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Friday, 9 October

JEE Main Maths · Class 11

Complex Numbers and Quadratic Equations: JEE Main previous year questions

Complex Numbers and Quadratic Equations had 79 questions in the 42 JEE Main shifts Lumi analysed, about 1.6 a shift, asked in 42 of 42 shifts. It ranks 3 of 22 Maths chapters by questions; 24% of its questions were hard.

Questions
79
in 42 of 42 shifts
A shift, on average
1.6
of 25 Maths questions
Since 2024
+0.4
1.5 a shift in 2017–23, 1.9 in 2024–26
Numerical answer
15
19% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
09181’178’206’218’227’2318’2415’2516’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20171
  • 20208
  • 20216
  • 20228
  • 20237
  • 202418
  • 202515
  • 202616
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

7 topics and 31 distinct ideas; 13 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

12 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
13 repeat

Study it on Lumi

Complex Numbers and Quadratic Equations: the interactive lesson

Every question

All 79 Complex Numbers and Quadratic Equations questions

Newest first. Each opens with its options and the official answer.

2026 16 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

2025 15 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

2024 18 questions

  1. 6 Apr 2024, Shift 2 · Q3If z1,z2z_1, z_2 are two distinct complex number such that ∣z1−2z212−z1z2ˉ∣=2\left|\frac{z_1-2z_2}{\frac{1}{2}-z_1\bar{z_2}}\right|=2, thenHardSingle correct
  2. 6 Apr 2024, Shift 2 · Q21Let α,β\alpha,\beta be roots of x2+2x−8=0x^2+\sqrt{2}x-8=0. If Un=αn+βnU_n=\alpha^n+\beta^n, then U10+2U92U8\frac{U_{10}+\sqrt{2}U_9}{2U_8} is equal to ________.EasyNumerical value
  3. 8 Apr 2024, Shift 1 · Q2Let zz be a complex number such that ∣z+2∣=1|z+2|=1 and Im(z+1z+2)=15\mathrm{Im}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}. Then the value of…MediumSingle correct
  4. 8 Apr 2024, Shift 1 · Q3The sum of all the solutions of the equation (8)2x−16⋅(8)x+48=0(8)^{2x}-16\cdot(8)^x+48=0 is :EasySingle correct
  5. 8 Apr 2024, Shift 1 · Q6If the set R={(a,b):a+5b=42,a,b∈N}R=\{(a,b): a+5b=42, a,b\in\mathbb{N}\} has mm elements and ∑n=1m(1−in!)=x+iy\sum_{n=1}^{m}\left(1-i^{n!}\right)=x+iy, where i=−1i=\sqrt{-1},…MediumSingle correct
  6. 9 Apr 2024, Shift 1 · Q2Let α,β\alpha,\beta be the roots of the equation x2+22 x−1=0x^2+2\sqrt{2}\,x-1=0. The quadratic equation, whose roots are α4+β4\alpha^4+\beta^4 and…MediumSingle correct
  7. 9 Apr 2024, Shift 1 · Q22The sum of the square of the modulus of the elements in the set…MediumNumerical value
  8. 9 Apr 2024, Shift 2 · Q2Let zz be a complex number such that the real part of z−2iz+2i\frac{z-2i}{z+2i} is zero. Then, the maximum value of ∣z−(6+8i)∣|z-(6+8i)| is equal toMediumSingle correct
  9. 9 Apr 2024, Shift 2 · Q3Let α,β; α>β\alpha, \beta;\ \alpha>\beta, be the roots of the equation x2−2x−3=0x^2-\sqrt{2}x-\sqrt{3}=0. Let Pn=αn−βn, n∈NP_n=\alpha^n-\beta^n,\ n\in\mathbb{N}.…MediumSingle correct
  10. 29 Jan 2024, Shift 1 · Q3If z=12−2iz=\frac{1}{2}-2i is such that ∣z+1∣=αz+β(1+i)|z+1|=\alpha z+\beta(1+i), i=−1i=\sqrt{-1} and α,β∈R\alpha,\beta\in\mathbb{R}, then α+β\alpha+\beta is…EasySingle correct
  11. 29 Jan 2024, Shift 1 · Q21Let α,β\alpha,\beta be the roots of the equation x2−x+2=0x^2-x+2=0 with Im(α)>Im(β)Im(\alpha)>Im(\beta). Then α6+α4+β4−5α2\alpha^6+\alpha^4+\beta^4-5\alpha^2 is…MediumNumerical value
  12. 30 Jan 2024, Shift 2 · Q2If zz is a complex number, then the number of common roots of the equations z1985+z100+1=0z^{1985} + z^{100} + 1 = 0 and z3+2z2+2z+1=0z^3 + 2z^2 + 2z + 1 = 0,…MediumSingle correct
  13. 31 Jan 2024, Shift 1 · Q2Let S be the set of postive integral values of aa for which ax2+2(a+1)x+9a+4x2−8x+32<0, ∀x∈R\frac{ax^2+2(a+1)x+9a+4}{x^2-8x+32}<0,\ \forall x\in\mathbb{R}. Then, the…EasySingle correct
  14. 31 Jan 2024, Shift 1 · Q7Let aa be the sum of all coefficients in the expansion of (1−2x+2x2)2023(3−4x2+2x3)2024(1-2x+2x^2)^{2023}(3-4x^2+2x^3)^{2024} and…HardSingle correct
  15. 31 Jan 2024, Shift 1 · Q8For 0<c<b<a0<c<b<a, let (a+b−2c)x2+(b+c−2a)x+(c+a−2b)=0(a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 and α≠1\alpha\neq1 be one of its root. Then, among the two statements (I) If…MediumTwo statements
  16. 31 Jan 2024, Shift 1 · Q22If α\alpha denotes the number of solutions of ∣1−i∣x=2x|1-i|^x=2^x and β=(∣z∣arg⁡(z))\beta=\left(\frac{|z|}{\arg(z)}\right), where…MediumNumerical value
  17. 31 Jan 2024, Shift 2 · Q3Let z1z_1 and z2z_2 be two complex numbers such that z1+z2=5z_1+z_2=5 and z13+z23=20+15iz_1^3+z_2^3=20+15i. Then, ∣z14+z24∣|z_1^4+z_2^4| equals -HardSingle correct
  18. 31 Jan 2024, Shift 2 · Q24Let a,b,ca, b, c be the lengths of three sides of a triangle satisfying the condition (a2+b2)x2−2b(a+c)x+(b2+c2)=0(a^2+b^2)x^2-2b(a+c)x+(b^2+c^2)=0. If the set of all…HardNumerical value

