Correct option is A
The correct option to fill in the blank is (A) the.
Explanation: The noun 'demise' is followed by the prepositional phrase 'of your mother', which makes the 'demise' specific. When a noun is made specific by a following qualifying phrase or clause, we use the definite article 'the'.
Example: The death of the king shocked everyone.
Information Booster: Rule: The + Noun + Of + Noun. This structure usually requires a definite article because it identifies a specific instance.
So the correct answer is (a)