Step 1: Identify the voice of the sentence.
The sentence
\[
\text{``Who wrote \textit{King Lear}?''}
\]
is in the Active Voice.
Here,
• Subject : Who
• Verb : wrote
• Object : King Lear
Step 2: Apply the rule for changing the voice.
For an interrogative sentence in the Simple Past Tense,
\[
\boxed{\text{By whom + was + Object + Past Participle?}}
\]
The past participle of write is written.
Step 3: Analyse the options.
• (A) Incorrect. The tense has been changed.
• (B) Correct. It follows the correct passive voice structure.
• (C) Incorrect. The sentence is grammatically incomplete.
• (D) Incorrect. It is not a valid interrogative sentence.
Step 4: Final conclusion.
\[
\boxed{\text{By whom was \textit{King Lear} written?}}
\]
Hence, the correct option is \(\boxed{(B)}\).