2023 7 questions

  1. 6 Apr 2023, Shift 1 · Q2The sum of all the roots of the equation ∣x2−8x+15∣−2x+7=0|x^2-8x+15|-2x+7=0 is:MediumSingle correct
  2. 8 Apr 2023, Shift 2 · Q2Let A={θ∈(0,2π):1+2isin⁡θ1−isin⁡θ is purely imaginary}A = \left\{\theta \in (0, 2\pi) : \frac{1 + 2i\sin\theta}{1 - i\sin\theta} \text{ is purely imaginary}\right\}. Then the sum of the…MediumSingle correct
  3. 8 Apr 2023, Shift 2 · Q22Let mm and nn be the numbers of real roots of the quadratic equations x2−12x+[x]+31=0x^2 - 12x + [x] + 31 = 0 and x2−5∣x+2∣−4=0x^2 - 5|x + 2| - 4 = 0…HardNumerical value
  4. 11 Apr 2023, Shift 1 · Q14Let w1w_1 be the point obtained by the rotation of z1=5+4iz_1 = 5 + 4i about the origin through a right angle in the anticlockwise direction,…MediumSingle correct
  5. 11 Apr 2023, Shift 1 · Q24If aa and bb are the roots of the equation x2−7x−1=0x^2 - 7x - 1 = 0, then the value of…MediumNumerical value
  6. 13 Apr 2023, Shift 2 · Q2Let S={z∈C:zˉ=i(z2+Re(zˉ))}S=\{z\in\mathbb{C}: \bar{z}=i(z^2+Re(\bar{z}))\}. Then ∑z∈S∣z∣2\sum_{z\in S}|z|^2 is equal toHardSingle correct
  7. 13 Apr 2023, Shift 2 · Q3Let α,β\alpha, \beta be the roots of the equation x2−2x+2=0x^2-\sqrt{2}x+2=0. Then α14+β14\alpha^{14}+\beta^{14} is equal toMediumSingle correct

