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A physical quantity x is represented by $X = (M^{x} L^{- y} T^{- z})$ .The maximum percentage errors in the measurement of M, L, and T, respectively, are a%, b% and c%. The maximum percentage error in the measurement of X will be

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$(ax + by - cz) %$

$(ax - by - cz) %$

$(ax + by + cz) %$

$(ax - by + cz) %$

answer is C.

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Detailed Solution

$\begin{array}{l} X = M^{x} L^{- y} T^{- z} \\ ∴ \frac{ΔX}{X} \times 100 = x (\frac{ΔM}{M} \times 100) + y (\frac{ΔL}{L} \times 100) + z (\frac{ΔT}{T} \times 100) \end{array}$

(errors are always added)

$= (ax + by + cz) percent$

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