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Saturday, 31 October

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:R→Rf:\mathbf{R}\to\mathbf{R} be such that f(xy)=f(x)f(y)f(xy)=f(x)f(y), for all x,y∈Rx,y\in\mathbf{R} and f(0)≠0f(0)\neq0. Let g:[1,∞)→Rg:[1,\infty)\to\mathbf{R} be a differentiable function such that x2g(x)=∫1x(t2f(t)−tg(t))dtx^2g(x)=\int_1^x\left(t^2f(t)-tg(t)\right)dt. Then g(2)g(2) is equal to :
  1. (1)138\frac{13}{8}
  2. (2)1116\frac{11}{16}
  3. (3)1532\frac{15}{32}Official answer
  4. (4)1764\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 3× in all
  1. 28 Jul 2022, Shift 1 · Q20The minimum value of the twice differentiable function f(x)=∫0xex−tf′(t) dt−(x2−x+1)ex, x∈Rf(x)=\int_0^x e^{x-t}f'(t)\,dt-(x^2-x+1)e^x,\ x\in\mathbf{R}, is :HardSingle correct
  2. 26 Feb 2021, Shift 2 · Q67Let f(x)=∫0xetf(t) dt+exf(x)=\int_0^x e^t f(t)\,dt + e^x be a differentiable function for all x∈Rx \in \mathbf{R}. Then f(x)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.