JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 April 2024, Shift 2, Maths Q22

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

Let

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

\alpha

and

\beta

be the smallest and largest elements of the set S, respectively, then

3\left((\alpha-2)^2+(\beta-1)^2\right)

equals __________

Official answer

NTA final key.

Chapter: Complex Numbers and Quadratic Equations
Topic: Quadratic Roots
Idea tested: Nature of Roots

Same idea in other shifts

Asked 9× in all

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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.