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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mathematics in Physics

JEE Main · Physics · Mathematics in Physics

If Z = A^ 4 B^ 1 / 3 CD^ 3 / 2 and ∆ A, ∆ B, ∆ Cand ∆ D are their...

If Z=A4B1/3CD3/2Z = \dfrac{A^{4}B^{1 / 3}}{CD^{3 / 2}} and ∆A,∆B,∆Cand∆D∆ A, ∆ B, ∆ C\text{and} ∆ D are their absolute errors in A,B,CA, B, C~and~DD~respectively. The relative error in ZZ is

Options

  1. A∆ZZ=4∆AA+13∆BB+∆CC+32∆DD\dfrac{∆ Z}{Z} = 4\dfrac{∆ A}{A} + \dfrac{1}{3}\dfrac{∆ B}{B} + \dfrac{∆ C}{C} + \dfrac{3}{2}\dfrac{∆ D}{D}
  2. B∆ZZ=4∆AA+13∆BB−∆CC−32∆DD\dfrac{∆ Z}{Z} = 4\dfrac{∆ A}{A} + \dfrac{1}{3}\dfrac{∆ B}{B} - \dfrac{∆ C}{C} - \dfrac{3}{2}\dfrac{∆ D}{D}
  3. C∆ZZ=4∆AA+13∆BB+∆CC−32∆DD\dfrac{∆ Z}{Z} = 4\dfrac{∆ A}{A} + \dfrac{1}{3}\dfrac{∆ B}{B} + \dfrac{∆ C}{C} - \dfrac{3}{2}\dfrac{∆ D}{D}
  4. D∆ZZ=4∆AA+13∆BB−∆CC+32∆DD\dfrac{∆ Z}{Z} = 4\dfrac{∆ A}{A} + \dfrac{1}{3}\dfrac{∆ B}{B} - \dfrac{∆ C}{C} + \dfrac{3}{2}\dfrac{∆ D}{D}

Correct answer

A. ∆ZZ=4∆AA+13∆BB+∆CC+32∆DD\dfrac{∆ Z}{Z} = 4\dfrac{∆ A}{A} + \dfrac{1}{3}\dfrac{∆ B}{B} + \dfrac{∆ C}{C} + \dfrac{3}{2}\dfrac{∆ D}{D}

Step-by-step solution

Given:

Z=A4B1/3CD3/2Z = \dfrac{A^{4}B^{1 / 3}}{CD^{3 / 2}}, The relative error in ZZ is given by ∆ZZ=4∆AA+13∆BB+∆CC+32∆DD\dfrac{∆ Z}{Z} = 4\dfrac{∆ A}{A} + \dfrac{1}{3}\dfrac{∆ B}{B} + \dfrac{∆ C}{C} + \dfrac{3}{2}\dfrac{∆ D}{D}

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