A physical quantity P is related to four observations a, b, c and d as follows:
P = a³b² / c√d
The percentage errors of measurement in a, b, c and d are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity P is:

Question

Question

This question was previously asked in

NEET 2025 Official Paper (Held On: 04 May, 2025)

Answer 1

Calculation:
Given: P = a³ × b² × c^−1/2 × d⁻¹

Taking logarithm on both sides:

ln P = 3 ln a + 2 ln b − (1/2) ln c − ln d

Now, taking error on both sides:

|ΔP / P| = 3 × |Δa / a| + 2 × |Δb / b| + (1/2) × |Δc / c| + |Δd / d|

⇒ Percentage error in P

= 3(1%) + 2(3%) + (1/2)(4%) + 2%

= (3 + 6 + 2 + 2)%

= 13%