1. Given data

• Concave mirror focal length: $f = 24\,\text{cm}$
• Maximum error in image location: $\pm 0.2\,\text{cm}$
• Optical bench length: $1.5\,\text{m} = 150\,\text{cm}$

Recorded pairs:

We must identify which data sets cannot come from the experiment.

2. Mirror formula

For a concave mirror (using magnitudes),

Given $f=24\,\text{cm}$,

A recorded pair is acceptable if the observed $v$ can differ from the true value by at most $0.2\,\text{cm}$.

So for each given $u$, compute theoretical $v$:

and compare with the recorded value.

3. Check option A: $(42,56)$

For $u=42$,

Recorded value is exactly $56\,\text{cm}$.

So this is possible.

4. Check option B: $(48,48)$

For $u=48$,

Recorded value is exactly $48\,\text{cm}$.

So this is possible.

5. Check $(60,40)$

For $u=60$,

This is exact, so this set is also possible.

6. Check option C: $(66,33)$

For $u=66$,

But recorded $v=33\,\text{cm}$.

Error in image location:

This is much greater than $0.2\,\text{cm}$.

So $(66,33)$ is incorrectly recorded.

7. Check option D: $(78,39)$

For $u=78$,

But recorded $v=39\,\text{cm}$.

Error:

Again this is much greater than $0.2\,\text{cm}$.

So $(78,39)$ is incorrectly recorded.

8. Bench length check

On an optical bench of length $150\,\text{cm}$, object and image positions must be accommodable. For all valid pairs here,

For example:

• $42+56=98$
• $48+48=96$
• $60+40=100$
• theoretical for $u=66$: $66+37.7\approx 103.7$
• theoretical for $u=78$: $78+34.7\approx 112.7$

So bench length does not invalidate any otherwise-correct pair. The inconsistency comes only from mirror formula beyond allowed error.

9. Final answer

The data sets that cannot come from the experiment are:

So the correct options are C and D.