Step 1: Lanthanide contraction is the steady decrease in the size (atomic and ionic radii) of the elements as we move across the lanthanide series from La (Z = 57) to Lu (Z = 71).
Step 2: The lanthanides are the 14 elements in which the last electron enters the inner \(4f\) subshell. Hence they belong to the f-block.
Step 3: The contraction happens because the \(4f\) electrons shield the nuclear charge very poorly, so the effective nuclear charge felt by the outer electrons increases along the series, pulling them closer.
Why the others are wrong: s-block and p-block elements have no \(f\) electrons, and in d-block elements the electron enters the \(d\) subshell (that effect is called d-block or scandide contraction, not lanthanide contraction).
Therefore the correct answer is (iv) f-block element.