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A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, Y, Z$  with the corresponding time responses for $t \geq 0 $:

$\begin{array}{ll}\text{X:Impulse}&\text{P: $1 – e^{-t/T}$}\\\text{Y:Unit step}&\text{Q: $t – T(1 – e^{-t/T})$ }\\\text{Z:Ramp}&\text{R: $e^{-t/T}$}\end{array}$ 

  1. $X \to R, \: Y\to Q, \: Z \to P$
  2. $X \to Q, \: Y\to P, \: Z \to R$
  3. $X \to R, \: Y\to P, \: Z \to Q$
  4. $X \to P, \: Y\to R, \: Z \to Q$
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