JEE Main 2021 · MathsMultiple choiceSingle correctEasyApplication

JEE Main 26 August 2021, Shift 2, Maths Q61

Question 61 of 90 in this shift, Maths question 1 of 30, Section A.

The domain of the function

\mathrm{cosec}^{-1}\left(\frac{1+x}{x}\right)

is :

(1) $\left[-\frac{1}{2},\infty\right)-\{0\}$ Official answer
(2) $\left(-\frac{1}{2},\infty\right)-\{0\}$
(3) $\left[-\frac{1}{2},0\right)\cup[1,\infty)$
(4) $\left(-1,-\frac{1}{2}\right]\cup(0,\infty)$

Official answer

Option 1

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Domains
Idea tested: Sec-1 and Csc-1 Domains

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.