JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 6 April 2024, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

\int_0^{\pi/4}\frac{\cos^2 x\ \sin^2 x}{(\cos^3 x+\sin^3 x)^2}dx

is equal to

(1) $1/3$
(2) $1/6$ Official answer
(3) $1/9$
(4) $1/12$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Trigonometric Substitution

Same idea in other shifts

Asked 3× in all

10 Apr 2023, Shift 1 · Q8If $I(x)=\int e^{\sin^2x}(\cos x\sin 2x-\sin x)\,dx$ and $I(0)=1$ , then $I\left(\frac{\pi}{3}\right)$ is equal toHardSingle correct
3 Sep 2020, Shift 2 · Q61If the value of the integral $\int_0^{1/2} \frac{x^2}{(1 - x^2)^{3/2}} dx$ is $\frac{k}{6}$ , then k is equal to :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.