Choose the most appropriate preposition to fill in the blank in the f…

The correct answer is Option (2) → since

Note: The given answer is as per the official NTA Answer Key. However, more than one answer is possible here: Option (1) "from" and Option (2) "since" both make a correct sentence, as explained below.

Time immemorial means a time so far back in the past that no record or memory of it survives. "In vogue" means in fashion or in common use.

Option 1: from — Can also be considered as correct. From time immemorial is a fixed, widely used phrase meaning from very ancient times, and it is common with the present perfect: "has been in vogue from time immemorial".
Example: Pilgrims have visited this temple from time immemorial.

Option 2: since — Correct (Answer as per NTA). Since marks the starting point of an action that continues up to now, and it goes with the present perfect "has been". The custom started in the remote past and is still followed, so "has been in vogue since time immemorial" is correct.
Complete sentence: This custom has been in vogue since time immemorial.

Option 3: by — Incorrect. By with time means not later than a point. It marks a deadline, not a starting point.
Example: Submit the form by Friday.

Option 4: about — Incorrect. About with time means approximately. "About time immemorial" makes no sense.
Example: The train will arrive at about six o'clock.

Contrast: "since" and "from" mark the starting point, "by" marks a deadline, and "about" means approximately.