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

Question

Quantrex Academy · Accepted Answer

Correct answer: C. (P)-(2), (Q)-(1), (R)-(4), (S)-(3)

The maximum percentage error for a quantity

Q = \dfrac{A^a B^b}{C^c}

is given by

\dfrac{\Delta Q}{Q} \times 100 = a\left(\dfrac{\Delta A}{A} \times 100\right) + b\left(\dfrac{\Delta B}{B} \times 100\right) + c\left(\dfrac{\Delta C}{C} \times 100\right)

.

For (P):

X = \dfrac{A \cdot B^2}{C^{1/2}}

\%X = 1\% + 2(2\%) + \dfrac{1}{2}(4\%) = 1\% + 4\% + 2\% = 7\%

. (Matches 2)

For (Q):

Y = \dfrac{A^2 \cdot B}{C}

\%Y = 2(1\%) + 2\% + 4\% = 2\% + 2\% + 4\% = 8\%

. (Matches 1)

For (R):

Z = \dfrac{A^{1/2} \cdot B^3}{C}

\%Z = \dfrac{1}{2}(1\%) + 3(2\%) + 4\% = 0.5\% + 6\% + 4\% = 10.5\%

. (Matches 4)

For (S):

W = \dfrac{A^3}{B \cdot C}

\%W = 3(1\%) + 2\% + 4\% = 3\% + 2\% + 4\% = 9\%

. (Matches 3)

Therefore, the correct matching is (P)-(2), (Q)-(1), (R)-(4), (S)-(3).

Answer: (P)-(2), (Q)-(1), (R)-(4), (S)-(3)

List-I	List-II
(P) $X = \dfrac{A \cdot B^2}{\sqrt{C}}$	(1) $8\%$
(Q) $Y = \dfrac{A^2 \cdot B}{C}$	(2) $7\%$
(R) $Z = \dfrac{\sqrt{A} \cdot B^3}{C}$	(3) $9\%$
(S) $W = \dfrac{A^3}{B \cdot C}$	(4) $10.5\%$

In an experiment, the percentage errors in the measurement of three...

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