JEE Main 2026 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 April 2026, Shift 2, Maths Q25

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

Let

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

x\in\left(-\frac\pi2,\frac\pi2\right)

. Then

f''\left(\frac\pi6\right)+12f'\left(-\frac\pi6\right)+f\left(\frac\pi6\right)

is equal to ________

Official answer

NTA final key.

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

Same idea in other shifts

Asked 4× in all

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
2 Apr 2025, Shift 2 · Q20Let $f : [1, \infty) \to [2, \infty)$ be a differentiable function. If $10\int_1^x f(t)\,\mathrm{d}t = 5xf(x) - x^5 - 9$ for all…MediumSingle 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.