A physical quantity P is described by the relation p = a^(1/2)b^2c^3d. If the relative errors in the measurement of a, b, c, and d respectively, are 2, 1, 3, and 5, then the relative error in P will be:

The correct option is D 32

Let P = a^(1/2)b^2c^3d
Taking logarithm on both sides,
ln P = (1/2)ln a + 2ln b + 3ln c + ln d
Differentiating both sides,
(ΔP/P) = (1/2)(Δa/a) + 2(Δb/b) + 3(Δc/c) + (Δd/d)
Given that the relative errors in a, b, c, and d are 2, 1, 3, and 5 respectively.
Therefore,
(Δa/a) = 0.02
(Δb/b) = 0.01
(Δc/c) = 0.03
(Δd/d) = 0.05
Substituting these values in the equation for (ΔP/P),
(ΔP/P) = (1/2)(0.02) + 2(0.01) + 3(0.03) + 0.05
(ΔP/P) = 0.01 + 0.02 + 0.09 + 0.05
(ΔP/P) = 0.17
Relative error in P = 0.17
Percentage error in P = 0.17 × 100 = 17%
However, none of the given options match this result. There might be an error in the question or the given options. Let's re-examine the calculation.

The relative error in P is given by:
ΔP/P = (1/2)(Δa/a) + 2(Δb/b) + 3(Δc/c) + (Δd/d)
ΔP/P = (1/2)(2%) + 2(1%) + 3(3%) + 5% = 1% + 2% + 9% + 5% = 17%
The percentage error is 17%. This is not one of the options provided. There's likely a mistake in the problem statement or the provided options.