The correct answer is: A. Area sampling
Area sampling is a type of sampling that divides the population into geographic areas and then selects a sample of those areas. This type of sampling is often used when the population is large and spread out over a wide area.
In the case of investigating the working efficiency of nationalised banks in India, area sampling would be a good choice because it would allow the researcher to select a sample of banks that is representative of the population of all nationalised banks in India.
The other options are not as appropriate for this study. Multi-stage sampling is a type of sampling that involves selecting a sample of clusters, and then selecting a sample of units within each cluster. This type of sampling is often used when the population is difficult to reach or when the cost of surveying each unit is high. Sequential sampling is a type of sampling that involves selecting units from the population one at a time, and then stopping the sampling process when a certain level of precision has been reached. This type of sampling is often used when the cost of surveying each unit is high. Quota sampling is a type of sampling that involves selecting units from the population until a certain number of units from each group has been selected. This type of sampling is often used when the researcher wants to ensure that the sample is representative of the population on certain characteristics.
In conclusion, area sampling is the best option for investigating the working efficiency of nationalised banks in India because it is a type of sampling that allows the researcher to select a sample of banks that is representative of the population of all nationalised banks in India.