It's a property of Context Free Languages. Same is given in the Peterlinz's book.
I mean, CFL is closed under right quotient operation with Regular language.
As shown in the below example by Rahul
L = {a^n b^n | n>0 }
R ={a^n | n>0}
Here L/R is Φ which is regular as well as CFL, hence option B is false.