ભૌતિક રાશિ \(y\) ને \(y=m^{2}\, r^{-4}\, g^{x}\,l^{-\frac{3}{2}}\) સૂત્ર મુજબ આપવામાં આવે છે. જો \(y, m, r, l\) અને \(g\) માં પ્રતિશત ત્રુટિ \(18,1,0.5,4\) અને \(p\) હોય, તો \(x\) અને \(p\) નું મૂલ્ય કેટલું હોય શકે?

A \(4\) અને \(\pm 3\)
B \(5\) અને \(\pm 2\)
C \(8\) અને \(\pm 2\)
D \(\frac{16}{3}\) અને \(\pm \frac{3}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{16}{3}\) અને \(\pm \frac{3}{2}\)

Step-by-step Solution

Detailed explanation

\(\frac{\Delta y}{y}=\frac{2 \Delta m}{m}+\frac{4 \Delta r}{r}+\frac{x \Delta g}{g}+\frac{3}{2} \frac{\Delta \ell}{\ell}\) \(18=2(1)+4(0.5)+x p+\frac{3}{2}(4)\) \(8=x p\) By checking from options. \(x=\frac{16}{3}, p=\pm \frac{3}{2}\)

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

યાદી - I ને યાદી - II સાથે જોડો.

યાદી - I	યાદી - II
(A) શૂન્યાવકાશની પરમિએબિલિટી	(I) \(\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
(B) ચુંબકીય ક્ષેત્ર	(II) \(\left[\mathrm{M} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)
(C) ચુંબકીય મોમેન્ટ	(III) \(\left[\mathrm{M} \mathrm{~L} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]\)
(D) વળ અચળાંક	(IV) \(\left[\mathrm{L}^2 \mathrm{~A}\right]\)

નીચે\(\text{ }\)આપેલા\(\text{ }\)વિકલ્પોમાંથી\(\text{ }\)સાચો\(\text{ }\)જવાબ\(\text{ }\)પસંદ\(\text{ }\)કરો\(\text{ }\):

JEE Mains 2025 Easy

Explore more questions on app

From JEE Mains

Explore more questions on app