Productivity

Solar energy is the ultimate energy driver for all ecosystems except deep-sea hydrothermal vents. The total rate of organic matter synthesis during photosynthesis is Gross Primary Productivity (GPP). Net primary productivity equals $NPP = GPP - R$. Hence Statement I is correct and Statement II is incorrect.

Gross primary productivity minus respiration losses (R), is the net primary productivity (NPP).

The amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis is defined as primary production.

Gross primary productivity (GPP) is the rate of production of organic matter during photosynthesis. Net primary productivity: NPP = GPP – R (respiration losses) So GPP is always more than NPP.

Gross primary productivity is the rate of production of organic matter during photosynthesis per unit area per unit time.
Net primary productivity is GPP minus respiration losses; secondary productivity is the rate of formation of new organic matter by consumers.

Secondary productivity is the rate of formation of new organic matter by consumers.

Primary productivity is the rate at which producers (green plants) form biomass by photosynthesis; gross and net primary productivity both refer to producers.
Secondary productivity is defined as the rate of formation of new organic matter by consumers.
A rabbit is a herbivore, i.e., a primary consumer feeding on the grass.
Therefore the organic matter it forms from the food it eats is secondary productivity.
Hence the answer is secondary productivity.

Gross primary productivity (GPP) is the rate of production of organic matter during photosynthesis.
A considerable amount of GPP is used by the plants themselves in respiration (R).
Net primary productivity: NPP = GPP − R
NPP is the biomass available for consumption by the heterotrophs (herbivores and decomposers).
Secondary productivity is the rate of formation of new organic matter by consumers, and standing crop is the mass of living material at a trophic level at a given time.
Hence the answer is net primary productivity.

Net primary productivity (NPP) is the gross primary productivity minus the respiration losses of the producers; it is the biomass available to the heterotrophs.
Productivity depends on sunlight, temperature, rainfall and the availability of nutrients.
Tropical rain forests are found in the equatorial regions, where the temperature is high throughout the year and the rainfall exceeds 140 cm.
The warm, humid climate supports dense, broad-leaved evergreen vegetation arranged in several well-defined layers (stratification), which photosynthesises all the year round.
As a result the tropical rain forest has the highest annual net primary productivity among terrestrial ecosystems.
Deciduous forests shed their leaves in one season and temperate forests have a short growing season, so their productivity is lower.
So the answer is tropical rain forest.

Gross primary production (GPP) is the total rate at which producers fix solar energy as organic matter by photosynthesis.
Net primary production (NPP) = GPP $-$ respiration losses of the plants. So NPP is always less than GPP.
Only a small part (about 10 percent) of the energy of one trophic level passes to the next. So secondary production (by herbivores) is much less than NPP, and tertiary production (by carnivores) is even less.
So the order is: GP $\gt$ NP $\gt$ secondary production $\gt$ tertiary production.
The highest value is that of gross production (GP).