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JEE Main 201816 AprilOnline

Exam: JEE Main
Year: 2018
Date: 16 April
Mode: Online
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2018 · 16 April · Online · Physics · Mathematics in Physics

The percentage errors in quantities P , Q , R and S are 0 . 5 % , 1...

The percentage errors in quantities

P

,

Q

,

R

and

S

are

0 . 5 %

,

1 %

,

3 %

and

1 . 5 %

respectively in the measurement of a physical quantity

A= \dfrac{{P}^{3} {Q}^{2}}{\sqrt{R} S}

. The maximum percentage error in the value of

A

will be:

Options

A $6.5%$
B $7.5%$
C $6.0%$
D $8.5%$

Correct answer

A. $6.5%$

Step-by-step solution

100 \times \left(\dfrac{∆ A}{A}\right) = \left(\dfrac{3 ∆ P}{P} + \dfrac{2 ∆ Q}{Q} + \dfrac{1}{2}\dfrac{∆ R}{R} + \dfrac{∆ S}{S}\right) \times 100

max percentage error,

A = 3 \times 0.5 + 2 \times 1 + \dfrac{1}{2} \times 3 + 1.5

= 1.5 + 2 + 1.5 + 1.5

= 6.5%

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