Option 1 states that a high growth rate of population is characterised by high birth and high death rates. This option is incorrect because high death rates would actually decrease the population growth rate, as more people are dying than being born.

Option 2 states that a high growth rate of population is characterised by high birth and low death rates. This option is correct. When birth rates are high and death rates are low, the population is increasing at a rapid rate, leading to high population growth.

Option 3 states that a high growth rate of population is characterised by low birth and low death rates. This option is incorrect because low birth and death rates would actually result in a low or stagnant population growth.

Option 4 states that a high growth rate of population is characterised by low birth and high death rates. This option is also incorrect because high death rates would counterbalance the low birth rates, resulting in a low or negative population growth.

In conclusion, option 2 is the correct answer as it accurately characterizes a high growth rate of population with high birth and low death rates.