An elastic cord can be stretched to it's elastic limit by a load of 2N. If a 35cm length of the cord is extended 0.6cm by a force of 0.5N, what will be the length of the cord when the stretching force is 2.5N

Just put 2 N on it, that is the limit. It will either stop stretching or break.

F = k x
.5 N = k * .6 cm
then
2 N= 4*.5 N ----> 4* .6 cm = 2.4 cm
35 + 2.4= 37.4 cm