કોઈ ભૌતિક રાશિ \(p\) ને \(p\, = a^{1/2}\, b^2\, c^3\, d^{-4}\) થી દર્શાવેલ છે. જો \(a, b, c\) અને \(d\) ના માપનમાં રહેલી સાપેક્ષ ત્રુટિ અનુક્રમે \(2\% , 1\%, 3\%\) અને \(5\%\) હોય, તો \(P\) માં રહેલી સાપેક્ષ ત્રુટિ ........... \(\%\) હશે.

A \(8\)
B \(12\)
C \(32\)
D \(25\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(32\)

Step-by-step Solution

Detailed explanation

\begin{array}{l} Give,\,p = {a^{1/2}}{b^2}{c^3}{d^{ - 4}},\\ Maximum\,relative\,error,\\ \frac{{\Delta p}}{p} = \frac{1}{2}\frac{{\Delta a}}{a} + 2\frac{{\Delta b}}{b} + 3\frac{{\Delta c}}{c} + 4\frac{{\Delta d}}{d}\\ = \frac{1}{2} \times 2 + 2 \times 1 + 3 \times 3 + 4 \times…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

લીસ્ટ \(I\) સાથે લીસ્ટ \(II\) યોગ્ય રીતે જોડો.

લીસ્ટ \(I\) (ભૌતિક રાશી)	લીસ્ટ \(II\) (પારિમાણિક સૂત્ર)
\((A)\) દબાણ પ્રચલન	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) ઊર્જા-ઘનતા	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) વિદ્યુતક્ષેત્ર	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) ગુપ્ત ઉષ્મા	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

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