Which of the following sentences is correct?

The correct sentence is:

a) "All the furniture has been bought by my mother."

Explanation:

"Furniture" is an uncountable noun, so it does not have a plural form. This means it should be treated as a singular noun, and the verb should be in the singular form to agree with it.

The singular form of the verb "to have" is "has," and it correctly matches with the singular noun "furniture."

The other options are incorrect because: 

b) "All the furnitures" is incorrect because "furniture" is not a countable noun and should not be pluralized. 

c) "All the furnitures has" is incorrect due to subject-verb agreement; it should be "furniture" instead of "furnitures" as it is an uncountable noun. 

d) "All the furniture have" is incorrect because "furniture" is still a singular noun, so it should be "has" instead of "have."