Gate2019 cs Q17 Multiple Choice Questions

Option : B
Explanation :
If L is regular, L.L^R is also regular by closure property.
Suffix (L) and Prefix (L) are also regular by closure property.
However option (b) {ww^R |w∈L} need not be regular since if L is an infinite regular language, then {ww^R |w ∈ L} will not only be infinite, but also non-regular. Since it involves string matching and we can increase in length indefinitely and then finite automata FA will run out of memory.