2022 8 questions

  1. 25 Jul 2022, Shift 1 · Q2If α, β, γ, δ\alpha,\ \beta,\ \gamma,\ \delta are the roots of the equation x4+x3+x2+x+1=0x^4+x^3+x^2+x+1=0, then…MediumSingle correct
  2. 28 Jul 2022, Shift 1 · Q15Let S1={z1∈C:∣z1−3∣=12}S_1=\left\{z_1\in\mathbf{C}:|z_1-3|=\frac{1}{2}\right\} and S2={z2∈C:∣z2−∣z2+1∣∣=∣z2+∣z2−1∣∣}S_2=\{z_2\in\mathbf{C}:|z_2-|z_2+1||=|z_2+|z_2-1||\}. Then, for…HardSingle correct
  3. 28 Jul 2022, Shift 1 · Q26For p,q∈Rp,q\in\mathbf{R}, consider the real valued function f(x)=(x−p)2−q, x∈Rf(x)=(x-p)^2-q,\ x\in\mathbf{R} and q>0q>0. Let a1,a2,a3a_1,a_2,a_3 and a4a_4 be in…MediumNumerical value
  4. 28 Jul 2022, Shift 1 · Q30The sum of all real values of xx for which 3x2−9x+17x2+3x+10=5x2−7x+193x2+5x+12\frac{3x^2-9x+17}{x^2+3x+10}=\frac{5x^2-7x+19}{3x^2+5x+12} is equal to __________.MediumNumerical value
  5. 24 Jun 2022, Shift 1 · Q1Let A={z∈C:1≤∣z−(1+i)∣≤2}A = \{z \in \mathbb{C} : 1 \le |z-(1+i)| \le 2\} and B={z∈A:∣z−(1−i)∣=1}B = \{z \in A : |z-(1-i)| = 1\}. Then, B :MediumSingle correct
  6. 24 Jun 2022, Shift 1 · Q7If the sum of the squares of the reciprocals of the roots α\alpha and β\beta of the equation 3x2+λx−1=03x^2+\lambda x-1=0 is 15, then…MediumSingle correct
  7. 29 Jun 2022, Shift 1 · Q8Let α\alpha and β\beta be the roots of the equation x2+(2i−1)=0x^2 + (2i - 1) = 0. Then, the value of ∣α8+β8∣|\alpha^8 + \beta^8| is equal to :MediumSingle correct
  8. 29 Jun 2022, Shift 1 · Q21Let S={z∈C:∣z−2∣≤1,z(1+i)+zˉ(1−i)≤2}S = \{z \in \mathbf{C} : |z - 2| \le 1, z(1 + i) + \bar{z}(1 - i) \le 2\}. Let ∣z−4i∣|z - 4i| attains minimum and maximum values,…HardNumerical value

