Correct Option: C

Given, the impulse response of the system is
h(t) = δ(t – 0·5)

Now, according to question if two such systems are cascaded, i.e.,

then in order to determine the impulse response of the cascaded system, the over all transfer function of cascaded system must be calculate.
H(s) = H(s).H(s) = e^{– 0·5s}.e^{– 0·5s} = e^{– s}
x(t) = δ(t)
⇒ X(s)= 1
Now, Y(s) = H(s).X(s) = e^{– s}.1 = e^{– s} and impulse response.
y(t) = δ(t – 1)
Hence, alternative (C) is the correct choice.