Step 1: About DVC.
The Damodar Valley Project is a multipurpose project launched in 1948 on the Damodar River.
Step 2: Location.
It spans across Jharkhand and West Bengal, but its headquarters and major works are in West Bengal.
Step 3: Eliminate wrong options.
(A) Jharkhand: Partly included but not the main administrative state.
(C) Bihar: Incorrect (now Jharkhand covers that region).
(D) Odisha: Not related.
Step 4: Conclusion.
Correct answer: (B) West Bengal.