JEE Main 2022 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 27 June 2022, Shift 1, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

\sin^{-1}\left(\sin\frac{2\pi}{3}\right)+\cos^{-1}\left(\cos\frac{7\pi}{6}\right)+\tan^{-1}\left(\tan\frac{3\pi}{4}\right)

is equal to :

(1) $\frac{11\pi}{12}$ Official answer
(2) $\frac{17\pi}{12}$
(3) $\frac{31\pi}{12}$
(4) $-\frac{3\pi}{4}$

Official answer

Option 1

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Domains
Idea tested: Evaluating arcsin(sin x) Outside Principal Branch

Same topic in other shifts

All Inverse Trig Domains questions

4 Apr 2026, Shift 1 · Q1Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\cos^{-1}\left(\frac{4x+2[x]}{3}\right)$ is…MediumSingle correct
6 Apr 2026, Shift 1 · Q1Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\sin^{-1}\left(\frac{x+[x]}{3}\right)$ is…MediumSingle correct
4 Apr 2025, Shift 2 · Q1Let the domains of the functions $f(x)=\log_4\log_3\log_7(8-\log_2(x^2+4x+5))$ and $g(x)=\sin^{-1}\left(\frac{7x+10}{x-2}\right)$ be…MediumSingle correct
9 Apr 2024, Shift 1 · Q1If the domain of the function $f(x)=\sin^{-1}\left(\frac{x-1}{2x+3}\right)$ is $\mathbf{R}-(\alpha,\beta)$ , then $12\alpha\beta$ is equal…MediumSingle correct
28 Jul 2022, Shift 1 · Q2Considering only the principal values of the inverse trigonometric functions, the domain of the function…EasySingle correct
29 Jul 2022, Shift 2 · Q19The domain of the function $f(x)=\sin^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right)$ 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.