GATE IN 2024 | Question: 30

Question

• A.
• B.
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Laplace transform of a signal $x(t)$ is
\[
X(s)=\frac{1}{s^{2}+13 s+42}
\]

Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if the region of convergence is $-7<\operatorname{Re}\{s\}<-6$.</p>

$-e^{-6 t} u(t)-e^{-7 t} u(-t)$

$-e^{-6 t} u(-t)-e^{-7 t} u(t)$

$e^{-6 t} u(t)-e^{-7 t} u(-t)$

$-e^{-6 t} u(-t)-e^{-7 t} u(-t)$