According to the textbook context, 'If r = 0 the two variables are uncorrelated. There is no linear relation between them. However other types of relation may be there.' This clearly indicates that when the correlation coefficient (rxy) equals zero, there is no linear relationship between variables X and Y. Option (i) is incorrect because the text explicitly states there is no linear relation. Option (iii) 'independent' is also incorrect because the textbook mentions that 'other types of relation may be there' - meaning the variables could still have non-linear relationships and are therefore not necessarily independent.