Choose the correct option to fill in the blank in the given sentence:…

The correct answer is Option (2) → have written

Present perfect with "since":

• The present perfect (have/has + past participle) shows an action that started in the past and continues up to now, or a total that counts up to now.
• Clue word: since (since this morning) marks a starting point in the past and links it with the present.
• The number of letters written from the morning until now therefore takes have written.
• Complete sentence: I have written six letters since this morning.
  Example: She has visited three museums since Monday.

Why the Other Options are Incorrect?

Option 1: write — Incorrect. The simple present is for habits and general facts; it cannot link a past starting point with now.
Example: I write in my diary every night.

Option 3: wrote — Incorrect. The simple past is for a finished action at a past time (yesterday, last week); "since" needs the present perfect.
Example: I wrote to her last week.

Option 4: had written — Incorrect. The past perfect is for an action completed before another past action; here the time runs up to the present.
Example: I had written the letter before she called.

Contrast: "since" or "for" with a time running up to now takes the present perfect (have written); a finished past time such as "yesterday" takes the simple past (wrote).