Correct Option: A

Given the unit step response is 1– e^–αt, means
If r(t) = u(t)
then
R(s) = 1/s
y(t) = 1 – e^–αt then
Y(s) = 1/s – 1/s + α = α/s(s + α)
Therefore, the transfer function of the system,

H(s) =	Y(s)
	R(s)

=	Y(s)
	s(s + α) 1/s

=	α
	s + α

Now, for input, r(t) = δ (t)
i.e., R(s) = 1
Y(s) = H(s) R(s)
or

Y(s) =	α	·1
	s + α

or
Y(t) = α·e^–αt
Alternative method: Unit impulse response of a linear, time invariant network is the derivative of unit step function response of the network. Unit step response is (1 – e^–αt)
∴ Unit impulse response is – (– α) e^–αt = αe^–αt