If 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 to :

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 9 April 2024, Shift 1, Maths Q1

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

If the domain of the function

f(x)=\sin^{-1}\left(\frac{x-1}{2x+3}\right)

\mathbf{R}-(\alpha,\beta)

, then

12\alpha\beta

is equal to :

(1) $24$
(2) $32$ Official answer
(3) $36$
(4) $40$

Official answer

Option 2

NTA final key.

Chapter: Relations and Functions
Topic: Inverse Trig Domains
Idea tested: Domain of Inverse Trig with Rational Arguments

Same topic in other shifts

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2 Sep 2020, Shift 1 · Q69The domain of the function $f(x)=\sin^{-1}\left(\frac{|x|+5}{x^{2}+1}\right)$ is $(-\infty, -a]\cup[a, \infty)$ . Then a is equal to :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 42 of the 174 JEE Main shifts held from 2017 to 2026.