JEE Main 2022 · MathsMultiple choiceSingle correctHardCalculation

JEE Main 28 July 2022, Shift 2, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

Let

x(t)=2\sqrt{2}\cos t\sqrt{\sin 2t}

and

y(t)=2\sqrt{2}\sin t\sqrt{\sin 2t},\ t\in\left(0,\frac{\pi}{2}\right)

. Then

\frac{1+\left(\frac{dy}{dx}\right)^2}{\frac{d^2y}{dx^2}}

t=\frac{\pi}{4}

is equal to :

(1) $\frac{-2\sqrt{2}}{3}$
(2) $\frac{2}{3}$
(3) $\frac{1}{3}$
(4) $\frac{-2}{3}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Chain Rule in Parametric Differentiation

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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.