JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 26 February 2021, Shift 2, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

Let

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 :

(1) $2e^{(e^x-1)}-1$ Official answer
(2) $e^{(e^x-1)}$
(3) $e^{e^x}-1$
(4) $2e^{e^x}-1$

Official answer

Option 1

NTA final key.

Chapter: Differential Equations
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
28 Jul 2022, Shift 1 · Q20The 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 :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.