots of z^2 + z + 1 = 0 · Hard · Numerical value
  34. 27 Jun 2022, Shift 1 · Q1Roots of z^n = z_0 · Medium · Single correct
  35. 27 Jun 2022, Shift 1 · Q22Exponential Reducible to Quadratic · Medium · Numerical value
  36. 27 Jun 2022, Shift 2 · Q1Open the question · Medium · Single correct
  37. 27 Jun 2022, Shift 2 · Q22Symmetric Functions · Hard · Numerical value
  38. 28 Jun 2022, Shift 1 · Q29Open the question · Medium · Numerical value
  39. 28 Jun 2022, Shift 2 · Q2Root-Coefficient Relation · Medium · Single correct
  40. 28 Jun 2022, Shift 2 · Q28Polar Conjugate and Inverse · Hard · Numerical value
  41. 29 Jun 2022, Shift 1 · Q8Symmetric Functions · Medium · Single correct
  42. 29 Jun 2022, Shift 1 · Q21Open the question · Hard · Numerical value
  43. 29 Jun 2022, Shift 2 · Q1Equations Reducible to Roots of Unity · Medium · Single correct
  44. 29 Jun 2022, Shift 2 · Q2Locus of Argument Ratio (Circular Arc) · Medium · Single correct
  45. 30 Jun 2022, Shift 1 · Q1Exponential Reducible to Quadratic · Medium · Single correct
  46. 30 Jun 2022, Shift 1 · Q2Polar Form for Binomial Powers · Medium · Single correct
  47. 30 Jun 2022, Shift 1 · Q3Symmetric Functions · Medium · Single correct

JEE Main 202143 questions

  1. 3 Aug 2021, Shift 1 · Q81Cyclic Powers of Omega Modulo 3 · Medium · Numerical value
  2. 3 Aug 2021, Shift 1 · Q82Reducible Biquadratics · Medium · Numerical value
  3. 3 Aug 2021, Shift 2 · Q62Common Root Condition · Easy · Single correct
  4. 4 Aug 2021, Shift 1 · Q61Exponential Reducible to Quadratic · Medium · Single correct
  5. 4 Aug 2021, Shift 1 · Q62Modulus and Argument · Medium · Single correct
  6. 4 Aug 2021, Shift 2 · Q81De Moivre's Theorem for Integer Powers · Medium · Numerical value
  7. 4 Aug 2021, Shift 2 · Q82Resolution into Two Linear Factors · Hard · Numerical value
  8. 26 Aug 2021, Shift 1 · Q62Locus of Argument Ratio (Circular Arc) · Medium · Single correct
  9. 26 Aug 2021, Shift 1 · Q83Nature of Roots · Medium · Numerical value
  10. 26 Aug 2021, Shift 1 · Q89De Moivre's Theorem · Hard · Numerical value
  11. 26 Aug 2021, Shift 2 · Q62De Moivre's Theorem for Integer Powers · Medium · Single correct
  12. 26 Aug 2021, Shift 2 · Q81Common Root Condition · Medium · Numerical value
  13. 26 Aug 2021, Shift 2 · Q88De Moivre's Theorem for Integer Powers · Medium · Numerical value
  14. 27 Aug 2021, Shift 1 · Q62Collinearity via Argument · Medium · Single correct
  15. 27 Aug 2021, Shift 2 · Q62Nature of Roots · Hard · Single correct
  16. 27 Aug 2021, Shift 2 · Q81Open the question · Hard · Numerical value
  17. 31 Aug 2021, Shift 1 · Q62Exponential Reducible to Quadratic · Medium · Single correct
  18. 31 Aug 2021, Shift 1 · Q82Locus of Argument Ratio (Circular Arc) · Hard · Numerical value
  19. 31 Aug 2021, Shift 2 · Q62Locus of Argument Ratio (Circular Arc) · Medium · Single correct
  20. 31 Aug 2021, Shift 2 · Q63Exponential Reducible to Quadratic · Medium · Single correct
  21. 24 Feb 2021, Shift 1 · Q62Symmetric Functions · Medium · Single correct
  22. 24 Feb 2021, Shift 1 · Q81Nature of Roots · Hard · Numerical value
  23. 24 Feb 2021, Shift 2 · Q84De Moivre's Theorem for Integer Powers · Medium · Numerical value
  24. 24 Feb 2021, Shift 2 · Q90Roots of Modulus Quadratics · Medium · Numerical value
  25. 25 Feb 2021, Shift 1 · Q62Normal Passes Through Center · Hard · Single correct
  26. 25 Feb 2021, Shift 1 · Q63Always Positive Condition · Medium · Single correct
  27. 25 Feb 2021, Shift 2 · Q66Newton's Sums · Medium · Single correct
  28. 25 Feb 2021, Shift 2 · Q69Complex Conjugate Roots · Easy · Single correct
  29. 26 Feb 2021, Shift 1 · Q82Sum of p-th Powers of Roots · Medium · Numerical value
  30. 26 Feb 2021, Shift 2 · Q82Polar Triangle Inequality Extrema · Hard · Numerical value
  31. 26 Feb 2021, Shift 2 · Q87Newton's Sums · Easy · Numerical value
  32. 22 Jul 2021, Shift 2 · Q78Polar Conjugate and Inverse · Medium · Single correct
  33. 25 Jul 2021, Shift 1 · Q72Exponential Reducible to Quadratic · Hard · Single correct
  34. 25 Jul 2021, Shift 1 · Q90Newton's Sums · Medium · Numerical value
  35. 25 Jul 2021, Shift 2 · Q74Roots of Modulus Quadratics · Easy · Single correct
  36. 25 Jul 2021, Shift 2 · Q84Newton's Sums · Medium · Numerical value
  37. 16 Mar 2021, Shift 2 · Q76Open the question · Medium · Single correct
  38. 17 Mar 2021, Shift 1 · Q62Area of Rotated Complex Triangles · Easy · Single correct
  39. 17 Mar 2021, Shift 2 · Q74Open the question · Medium · Single correct
  40. 18 Mar 2021, Shift 1 · Q62Open the question · Medium · Single correct
  41. 18 Mar 2021, Shift 1 · Q81Equilateral Triangle Condition via Omega · Medium · Numerical value
  42. 18 Mar 2021, Shift 2 · Q77Area of Rotated Complex Triangles · Medium · Single correct
  43. 18 Mar 2021, Shift 2 · Q81Polynomial Remainder via Roots · Medium · Numerical value

