Explanation: An L.T.I. system is stable if and only if both the conditions Poles lie on left half of s-plane and R.O.C. encompasses the imaginary axis are satisfied.

Explanation: We find that the pole of the given transfer function lies in the right half of s-plane. The system is not stable so we cannot apply the final value theorem and the final value is not calculable.

Explanation: It is seen that the number of possible inverse laplace transform of any function is equal to the number of poles it has +1. Considering a function F(s)=A/s+1 + B/s+3=F1(s)+F2(s), the inverse laplace transform would exist if the inverse laplace transform is absolutely converging in a region. There are 3 regions that can have an absolutely converging state for F1(s) and F2(s) simultaneously and hence, only option the number of poles+1 is correct.

Explanation: The classical way is more tideous while the laplace transform allows it to represent the differential function in an algebraic form. Thereafter, the inverse laplace transform does the work.

Explanation: The input to the laplace command cannot be within []. Since the input is given within [], this will result in an error. The output would’ve been option 1/16 if the input was given within parentheses.

Explanation: It’s necessary for the individual systems, in a cascaded system, to have a common R.O.C.- otherwise the Laplace transform won’t be absolutely converging in a region. If ti doesn’t converge, the transform is not defined.

Explanation: The transfer function is an s-domain representation of the impulse response of a system. So, the inverse laplace transform of a function might generate the impulse response of a system but the transfer function is represented in s domain and so the above statement is false.

Explanation: The inverse laplace transform, in MATLAB, yields the time domain representation of the function for which the function is causal(t>=0). Hence, option t>=0 is correct only.

Explanation: It is not stated whether there are any initial conditions or not for the given differential equation. Hence, it’s not possible to state the solution of the above equation. If the initial conditions are 0, the laplace transform of the given equation yields- s2p(s)=9/s2 and a solution is reached by using option ilaplace(9/s4) in MATLAB and that solution is option 3/(2*t3). But we cannot talk about a solution until we know about the existence of the initial conditions.