GATE CSE 2025 Session 2 Q3: Constants P and Q with Pe^x = Qe^(−x) for all x

If $Pe^{x} = Qe^{-x}$ for all real values of $x$ , which one of the following statements is true?

Try it: multiple choice: exactly one correct option

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Answer: A (official GATE 2025 final answer key)

Concept used: An identity that holds for every $x$ forces the coefficients, since $e^{2x}$ is not constant.

First step: Rewrite as $Pe^{2x} = Q$ for all $x$ ; put $x = 0$ and $x = 1$ and compare.

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key