JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q70

Question 70 of 90 in this shift, Maths question 10 of 30, Section A.

y(x) = \tan x - \int_0^{2x} (x^2 - xt + 1) \sin t\, dt

, then at

x = \frac{\pi}{3}

, the value of

2y''' - y''

is equal to

(1)158Official answer
(2) $159 - 4\sqrt{3}$
(3)126
(4) $127 - 4\sqrt{3}$

Official answer

Option 1

NTA final key.

Chapter: Continuity and Differentiability
Topic: Leibniz Rule
Idea tested: Higher Order Derivatives

Same topic in other shifts

All Leibniz Rule questions

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2 Apr 2025, Shift 2 · Q20Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9$ for all…MediumSingle correct
4 Apr 2024, Shift 2 · Q9Let $f(x)=\int_0^x\left(t+\sin\left(1-e^t\right)\right)dt,\ x\in\mathbb{R}$ . Then, $\lim_{x\to0}\frac{f(x)}{x^3}$ is equal toHardSingle correct
9 Apr 2024, Shift 2 · Q9…HardSingle correct
9 Apr 2024, Shift 2 · Q13Let $\int_0^x\sqrt{1-(y'(t))^2}\,dt=\int_0^x y(t)\,dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0$ . Then at $x=2$ , $y''+y+1$ is equal toHardSingle 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.