Step 1: Understand Passive Voice Formation.
To convert an active sentence into its passive form, follow these steps:
1. Identify the subject, verb, and object in the active sentence.
Active sentence: "Pradeep writes a letter."
Subject: Pradeep
Verb: writes
Object: a letter
2. In the passive voice, the object becomes the subject, and the verb changes to reflect the passive form. The structure is:
$$
\text{Object} + \text{be verb (in appropriate tense)} + \text{past participle of the main verb} + \text{by} + \text{agent (optional)}.
$$
Step 2: Analyze Each Option.
Option (1): A letter was written by Pradeep. — Correct, as this is the simple past passive form of the sentence. It matches the original meaning and tense.
Option (2): A letter has been written by Pradeep. — Incorrect, as this uses the present perfect tense, which implies that the action has been completed recently or has relevance to the present. The original sentence does not suggest this.
Option (3): A letter is written by Pradeep. — Incorrect, as this uses the simple present tense, which does not match the original sentence's tense.
Option (4): A letter will be written by Pradeep. — Incorrect, as this uses the future tense, which does not match the original sentence's tense.
Step 3: Final Answer.
$$
(1) \mathbf{\text{A letter was written by Pradeep.}}
$$