Choose the most appropriate reported speech construction of the given…

The correct answer is Option (3) → Sanika asked me if I was coming to the Tech fest the next day.

Direct	Indirect
Sanika asked, "Are you coming to the Tech fest tomorrow?"	Sanika asked me if I was coming to the Tech fest the next day.

Yes/no question in indirect speech:

• Reporting verb: "asked" stays; the person asked is added as me, and if (or whether) joins the question, since there is no question word.
• Word order: the question becomes a statement, subject before verb: "are you coming" → "I was coming"; the question mark is dropped.
• Tense change: the reporting verb is in the past, so the present continuous "are coming" moves back to the past continuous was coming.
• Pronoun changes: "you" (the person asked, the one who reports) → I.
• Yes/no questions: reported as "asked (someone) if/whether + statement"; a reply such as "Yes, I am" is joined with "that" (she replied that she was).
• Other standard changes: am/is/are → was/were; do/does → did; has/have → had; will → would; can → could; may → might; today → that day; here → there.
• Words of nearness: "tomorrow" → the next day.
  Example: He asked, "Do you like tea?" → He asked me if I liked tea.

Why the Other Options are Incorrect?

Option 1: Sanika asked me if she was coming to be at the Tech fest the next day. — Incorrect.

• "she" makes the question about Sanika herself; the question was about the person asked.
• "to be at" adds words that are not in the original.

Option 2: Sanika asked me to come to the Tech fest with her the following day. — Incorrect. "Asked me to come" reports a request or invitation, not a question, and "with her" is added.

Option 4: Sanika inquired if I had gone to the Tech fest the day before. — Incorrect.

• "had gone" changes the present continuous into the past perfect.
• "the day before" turns "tomorrow" into yesterday; the original asks about the next day.