Learn

Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 September 2020, Shift 1, Maths Q52

Question 52 of 75 in this shift, Maths question 2 of 25.

If α\alpha and β\beta are the roots of the equation x2+px+2=0x^2+px+2=0 and 1α\frac{1}{\alpha} and 1β\frac{1}{\beta} are the roots of the equation 2x2+2qx+1=02x^2+2qx+1=0, then (α−1α)(β−1β)(α+1β)(β+1α)\left(\alpha-\frac{1}{\alpha}\right)\left(\beta-\frac{1}{\beta}\right)\left(\alpha+\frac{1}{\beta}\right)\left(\beta+\frac{1}{\alpha}\right) is equal to :
  1. (1)94(9−p2)\frac{9}{4}(9-p^2)Official answer
  2. (2)94(9+p2)\frac{9}{4}(9+p^2)
  3. (3)94(9+q2)\frac{9}{4}(9+q^2)
  4. (4)94(9−q2)\frac{9}{4}(9-q^2)

Official answer

Option 1

NTA final key (Sep 2020).

Chapter
Complex Numbers and Quadratic Equations
Topic
Quadratic Roots
Idea tested
Root-Coefficient Relation

Same idea in other shifts

Asked 15× in all
  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. 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
  3. 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
  4. 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
  5. 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
  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. 6 Apr 2024, Shift 1 · Q21Let x1,x2,x3,x4x_1, x_2, x_3, x_4 be the solution of the equation 4x4+8x3−17x2−12x+9=04x^4+8x^3-17x^2-12x+9=0 and…HardNumerical value
  8. 1 Feb 2024, Shift 2 · Q4Let α\alpha and β\beta be the roots of the equation px2+qx−r=0px^2+qx-r=0, where p≠0p\neq 0. If pp, qq and rr be the consecutive terms of a…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.