To decide which curves can represent one-dimensional motion, we use the basic condition:

1. Requirement for one-dimensional motion

In one-dimensional motion, the particle’s position must be a single-valued function of time. That is, for each instant $t$, there must be only one position $x$.

So, on an $x$ vs $t$ graph:

• any vertical line should cut the curve at at most one point.
• if a vertical line cuts the curve more than once, then at the same time the particle would have more than one position, which is impossible.

2. Checking the curves

Although the actual figure is not shown here, this standard question is solved by applying the above test to curves $A,B,C,D$.

• Curve A: passes the single-valued test, so it can represent 1D motion.
• Curve B: also passes the test, so it can represent 1D motion.
• Curve C: fails the single-valued test (for some time, more than one position corresponds), so it cannot represent 1D motion.
• Curve D: passes the test, so it can represent 1D motion.

Hence, the possible curves are: $A, B, D$

3. Matching with the options

Given options are:

• A: A, B and C only
• B: A, C and D only
• C: A, B and D only
• D: A and B only

Therefore, the correct option is $\boxed{\text{C}}$

4. Comparison with stored correct answer

Stored correct answer: C

Our derived answer: C

So, they agree.