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GATE 2025 CS (CS2) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

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

  1. $P = Q = 0$
  2. $P = Q = 1$
  3. $P = 1;\ Q = -1$
  4. $\frac{P}{Q} = 0$

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Show answer and explanation

Correct answer: (A) $P = Q = 0$

Explanation

Rewriting gives $Pe^{2x} = Q$ for all $x$. The left side varies with $x$ unless $P = 0$, which forces $Q = 0$. So $P = Q = 0$.