2021 6 questions

  1. 3 Aug 2021, Shift 2 · Q62If the equations 2x2+kx−5=02x^2 + kx - 5 = 0 and x2−3x−4=0x^2 - 3x - 4 = 0 have one root in common, then a value of 'kk' isEasySingle correct
  2. 25 Jul 2021, Shift 1 · Q72The number of real roots of the equation e6x−e4x−2e3x−12e2x+ex+1=0e^{6x}-e^{4x}-2e^{3x}-12e^{2x}+e^x+1=0 is :HardSingle correct
  3. 25 Jul 2021, Shift 1 · Q90If α,β\alpha,\beta are roots of the equation x2+5(2)x+10=0x^2+5(\sqrt2)x+10=0, α>β\alpha>\beta and Pn=αn−βnP_n=\alpha^n-\beta^n for each positive integer n,…MediumNumerical value
  4. 16 Mar 2021, Shift 2 · Q76The least value of ∣z∣|z| where zz is complex number which satisfies the inequality…MediumSingle correct
  5. 18 Mar 2021, Shift 1 · Q62If the equation a∣z∣2+αˉz+αzˉ+d=0a|z|^2 + \bar{\alpha}z + \alpha\bar{z} + d = 0 represents a circle where a, d are real constants, then which of the…MediumSingle correct
  6. 18 Mar 2021, Shift 1 · Q81Let z1,z2z_1, z_2 be the roots of the equation z2+az+12=0z^2+az+12=0 and z1,z2z_1, z_2 form an equilateral triangle with origin. Then, the value of…MediumNumerical value

2020 8 questions

  1. 8 Jan 2020, Shift 1 · Q52If the equation, x2+bx+45=0x^2+bx+45=0 (b∈Rb\in R) has conjugate complex roots and they satisfy ∣z+1∣=210|z+1|=2\sqrt{10}, then :MediumSingle correct
  2. 8 Jan 2020, Shift 1 · Q71The least positive value of 'a' for which the equation, 2x2+(a−10)x+332=2a2x^2+(a-10)x+\frac{33}{2}=2a has real roots is ______.EasyNumerical value
  3. 9 Jan 2020, Shift 2 · Q52Let a,b∈Ra,b\in\mathbf{R}, a≠0a\ne0 be such that the equation, ax2−2bx+5=0ax^2-2bx+5=0 has a repeated root α\alpha, which is also a root of the…MediumSingle correct
  4. 9 Jan 2020, Shift 2 · Q53If zz be a complex number satisfying ∣Re(z)∣+∣Im(z)∣=4|\mathrm{Re}(z)|+|\mathrm{Im}(z)|=4, then ∣z∣|z| cannot be :MediumSingle correct
  5. 2 Sep 2020, Shift 1 · Q52Let α\alpha and β\beta be the roots of the equation, 5x2+6x−2=05x^{2}+6x-2=0. If Sn=αn+βnS_n=\alpha^{n}+\beta^{n}, n=1,2,3,…n=1, 2, 3, \ldots, then :EasySingle correct
  6. 2 Sep 2020, Shift 1 · Q53The value of (1+sin⁡2π9+icos⁡2π91+sin⁡2π9−icos⁡2π9)3\left(\frac{1+\sin\frac{2\pi}{9}+i\cos\frac{2\pi}{9}}{1+\sin\frac{2\pi}{9}-i\cos\frac{2\pi}{9}}\right)^{3} is :MediumSingle correct
  7. 6 Sep 2020, Shift 2 · Q52If α\alpha and β\beta are the roots of the equation 2x(2x+1)=12x(2x+1)=1, then β\beta is equal to :MediumSingle correct
  8. 6 Sep 2020, Shift 2 · Q53Let z=x+iyz=x+iy be a non-zero complex number such that z2=i∣z∣2z^2=i|z|^2, where i=−1i=\sqrt{-1}, then zz lies on the :MediumSingle correct

2017 1 questions

  1. 2 Apr 2017 (offline) · Q62If, for a positive integer n, the quadratic equation, x(x+1)+(x+1)(x+2)+…+(x+n−1‾)(x+n)=10nx(x+1)+(x+1)(x+2)+\ldots+(x+\overline{n-1})(x+n)=10n has two consecutive integral…HardSingle correct

Pattern: Asked most years.