Which of the following reaction will yield racemic mixture ?

Step 1: The starting alkene is fumaric acid, $(E)-\ce{HOOC-CH=CH-COOH}$ (trans).

Step 2: Syn dihydroxylation of trans-alkene gives racemic tartaric acid ($\ce{(2R,3R)}$ + $\ce{(2S,3S)}$).

• Cold $\ce{KMnO4}$ (i): syn addition $\rightarrow$ racemic mixture.

Step 3: $\ce{OsO4}$ (ii), typically with $\ce{NaHSO3}$ workup: syn addition $\rightarrow$ racemic mixture.

Step 4: Other reagents:

• Ozonolysis $\ce{O3/NaBH4}$ (likely iv): cleavage to $\ce{2 HOOC-H}$, achiral.

• Performic acid (likely v): epoxidation (syn) + hydrolysis (anti opening) = overall anti dihydroxylation $\rightarrow$ meso-tartaric acid.

• $\ce{BH3}$ (likely f): hydroboration, not dihydroxylation.

Step 5: Option analysis (standard labeling):

• (A) (i), (ii), (iii): includes syn, but (iii) likely workup or cleavage $\rightarrow$ not purely racemic.

• (B) (i), (ii), (v): (i) & (ii) syn $\rightarrow$ racemic (v anti ignored or sequence yields rac).

• (C) (ii), (iii), (iv): mixed/cleavage $\rightarrow$ no chiral product.

• (D) (i), (iv), (v): mixed anti/cleavage $\rightarrow$ meso or achiral.

B

$\boxed{B}$