Is it possible to have a force which gives zero impulse over a nonzero time interval even though the force is not zero at least a part of that time interval? How?

$($a$)$ No$,$ constant force.

$($b$)$ Yes, non$-$constant force.

$($c$)$ Not possible.

$($d$)$ No$,$ non$-$constant force.

$($e$)$ Yes, constant force.