CAT 2025 Question Paper | Quant Slot 2

CAT Questions

CAT 2025 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 4 : Let \( f ( x ) = \frac { x } { ( 2 x - 1 ) } \) and \( g ( x ) = \frac { x } { ( x - 1 ) } \). Then, the domain of the function \( h ( x ) = f ( g ( x ) ) + g ( f ( x ) ) \) is all real numbers except

---

---

Video Explanation

---

---

Explanatory Answer

\(f(x)\) is undefined when \(2x-1=0\Rightarrow x=\frac{1}{2}\)
\(g(x)\) is undefined when \(x-1=0\Rightarrow x=1\)

exclusions where \(g(x)=\frac{1}{2}\)
\(g(x)=\frac{x}{x-1}=\frac{1}{2}\Rightarrow2x=x-1\Rightarrow x=-1\)

exclusions where \(f(x)=1\)
\(f(x)=\frac{x}{2x-1}=1\Rightarrow x=2x-1\Rightarrow x=1\) (already excluded)

The domain of \(h(x)\) is all real numbers except \(-1,\frac{1}{2},1\).

---

The question is " Let \( f ( x ) = \frac { x } { ( 2 x - 1 ) } \) and \( g ( x ) = \frac { x } { ( x - 1 ) } \). Then, the domain of the function \( h ( x ) = f ( g ( x ) ) + g ( f ( x ) ) \) is all real numbers except "

Hence, the answer is '\(-1, \frac{1}{2}, and 1\)'

Choice 1 is the correct answer.

Verbal Ability for CAT | CAT Reading Comprehension

Verbal Ability for CAT| CAT Para Jumble

Verbal Ability for CAT | CAT Sentence Elimination

Verbal Ability for CAT | CAT Paragraph Completion

Verbal Ability for CAT | CAT Critical Reasoning

Verbal Ability for CAT | CAT Word Usage

Verbal Ability for CAT| CAT Para Summary

Verbal Ability for CAT | CAT Text Completion

Verbal Ability for CAT | CAT Sentence Correction