Let 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 $(\alpha,\beta)$ and $[\gamma,\delta]$, respectively. Then $\alpha^2+\beta^2+\gamma^2+\delta^2$ is equal to :

JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2025, Shift 2, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

Let 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)

(\alpha,\beta)

and

[\gamma,\delta]

, respectively. Then

\alpha^2+\beta^2+\gamma^2+\delta^2

is equal to :

(1)13
(2)14
(3)15Official answer
(4)16

Official answer

Option 3

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Domains
Idea tested: Domain of Inverse Trig with Log/Exp Arguments

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
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 Jun 2022, Shift 1 · Q15The domain of the function $\cos^{-1}\left(\frac{2\sin^{-1}\left(\frac{1}{4x^2 - 1}\right)}{\pi}\right)$ is :MediumSingle correct
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.