The three key dimensions used to calculate HDI are:

Income, population, inequality
Health, education, standard of living
Democracy, corruption, human rights
Climate vulnerability, infrastructure, tourism

The correct answer is: b) Health, education, standard of living.

The Human Development Index (HDI) is a composite statistic of life expectancy, education, and per capita income indicators, which are used to rank countries into four tiers of human development. A country scores higher HDI when the values of these indicators are higher.

The HDI was developed by the United Nations Development Programme (UNDP) and is published annually as part of the Human Development Report. The HDI is used to measure the development of a country and to track progress over time.

The HDI is calculated as follows:

HDI = (Life expectancy at birth x 0.25) + (Mean years of schooling x 0.25) + (Gross national income per capita x 0.25)

The HDI is a valuable tool for measuring human development, but it has some limitations. One limitation is that it does not take into account inequality within a country. Another limitation is that it does not take into account environmental sustainability.

Despite its limitations, the HDI is a widely used and respected measure of human development. It is a valuable tool for tracking progress and for comparing countries.

Here is a brief explanation of each option:

a) Income, population, inequality: This option is incorrect because it does not include education. Education is an important component of human development, and it is included in the HDI.

b) Health, education, standard of living: This option is correct because it includes the three key dimensions used to calculate the HDI.

c) Democracy, corruption, human rights: This option is incorrect because it does not include health or education. Democracy, corruption, and human rights are important factors in human development, but they are not included in the HDI.

d) Climate vulnerability, infrastructure, tourism: This option is incorrect because it does not include health or education. Climate vulnerability, infrastructure, and tourism are important factors in human development, but they are not included in the HDI.