Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202225 Jun 2022Morning ShiftPhysicsMathematics in PhysicsActual

If Z = A 2 B 3 C 4 , then the relative error in Z will be

Options

  1. A2 Δ A A + 3 Δ B B + 4 Δ C C
  2. BΔ A A + Δ B B + Δ C C
  3. C2 Δ A A + 3 Δ B B - 4 Δ C C
  4. DΔ A A + Δ B B - Δ C C

Correct answer

A. 2 Δ A A + 3 Δ B B + 4 Δ C C

Step-by-step solution

Given: Z = A 2 B 3 C 4 When quantities are multiplied or divided, the relative error in the result is the sum of the relative errors in the multipliers. So, ∆ Z Z = ∆ A A + ∆ A A + ∆ B B + ∆ B B + ∆ B B + ∆ C C + ∆ C C + ∆ C C + ∆ C C Thus, relative error is ∆ Z Z = 2 × ∆ A A + 3 × ∆ B B + 4 × ∆ C C

Practice Mathematics in Physics on Quantrex Academy →

More from Mathematics in Physics

The density of a uniform cylinder is determined by measuring its mass m , length l and diameter d . The measured values of m , l and d are 97.42 0.02 g, 8.35 0.05 mm and 20.20 0.02 2026Four persons measure the length of a rod as 20.00 ~cm , 19.75 ~cm , 17.01 ~cm and 18.25 cm. The relative error in the measurement of average length of the rod is : 2026In an experiment the values of two spring constants were measured as k₁=(10 0.2) N / m and k₂=(20 0.3) N / m . If these springs are connected in parallel, then the percentage error 2026Length, breadth and thickness of a strip having a uniform cross section are measured to be 10.5 cm , 0.05 mm , and 6.0 ~m , respectively. Which of the following option(s) give(s) t 2025A quantity Q is formulated as X ⁻² Y ^ + 3 2 Z ^ - 2 5 X , Y and Z are independent parameters which have fractional errors of 0.1,0.2 and 0.5 , respectively in measurement. The max 2025A physical quantity C is related to four other quantities p , q , r and s as follows C = pq ^2 r ^3 ~s The percentage errors in the measurement of p , q , r and s are 1 %, 2 % 3 % 2025A physical quantity Q is related to four observables a, b, c, d as follows : Q = ab ^4 ~cd where, a =(60 3) Pa ; b =(20 0.1) m ; c =(40 0.2) Nsm ⁻² and d =(50 0.1) m , then the per 2025For an experimental expression y= 32.3 1125 27.4 , where all the digits are significant. Then to report the value of y we should write 2025 Full Mathematics in Physics list All JEE Main PYQs