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GATE ECE 2008 | Question-31

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at $s=-2$ and $s=-4$, and one simple zero at $s=-1$. A unit step $u(t)$ is applied at the input of the system. At steady state, the output has constant value of $1.$ The impulse response of this system is

  1. $[\exp (-2 t)+\exp (-4 t)] u(t)$
  2. $[-4 \exp (-2 t)+12 \exp (-4 t)-\exp (-t)] u(t)$
  3. $[-4 \exp (-2 t)+12 \exp (-4 t)] u(t)$
  4. $[-0.5 \exp (-2 t)+1.5 \exp (-4 t)] u(t)$
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