Intersection of any language (Regular , DCFL , CFL , CSL , RC , RE) with Regular language is definitely closed.
Regular INTERSECT Regular -------- Regular
DCFL INTERSECT Regular----------- DCFL
CFL INTERSECT Regular---------- CFL
CSL INTERSECT Regular ----------CSL
Recursive INTERSECT Regular --------- Recursive
Recursively Enumerable INTERSECT Regular --------- Recursively Enumerable
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According to this information , I think Option D is best....