Explanation:

Understanding the question:
The question is asking about the correct option to fill in the blank in the given sentence. The sentence states that the mother is in a hospital and she has kidney trouble.

Choosing the correct option:
To determine the correct option, we need to consider the context of the sentence and the rules of grammar.

Determining the context:
The sentence states that the mother is in a hospital. This means that she is currently receiving treatment at a hospital.

Applying the rules of grammar:
When talking about a specific hospital, we usually use the definite article "the." However, in this case, the sentence does not mention a specific hospital. It only states that the mother is in a hospital.

Using the indefinite article:
Since the sentence does not provide specific information about the hospital, the correct option is to use the indefinite article "a." This indicates that the mother is in any hospital, without specifying which one.

Eliminating incorrect options:
- Option 'a' (a): This option is incorrect because it does not use an article before the word "hospital." It would be grammatically incorrect to say "Mother is in hospital" without an article.
- Option 'c' (a/the): This option is incorrect because it uses both the indefinite article "a" and the definite article "the." Using both articles together in this context would be redundant and grammatically incorrect.
- Option 'd' (none): This option is incorrect because it suggests that no article should be used before the word "hospital." However, as mentioned earlier, the sentence requires the use of an article.

Correct option:
The correct option is option 'b' (the) as it uses the definite article "the" before the word "hospital."