JEE Main 202025 questions

  1. 8 Jan 2020, Shift 1 · Q52Complex Conjugate Roots · Medium · Single correct
  2. 8 Jan 2020, Shift 1 · Q71Nature of Roots · Easy · Numerical value
  3. 8 Jan 2020, Shift 2 · Q52Periodicity of Omega Powers · Medium · Single correct
  4. 8 Jan 2020, Shift 2 · Q53Roots of Modulus Quadratics · Medium · Single correct
  5. 9 Jan 2020, Shift 1 · Q52Exponential Reducible to Quadratic · Hard · Single correct
  6. 9 Jan 2020, Shift 1 · Q53Modulus and Argument · Medium · Single correct
  7. 9 Jan 2020, Shift 2 · Q52Common Root Condition · Medium · Single correct
  8. 9 Jan 2020, Shift 2 · Q53Modulus and Argument · Medium · Single correct
  9. 2 Sep 2020, Shift 1 · Q52Newton's Sums · Easy · Single correct
  10. 2 Sep 2020, Shift 1 · Q53Conversion of sin(θ) + i cos(θ) · Medium · Single correct
  11. 2 Sep 2020, Shift 2 · Q52Equation Formation · Medium · Single correct
  12. 2 Sep 2020, Shift 2 · Q53Square Root via Polar Form · Medium · Single correct
  13. 3 Sep 2020, Shift 1 · Q51Nature of Roots · Medium · Single correct
  14. 3 Sep 2020, Shift 1 · Q52Root-Coefficient Relation · Medium · Single correct
  15. 3 Sep 2020, Shift 1 · Q71Smallest Integer Power for Real/Imaginary · Easy · Numerical value
  16. 3 Sep 2020, Shift 2 · Q52Exactly one root in interval · Medium · Single correct
  17. 3 Sep 2020, Shift 2 · Q53Principal Argument Arithmetic · Hard · Single correct
  18. 4 Sep 2020, Shift 1 · Q53Open the question · Hard · Single correct
  19. 4 Sep 2020, Shift 1 · Q56Root-Coefficient Relation · Medium · Single correct
  20. 4 Sep 2020, Shift 2 · Q52Root-Coefficient Relation · Medium · Single correct
  21. 4 Sep 2020, Shift 2 · Q53Cube Roots of Unity · Medium · Single correct
  22. 5 Sep 2020, Shift 1 · Q52Geometric Rotation · Medium · Single correct
  23. 5 Sep 2020, Shift 1 · Q53Roots of Modulus Quadratics · Easy · Single correct
  24. 6 Sep 2020, Shift 2 · Q52Root-Coefficient Relation · Medium · Single correct
  25. 6 Sep 2020, Shift 2 · Q53Modulus and Argument · Medium · Single correct

JEE Main 20171 question

  1. 2 Apr 2017 (offline) · Q62Integer Roots Condition · Hard · 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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