For questions $1$ to $6,$ consider the linear and time$-$invariant $($LTI$)$ system with an

impulse response given by:

h$($t$)=$ e$-$t cos$(2$t$)$ u$($t$)$

where u$($t$)$ is the unit$-$step. The transfer function of the system is H$($s$)=$ L$[$h$($t$)]$

where L is the Laplace transform operator.

$1.$ Which of the following statements is true?

$($A$)$ The system is causal.

$($B$)$ The system is not causal.

$2.$ Suppose the input to the system is

x$($t$)=$ e$-10$tu$($t$)$

where u$($t$)$ is the unit$-$step.

Which of the following statements is true about the output y$($t$)?$

$($A$)$ y$($t$)$ is a bounded output

$($B$)$ y$($t$)$ is not a bounded output

$3.$ Which statement is true regarding the poles of the transfer function H$($s$)?$

$($A$)$ There is only one simple real pole.

$($B$)$ There are only two simple real poles.

$($C$)$ There is only one double real pole.

$($D$)$ There are only two complex poles.

$4.$ The region of convergence $($ROC$)$ of the transfer function H$($s$)$ is

$($A$)$ All values of s

$($B$)$ Re$($s$)>-2$

$($C$)$ Re$($s$)>-1$

$($D$)$ Re$($s$)>0$

$($E$)$ Re$($s$)>1$

$($F$)$ Re$($s$)>2$