JEE Main 9 April 2024, Shift 2, Maths Q11

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

The integral

\int_{1/4}^{3/4}\cos\left(2\cot^{-1}\sqrt{\frac{1-x}{1+x}}\right)dx

is equal to

(1) $1/4$
(2) $-1/4$ Official answer
(3) $1/2$
(4) $-1/2$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Inverse Trig Identities
Idea tested: Multiple Angle Inverse ID

Same idea in other shifts

Asked 2× in all

26 Aug 2021, Shift 1 · Q68Let $f(x) = \cos\left(2\tan^{-1}\sin\left(\cot^{-1}\sqrt{\frac{1-x}{x}}\right)\right)$ , $0 < x < 1$ . Then :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 108 of the 174 JEE Main shifts held from 2017 to 2026.