Step 1: Identify the Reaction Product X:
Reactant: Dodecylbenzene (Laurylbenzene).
Reagents: Sulfonation ($H_2SO_4$) followed by Neutralization ($NaOH$).
Product X: Sodium Dodecylbenzenesulfonate (SDBS).
Structure: $CH_3(CH_2)_{11}-C_6H_4-SO_3^- Na^+$.
Step 2: Classify the Detergent:
The large hydrocarbon part is attached to the anion ($SO_3^-$).
Therefore, it is an Anionic Detergent.
Step 3: Evaluate Statements:
(A) It is an anionic detergent - Correct.
(B) It is used in toothpastes - Correct (Anionic detergents like Sodium Lauryl Sulfate/Sulfonates are used).
(C) It is a cationic detergent - Incorrect. (Cationic detergents are usually quaternary ammonium salts).
(D) Its anionic part is involved in cleansing - Correct.
Step 4: Final Answer:
The incorrect statement is (C).