JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 28 July 2022, Shift 1, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

The minimum value of the twice differentiable function

f(x)=\int_0^x e^{x-t}f'(t)\,dt-(x^2-x+1)e^x,\ x\in\mathbf{R}

, is :

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

Official answer

Option 1

NTA final key (2022 Session 2).

Chapter: Application of Derivatives
Topic: Linear Differential Equations
Idea tested: LDEs Formed via Leibniz Integral Rule

Same idea in other shifts

Asked 3× in all

6 Apr 2026, Shift 2 · Q18Let $f:\mathbf{R}\to\mathbf{R}$ be such that $f(xy)=f(x)f(y)$ , for all $x,y\in\mathbf{R}$ and $f(0)\neq0$ . Let $g:[1,\infty)\to\mathbf{R}$ …HardSingle correct
26 Feb 2021, Shift 2 · Q67Let $f(x)=\int_0^x e^t f(t)\,dt + e^x$ be a differentiable function for all $x \in \mathbf{R}$ . Then $f(x)$ equals :MediumSingle 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.