The correct answer is option 'C' - 1951 to 1981.

Explanation:

The rapid growth phase of Indian population refers to the period when the population of India experienced a significant increase at a fast pace. This growth phase can be attributed to various factors such as improvements in healthcare, reduction in mortality rates, and better living conditions.

Here is a detailed explanation of each time period mentioned in the options:

a) 1901 - 1921:
During this period, India was under British rule, and the population growth rate was relatively slow. The growth rate was affected by various factors such as famines, epidemics, and poor healthcare facilities.

b) 1921 - 1951:
This period witnessed a gradual increase in population, but the growth rate was still not very high. The country was going through significant political and social changes, including the struggle for independence from British rule.

c) 1951 - 1981:
This was the period of rapid population growth in India. Several factors contributed to this growth phase. Firstly, there were advancements in medical science and healthcare facilities, leading to a significant decline in mortality rates. This resulted in a higher number of people surviving and reaching reproductive age. Additionally, there were improvements in living conditions, access to education, and better employment opportunities. This led to an increase in the average life expectancy and higher fertility rates.

d) 1981 - 2001:
While the population growth rate remained high during this period, it started to show signs of stabilization. The government implemented various family planning programs and awareness campaigns to control population growth. The focus shifted towards population control measures and creating awareness about the benefits of smaller families.

Overall, the rapid growth phase of the Indian population occurred between 1951 and 1981, during which the population of the country experienced a significant increase due to improvements in healthcare, living conditions, and other socio-economic factors.