JEE Main 2025 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 2 April 2025, Shift 2, Maths Q20

Question 20 of 75 in this shift, Maths question 20 of 25, Section A.

Let

f : [1, \infty) \to [2, \infty)

be a differentiable function. If

10\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9

for all

x \geq 1

, then the value of

f(3)

is :

(1) $18$
(2) $22$
(3) $26$
(4) $32$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Leibniz Rule
Idea tested: Solving Integral Equations

Same idea in other shifts

Asked 4× in all

4 Apr 2026, Shift 2 · Q25Let $f$ be a twice differentiable function such that $f(x)=\int_0^x\tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt$ ,…HardNumerical value
5 Apr 2026, Shift 2 · Q19Let $f:[1,\infty)\to\mathbf{R}$ be a differentiable function defined as $f(x)=\int_1^x f(t)\,dt+(1-x)(\log_e x-1)+e$ . Then the value of…HardSingle correct
9 Apr 2024, Shift 2 · Q13Let $\int_0^x\sqrt{1-(y'(t))^2}\,dt=\int_0^x y(t)\,dt,\ 0\le x\le 3,\ y\ge0,\ y(0)=0$ . Then at $x=2$ , $y''+y+1$ is equal toHardSingle 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.