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(C) For a concave mirror,the focal length $f = -24 \ cm$. The mirror formula is $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$,which gives $v = \frac{uf}{u

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$(C, D)$

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(C) For a concave mirror,the focal length $f = -24 \ cm$. The mirror formula is $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$,which gives $v = \frac{uf}{u-f}$.We check the recorded values against the theoretical values calculated using the mirror formula:$1$. For $u = -42 \ cm$: $v = \frac{(-42)(-24)}{-42+24} = \frac{1008}{-18} = -56 \ cm$. (Matches)$2$. For $u = -48 \ cm$: $v = \frac{(-48)(-24)}{-48+24} = \frac{1152}{-24} = -48 \ cm$. (Matches)$3$. For $u = -60 \ cm$: $v = \frac{(-60)(-24)}{-60+24} = \frac{1440}{-36} = -40 \ cm$. (Matches)$4$. For $u = -66 \ cm$: $v = \frac{(-66)(-24)}{-66+24} = \frac{1584}{-42} \approx -37.71 \ cm$. The recorded value is $33 \ cm$. The difference $|37.71 - 33| = 4.71 \ cm$,which is much greater than the error limit of $0.2 \ cm$.$5$. For $u = -78 \ cm$: $v = \frac{(-78)(-24)}{-78+24} = \frac{1872}{-54} \approx -34.66 \ cm$. The recorded value is $39 \ cm$. The difference $|34.66 - 39| = 4.34 \ cm$,which is much greater than the error limit of $0.2 \ cm$.Thus,the data sets $(66, 33)$ and $(78, 39)$ are incorrectly recorded.

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