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Saturday, 31 October

JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 30 January 2024, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let α,β∈N\alpha,\beta\in N be roots of the equation x2−70x+λ=0x^2-70x+\lambda=0, where λ2,λ3∉N\frac{\lambda}{2},\frac{\lambda}{3}\notin N. If λ\lambda assumes the minimum possible value, then (α−1+β−1)(λ+35)∣α−β∣\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|} is equal to :

Official answer

60

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
Quadratic Roots
Idea tested
Integer Roots Condition

Same idea in other shifts

Asked 2× in all
  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

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.