If x(t) is signal applied as input to LTI system with impulse response h(t). The output of the system is y(t) then value of $y (t) |_{t = 5}$ is ______.

75

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Solution

The correct option is A 75
We know that

y(t) = $\int_{- \infty}^{\infty} x (t - τ) h (τ) d τ$

and
y(5) = $\int_{- \infty}^{\infty} x (5 - τ) h (τ) d τ$

x(t) is u(t) and x(5 - $τ$ ) will be u(5 - $τ$ ) that is

also $h (τ)$ is same as given in question and x(5- $τ)$ . h( $τ)$ will be

so, $y (5) = \int_{- \infty}^{\infty} x (5 - τ) h (τ) d τ = 75$

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