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GATE 2025 MT – 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. $P/Q=0$

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Show answer and explanation

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

Explanation

At $x=0$, the equation gives $P=Q$. At $x=1$, substitution gives $P(e-e^{-1})=0$. Since $e-e^{-1}\ne0$, we obtain $P=0$ and hence $Q=0$.

Therefore **A** is correct. Option D would require a defined quotient; $0/0$ is undefined.