The primary production can be defined as:

The correct answer is Option (4) → The amount of biomass produced per unit area over a time period by plants

Primary production is the organic matter that plants (the autotrophs) make by photosynthesis. The rate at which they make it is called primary productivity.

(1) The amount of biomass produced per unit area over a time period by tertiary consumers — Incorrect. Biomass made by consumers is secondary production. Primary production belongs only to plants.

(2) The amount of energy produced per unit area over a time period by herbivores — Incorrect. Herbivores are consumers, so what they make is secondary production, and it is not primary.

(3) The amount of inorganic matter produced per unit area over a time period by plants — Incorrect. Plants make organic matter. They take in inorganic matter and convert it.

(4) The amount of biomass produced per unit area over a time period by plants — Correct. This is the definition of primary production.

NCERT Extract:
Productivity – “A constant input of solar energy is the basic requirement for any ecosystem to function and sustain. Primary production is defined as the amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis. It is expressed in terms of weight (gm⁻²) or energy (kcal m⁻²).”