Correct : a

We are given the equation P·e^x = Q·e^-x for all real x.

Multiplying both sides by e^x gives P·e^2x = Q.

Since this must hold true for all real values of x, and e^2x changes with x, the only way the left-hand side remains a constant equal to Q is if P = 0. Substituting P = 0 into the equation gives Q = 0.

✅ Final Answer: Option (a) — P = Q = 0.

Reason: The equation can only hold for all x if both P and Q are zero, since e^2x is not constant.