The ageing index is a measure that indicates the proportion of the elderly population in a country. In India, the ageing index has increased from 14% in 1951 to over 21% in 2001.

Option 1 states that there is a decline in the proportion of the child population. This means that the percentage of children in the total population is decreasing. This is directly opposite to the data provided, as the ageing index signifies an increase in the proportion of the elderly population, not a decline in the proportion of children. Therefore, option 1 is incorrect.

Option 2 states that there is an increase in the proportion of the old population. This aligns with the given data, as the ageing index increasing implies a higher percentage of elderly people in the population. Therefore, option 2 is correct.

Option 3 states that both option 1 and option 2 are correct. However, as explained above, option 1 is incorrect. Therefore, option 3 is incorrect.

Option 4 states that neither option 1 nor option 2 is correct. This is incorrect, as option 2 is correct. Therefore, option 4 is incorrect.

In conclusion, the correct answer is option 2, which states that only II is correct,