Sort the four lingual papillae into "tastes" versus "does not taste" and the answer falls out immediately.
Three of the four - fungiform (anterior tongue, mushroom-shaped), foliate (leaf-like folds on the posterolateral edges) and circumvallate/vallate (the large V-shaped row in front of the sulcus terminalis) - all house taste buds and so contribute to gustation.
The odd one out is the filiform papilla. These are the smallest and by far the most numerous papillae, they are keratinised and thread/cone-shaped, and crucially they carry no taste buds at all. Their job is purely mechanical - they roughen the tongue's surface to grip and move food and to sense texture, not flavour.
So the single papilla in which taste is absent is the filiform papilla; every other listed papilla detects taste.
Correct option: A.