JEE Main 6 April 2024, Shift 1, Maths Q30

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

For

n \in \mathbb{N}

, if

\cot^{-1}3+\cot^{-1}4+\cot^{-1}5+\cot^{-1}n=\frac{\pi}{4}

, then

n

is equal to __________.

Official answer

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Piecewise cot-1 to tan-1 Conversion

Same idea in other shifts

Asked 2× in all

4 Apr 2026, Shift 2 · Q20The integral $\int_0^1\cot^{-1}\left(1+x+x^2\right)dx$ is equal to: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.