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JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 8 April 2023, Shift 1, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let

f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}

,

x\in[0,\pi]-\left\{\frac{\pi}{4}\right\}

. Then

f\left(\frac{7\pi}{12}\right)f''\left(\frac{7\pi}{12}\right)

is equal to

(1) $\frac{-2}{3}$
(2) $\frac{-1}{3\sqrt{3}}$
(3) $\frac{2}{3\sqrt{3}}$
(4) $\frac{2}{9}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Continuity and Differentiability
Topic: Chain Rule
Idea tested: Second Derivative of Composite Functions

Same idea in other shifts

Asked 2× in all

5 Apr 2024, Shift 2 · Q20If $y(\theta) = \frac{2\cos\theta + \cos 2\theta}{\cos 3\theta + 4\cos 2\theta + 5\cos\theta + 2}$ , then at $\theta = \frac{\pi}{2}$ ,…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.