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JEE Main 2024 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 31 January 2024, Shift 1, Maths Q26

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

Let

f:\mathbb{R}\to\mathbb{R}

be a function defined by

f(x)=\frac{4^x}{4^x+2}

and

M=\int_{f(a)}^{f(1-a)}x\sin^4\left(x(1-x)\right)dx,\ N=\int_{f(a)}^{f(1-a)}\sin^4\left(x(1-x)\right)dx;\ a\neq\frac{1}{2}

. If

\alpha M=\beta N,\ \alpha,\beta\in\mathbb{N}

, then the least value of

\alpha^2+\beta^2

is equal to ______

Official answer

5

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: King's Property

Same idea in other shifts

Asked 3× in all

3 Apr 2025, Shift 2 · Q18The integral $\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x}$ is equal toMediumSingle correct
8 Apr 2025, Shift 2 · Q18Let $f(x)$ be a positive function and $I_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx$ and…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.