The GATE Grind

GATE 2022 IN – Question 40

Signals and Systems · Laplace and z-transforms · 2 marks · Multiple choice

The signal $x(t)=(t-1)^2u(t-1)$, where $u$ is the unit step, has Laplace transform $X(s)$. The value of $X(1)$ is ______.

  1. $1/e$
  2. $2/e$
  3. $2e$
  4. $e^2$

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Show answer and explanation

Correct answer: (B) $2/e$

Explanation

The undelayed t² has transform 2/s³. A one-second delay gives X(s)=2e⁻ˢ/s³. At s=1, **X(1)=2/e, B**.