If \(P{e^x} = Qe^{-x} \) for all real values of π‘₯, which one of the following…

GATE Β· 2025 Β· CS Β· Set 2 Β· General AptitudeGATE Β· 2025 Β· IN Β· General AptitudeGATE Β· 2025 Β· MT Β· General AptitudeGATE Β· 2025 Β· NM Β· General AptitudeGATE Β· 2025 Β· TF Β· General Aptitude

If Pex=Qeβˆ’xP{e^x} = Qe^{-x} for all real values of π‘₯, which one of the following statements is true?

  1. A.

    𝑃=𝑄=0𝑃 = 𝑄 = 0

  2. B.

    𝑃=𝑄=1𝑃 = 𝑄 = 1

  3. C.

    𝑃=1;𝑄=βˆ’1𝑃 = 1; 𝑄 = βˆ’1

  4. D.

    PQ=0\frac{P}{Q} = 0

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