JEE Main 2026 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 2 April 2026, Shift 1, Maths Q17

Question 17 of 75 in this shift, Maths question 17 of 25, Section A.

If the curve

y=f(x)

passes through the point

(1, e)

and satisfies the differential equation

dy=y(2+\log_e x)\,dx

x>0

, then

f(e)

is equal to :

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

Official answer

Option 3

NTA final key.

Chapter: Differential Equations
Topic: Variable Separable Form
Idea tested: Direct Integration

Same idea in other shifts

Asked 3× in all

30 Jun 2022, Shift 1 · Q12Let $\frac{dy}{dx} = \frac{ax - by + a}{bx + cy + a}$ , a, b, $c \in \mathbf{R}$ , represents a circle with center $(\alpha, \beta)$ . Then,…HardSingle correct
31 Aug 2021, Shift 2 · Q70If $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y}\log_e 2}$ , $y(0) = 0$ , then for $y = 1$ , the value of $x$ …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.