In the measurement of a physical quantity X=A2BC1/3D3. The percentage errors introduced in the measurements of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by:

Given X=A2BC1/3D3Taking logarithm of both sides, we havelog⁡X=2log⁡A+log⁡B−13log⁡C−3log⁡DPartially differentiating, we haveΔxx=2ΔAA+ΔBB−13ΔCC−3ΔDDPercentage error in A=2ΔAA=2×2%=4%Percentage error in B=ΔBB=2%Percentage error in C=13ΔCC=13×4%                                                   =43%Percentage error in D=3ΔDD=3×5%=15%We find that the minimum percentage error is contributed by C. Hence the correct choice is (3).