According to the Malthusian theory, the supply of food grains does not increase in geometric progression and the population does not grow in arithmetic progression. Therefore, the correct answer is option 'D' (none).

Explanation:
1. Malthusian Theory:
The Malthusian theory, proposed by Thomas Malthus in the late 18th century, focuses on the relationship between population growth and food supply. Malthus argued that the world's population tends to grow at a faster rate than the increase in the food supply, leading to a population crisis.

2. Food Grain Supply:
According to the Malthusian theory, the supply of food grains does not increase in geometric progression. Geometric progression refers to a pattern where each term is derived by multiplying the previous term by a constant factor. In the case of food grain supply, Malthus argued that it grows at a slower rate compared to the population growth. This is due to factors such as limited agricultural land, diminishing returns in agriculture, and other constraints on food production.

3. Population Growth:
Contrary to the statement in option ii, the population does not grow in arithmetic progression according to the Malthusian theory. Arithmetic progression refers to a pattern where each term is derived by adding a constant difference to the previous term. Malthus argued that population growth tends to occur at an exponential rate, meaning it grows at an increasing rate over time. This is due to factors such as high birth rates, improved living conditions, and reduced mortality rates.

4. Malthusian Population Crisis:
The Malthusian theory suggests that population growth eventually outpaces the growth of food supply, leading to a population crisis. Malthus believed that this crisis would be resolved through "positive checks" such as famine, disease, and war, which would reduce the population to a sustainable level. He also proposed "preventive checks" such as moral restraint and delayed marriage to control population growth.

In conclusion, the Malthusian theory does not support the statement that the supply of food grains increases in geometric progression or that the population grows in arithmetic progression. Instead, Malthus argued that population growth tends to be exponential while food supply growth is slower, leading to a population crisis.