In an experiment, the percentage errors in the measurement of three physical quantities A , B , and C are 1 % , 2 % , and 4 % respectively. Match the derived quantities in List-I with their maximum percentage errors in List-II. List-I List-II (P) X = A B^2 C (1) 8 % (Q) Y = A^2 B C (2) 7 % (R) Z = A B^3 C (3) 9 % (S) W = A^3 B C (4) 10.5 % Choose the correct answer from the options given below:

Step-by-step solution

The maximum percentage error for a quantity Q = A^a B^b C^c is given by Q Q 100 = a ( A A 100 ) + b ( B B 100 ) + c ( C C 100 ) . For (P): X = A B^2 C^ 1/2 %X = 1 % + 2(2 %) + 1 2 (4 %) = 1 % + 4 % + 2 % = 7 % . (Matches 2) For (Q): Y = A^2 B C %Y = 2(1 %) + 2 % + 4 % = 2 % + 2 % + 4 % = 8 % . (Matches 1) For (R): Z = A^ 1/2 B^3 C %Z = 1 2 (1 %) + 3(2 %) + 4 % = 0.5 % + 6 % + 4 % = 10.5 % . (Matches 4) For (S): W = A^3 B C %W = 3(1 %) + 2 % + 4 % = 3 % + 2 % + 4 % = 9 % . (Matches 3) Therefore, the correct matching