The number of integral solutions $x$ of $\log_{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2x-3}\right)^2 \ge 0$ is

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 11 April 2023, Shift 1, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

The number of integral solutions

x

\log_{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2x-3}\right)^2 \ge 0

(1)8
(2)7
(3)6Official answer
(4)5

Official answer

Option 3

NTA final key.

Chapter: Sequences and Series
Topic: Functions and Domain
Idea tested: Domain of Variable Base Logarithms

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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.