JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q8

Question 8 of 90 in this shift, Maths question 8 of 30, Section A.

The set of all values of k for which

(\tan^{-1}x)^3 + (\cot^{-1}x)^3 = k\pi^3,\ x \in \mathbf{R}

, is the interval :

(1) $\left[\frac{1}{32}, \frac{7}{8}\right)$ Official answer
(2) $\left(\frac{1}{24}, \frac{13}{16}\right)$
(3) $\left[\frac{1}{48}, \frac{13}{16}\right]$
(4) $\left[\frac{1}{32}, \frac{9}{8}\right)$

Official answer

Option 1

NTA final key (2022 Session 1).

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Complementary Identities

Same idea in other shifts

Asked 7× in all

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26 Jul 2022, Shift 2 · Q16If $0<x<\frac{1}{\sqrt{2}}$ and $\frac{\sin^{-1}x}{\alpha}=\frac{\cos^{-1}x}{\beta}$ , then a value of…MediumSingle correct
30 Jun 2022, Shift 1 · Q10Let m and M respectively be the minimum and the maximum values of $f(x) = \sin^{-1}2x + \sin 2x + \cos^{-1}2x + \cos 2x$ ,…MediumSingle correct
27 Aug 2021, Shift 1 · Q76If $(\sin^{-1}x)^2-(\cos^{-1}x)^2=a$ ; $0<x<1$ , $a\neq 0$ , then the value of $2x^2-1$ is :MediumSingle correct
26 Feb 2021, Shift 1 · Q76If $\frac{\sin^{-1}x}{a}=\frac{\cos^{-1}x}{b}=\frac{\tan^{-1}y}{c}$ ; $0<x<1$ , then the value of $\cos\left(\frac{\pi c}{a+b}\right)$ is :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.