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JEE Main 2021 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Maths Q61

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

If the domain of the function

f(x)=\frac{\cos^{-1}\sqrt{x^2-x+1}}{\sqrt{\sin^{-1}\left(\frac{2x-1}{2}\right)}}

is the interval

(\alpha, \beta]

, then

\alpha+\beta

is equal to :

(1) $1$
(2) $2$
(3) $\frac{1}{2}$
(4) $\frac{3}{2}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Domains
Idea tested: Domain Intersection of Multiple Inverse Trig Functions

Same idea in other shifts

Asked 2× in all

31 Aug 2021, Shift 2 · Q79The domain of the function $f(x) = \sin^{-1}\left(\frac{3x^2+x-1}{(x-1)^2}\right)+\cos^{-1}\left(\frac{x-1}{x+1}\right)$ is :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.