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JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2026, Shift 2, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

Let

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}

be a differentiable function such that

x^2g(x)=\int_1^x\left(t^2f(t)-tg(t)\right)dt

. Then

g(2)

is equal to :

(1) $\frac{13}{8}$
(2) $\frac{11}{16}$
(3) $\frac{15}{32}$ Official answer
(4) $\frac{17}{64}$

Official answer

Option 3

NTA final key.

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

Same idea in other shifts

Asked 2× in all

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 42 of the 174 JEE Main shifts held from 2017 to 2026.