JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q1

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

The domain of the function

f(x) = \sin^{-1}[2x^2 - 3] + \log_2\left(\log_{\frac{1}{2}}(x^2 - 5x + 5)\right)

, where [t] is the greatest integer function, is :

(1) $\left(-\sqrt{\frac{5}{2}}, \frac{5-\sqrt{5}}{2}\right)$
(2) $\left(\frac{5-\sqrt{5}}{2}, \frac{5+\sqrt{5}}{2}\right)$
(3) $\left(1, \frac{5-\sqrt{5}}{2}\right)$ Official answer
(4) $\left[1, \frac{5+\sqrt{5}}{2}\right)$

Official answer

Option 3

NTA final key.

Chapter: Relations and Functions
Topic: Functions and Domain
Idea tested: Inverse Trig Function Domain

Same idea in other shifts

Asked 6× in all

3 Apr 2025, Shift 1 · Q2If the domain of the function $f(x) = \log_e\left(\frac{2x-3}{5+4x}\right) + \sin^{-1}\left(\frac{4+3x}{2-x}\right)$ is $[\alpha, \beta)$ ,…MediumSingle correct
8 Apr 2025, Shift 2 · Q21Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of…MediumNumerical value
4 Apr 2024, Shift 1 · Q1If the domain of the function $\sin^{-1}\left(\frac{3x-22}{2x-19}\right)+\log_e\left(\frac{3x^2-8x+5}{x^2-3x-10}\right)$ is…MediumSingle correct
30 Jan 2024, Shift 1 · Q1If the domain of the function $f(x)=\cos^{-1}\left(\frac{2-|x|}{4}\right)+\{\log_e(3-x)\}^{-1}$ is $[-\alpha,\beta)-\{\gamma\}$ , then…MediumSingle correct
15 Apr 2023, Shift 1 · Q1If the domain of the function $f(x)=\log_e\left(4x^2+11x+6\right)+\sin^{-1}(4x+3)+\cos^{-1}\left(\frac{10x+6}{3}\right)$ 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.