JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 25 July 2022, Shift 2, Maths Q26

Question 26 of 90 in this shift, Maths question 26 of 30, Section B.

Let

f

be a twice differentiable function on

\mathbb{R}

. If

f'(0)=4

and

f(x)+\int_0^x(x-t)f'(t)\,dt=\left(e^{2x}+e^{-2x}\right)\cos 2x+\frac{2}{a}x

, then

(2a+1)^5a^2

is equal to ___________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 11× 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
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
1 Feb 2024, Shift 2 · Q24Let $f:(0,\infty)\to\mathbf{R}$ and $F(x)=\int_0^x t f(t)\,dt$ . If $F(x^2)=x^4+x^5$ , then $\sum_{r=1}^{12}f(r^2)$ is equal to ________.MediumNumerical value
10 Apr 2023, Shift 1 · Q9Let $f$ be a differentiable function such that $x^2f(x)-x=4\int_0^x tf(t)\,dt$ , $f(1)=\frac{2}{3}$ . Then $18f(3)$ is equal toMediumSingle correct
10 Apr 2023, Shift 2 · Q11Let $f$ be a continuous function satisfying $\int_0^{t^2} (f(x) + x^2)\, dx = \frac{4}{3}t^3,\ \forall t > 0$ . Then…MediumSingle correct
27 Jul 2022, Shift 2 · Q28Let f be a differentiable function satisfying $f(x) = \frac{2}{\sqrt{3}} \int_0^{\sqrt{3}} f\left(\frac{\lambda^2 x}{3}\right) d\lambda$ ,…HardNumerical value

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.