Let the domain of the function $f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)$ be $[\alpha, \beta]$ and the domain of $g(x) = \log_2(2 - 6\log_{27}(2x+5))$ be $(\gamma, \delta)$. Then $|7(\alpha + \beta) + 4(\gamma + \delta)|$ is equal to __________

JEE Main 2025 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 8 April 2025, Shift 2, Maths Q21

Question 21 of 75 in this shift, Maths question 21 of 25, Section B.

Let the domain of the function

f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right)

[\alpha, \beta]

and the domain of

g(x) = \log_2(2 - 6\log_{27}(2x+5))

(\gamma, \delta)

. Then

|7(\alpha + \beta) + 4(\gamma + \delta)|

is equal to __________

Official answer

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
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
27 Jul 2022, Shift 2 · Q1The 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…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.