If $\vec r$ and is the position vector of a point in motion and $r$ is its length/modulus/magnitude/size, then:

Can it be true that: 

$$\|\mbox{d} \vec r\| \neq \mbox{d}r? $$
I think that this is true in circular motion, but if this question is generic, i.e., for almost all cases, then do you think this is correct to say? 

**EDIT:** Thanks for the very prompt answers and comments, but please tell me, if this question is given in an exam, which option would you mark? (As a student, I am very interested in understanding physics, but at the end of the day, I also have to think of the exam point of view...)