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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

If α,β\alpha, \beta are the roots of the equation x2−(5+3log⁡35−5log⁡53)+3(3(log⁡35)13−5(log⁡53)23−1)=0x^2 - \left(5 + 3^{\sqrt{\log_3 5}} - 5^{\sqrt{\log_5 3}}\right) + 3\left(3^{(\log_3 5)^{\frac{1}{3}}} - 5^{(\log_5 3)^{\frac{2}{3}}} - 1\right) = 0, then the equation, whose roots are α+1β\alpha + \frac{1}{\beta} and β+1α\beta + \frac{1}{\alpha}, is :
  1. (1)3x2−20x−12=03x^2 - 20x - 12 = 0
  2. (2)3x2−10x−4=03x^2 - 10x - 4 = 0
  3. (3)3x2−10x+2=03x^2 - 10x + 2 = 0
  4. (4)3x2−20x+16=03x^2 - 20x + 16 = 0

Official answer

Dropped by NTA (marks given to all)

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Quadratic Roots
Idea tested
Transformation of Roots

Same idea in other shifts

Asked 2× in all
  1. 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
  2. 28 Jul 2022, Shift 2 · Q62Let α,β\alpha,\beta be the roots of the equation x2−2 x+6=0x^2-\sqrt{2}\,x+\sqrt{6}=0 and 1α2+1, 1β2+1\frac{1}{\alpha^2}+1,\ \frac{1}{\beta^2}+1 be the roots…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.