Answer: (i) no linear relationship between two objects

The Pearson correlation coefficient measures the strength of a linear relationship between two variables/objects, ranging from -1 to +1:

-1              0              +1
Strong        No linear      Strong
negative      relationship   positive
linear                       linear

A correlation of 0 means there is no linear relationship — but importantly, this does not rule out a strong non-linear relationship (e.g., y = x², which can have a correlation near 0 despite being a perfect functional dependency). So option (i) is correct, and (ii) is a common misconception — correlation says nothing definitive about non-linear relationships.